Efficient Robotic Walking by Learning Gaits and Terrain Properties

Transcription

1 Efficient Robotic Walking by Learning Gaits and Terrain Properties Sandeep Manjanna Master of Science School of Computer Science McGill University Montreal,Quebec A thesis submitted to McGill University in partial fulfillment of requirements for the degree of Master of Science in Computer Science c Sandeep Manjanna, 2013

2 DEDICATION I dedicate this work to my parents, Annapurna and Manjanna, my granny, my teachers, my brother Ajju and my girlfriend Rashmi. ii

3 ACKNOWLEDGEMENTS Studying at McGill has been a wonderful experience and I would like to thank all the people who have made the course of my graduate studies memorable. Foremost, I would like to express my gratitude to my supervisor Gregory Dudek for his encouragement, knowledgeable inputs, support and guidance throughout the research. I want to take this opportunity to thank every member of the Mobile Robotics Lab: Dave, Malika, Juan, Florian, Anqi, Yogi, Yiannis, David, Jimmy, Junaed, Mike, Arnold, Isabelle and Greg, for being helpful and inspiring me during the course of my research in the lab. I thank Philippe Giguere for his patience, kind tutoring and helping me understand the internals of the Aqua robot. I thank Bikram for his help in conducting experiments and sharing his knowledge about the mechanical design of the Aqua robot. I would like to thank my friends in Montreal who made it a very pleasant experience: Aditi, Aparna, Hari, Rohini; all my friends in India for all the encouragement they have given. Finally, I want to thank my mom, my dad, my granny, my brother and my girlfriend for being there when I needed them and supporting me with every decision I made. iii

4 ABSTRACT In this thesis, we investigate the question of how a legged robot can walk efficiently, and take advantage of its ability to alter its gait. This work targets the issue of increasing the efficiency of legged vehicles on different challenging terrains. We decompose the problem into three sub-problems: walking gait problem, physical adaptation problem, and terrain identification and gait adaptation problem. In the walking gait sub-problem, we investigate the effects of gait parameters on the performance of the robot. In particular, we assess the ground speed, power efficiency and terrain sensibility of the robot at varying leg cycle frequencies. In the physical adaptation sub-problem, we investigate the effects of different kinds of legs on the robot s performance. We also look at the influence of leg-compliance on walking behavior. In the terrain identification and gait adaptation sub-problem, we design a gait adaptation algorithm to identify the terrain by initially classifying the proprioceptive information collected over different terrains and then adapt its gait accordingly. Identifying the terrain in real-time helps the robot plan its gait on that terrain and effectively increase the walking efficiency in real-time. We use a cost-based unsupervised learning algorithm [28] to classify the terrain data. In our experiments, we use proprioceptive sensor data collected by running the robot on four different terrains. We also use synthetic data for verifying our algorithm. We conclude with an analysis of the data and validate the performance of our algorithm. iv

5 ABRÉGÉ Dans cette thèse, nous étudions les problèmes liés à l efficacité de marche des robots à pattes et construisons des solutions algorithmiques et physiques pour les régler. Ce travail vise à accroître l efficacité, en termes de mobilité, des véhicules à pattes sur différents terrains difficiles. Cette problématique est décomposée en trois sous-problèmes: la façon de marcher, l adaptation physique, et l identification de terrains associée à l adaptation de la démarche des robots. Dans le premier cas (la façon de marcher), nous étudions les effets des paramètres de la démarche sur la performance du robot. Nous évaluons plus particulièrement la vitesse au sol, le rendement énergétique et la sensibilité du robot vis-à-vis du terrain et ce, en fonction de la vitesse de déplacement des jambes. Dans le cas du deuxième sous-problème, soit l adaptation physique, nous étudions les effets de différents types de jambes sur la performance du robot. Nous examinons également l influence de la flexibilité des jambes sur la marche du robot. Troisièmement, le sous-problème d identification de terrains et d adaptation de la démarche des robots est l un des problèmes les plus importants pour les véhicules capables de marcher. Identifier le terrain en temps réel permet au robot de planifier sa démarche sur ce terrain et d augmenter efficacement son rendement de marche. Nous concevons un algorithme permettant d identifier le terrain en classant d abord les informations proprioceptives recueillies sur différents terrains pour ensuite adapter la démarche en conséquence. Dans nos expériences, nous utilisons un algorithme d apprentissage non supervisé pour classer les données de terrain, de même que les données issues de capteurs proprioceptifs collectées en employant le robot sur quatre types de terrains différents. Nous utilisons également des données synthétiques afin de vérifier notre algorithme d identification. Dans v

6 les résultats, nous présentons une analyse des données et validons les performances de notre algorithme. vi

7 TABLE OF CONTENTS DEDICATION ii ACKNOWLEDGEMENTS iii ABSTRACT iv ABRÉGÉ LIST OF TABLES v ix LIST OF FIGURES x 1 Introduction Introduction Problems Addressed Motivation Contribution of this Work Thesis Outline Background and Related Work Walking Gaits and Performance Amphibious Adaptations in Robots Terrain Sensing and Identification Gait Adaptation Gait and Performance of the Robot Walking gaits and Gait parameters Performance Factors Experiments Experimental Setup Data Collection Results and Observations Summary Physical Adaptation Ninja Legs Design Approach Mechanical Properties vii

8 4.2 Experimental Results and Observations Performance Evaluation Effective Arm Length Linear Variant of Tripod Gait Summary Terrain Identification in Real-time And Gait Adaptation Overview Sensor Data Feature Selection Classification Methodology On-line Terrain Identification Gait Switch Semi-supervised Gait Adaptation Algorithm Implementation Experimental Results and Observations Terrain Differentiability and Gait Parameters Performance of the Classifier On-line Terrain Identification and Gait Adaptation Summary Conclusion and Future Work Summary Future Work Final Word References viii

9 Table LIST OF TABLES page 2 1 Comparison of the amphibious leg designs Tabular representation of the experimental observations. The table presents a f c at which optimal performance is achieved on different terrains Mapping of terrain types and optimal gaits An example for value of switching gaits with ground speed as utility function. The speed data is taken from the results of Chapter ix

10 Figure LIST OF FIGURES page 1 1 Hexapod robots Amphibious Aqua robot equipped with Ninja legs [18] Graphical representation of Tripod Gait Plot showing the parameters of the tripod gait Experimental Setup Ground speed of the robot plotted against f c RMS of power consumed per unit distance walk of the robot plotted against f c Surf entry exit experiment with Ninja legs Ninja leg behaving as an offset wheel Illustrated diagram of the Ninja Leg Comparison of the effective arm length between the semicircular walking legs and the Ninja legs Mechanical properties of Ninja legs Trial runs of the Aqua robot on tiled surface Ground speed plotted against f c RMS power consumption plotted against f c Depiction of Aqua robot going from sit mode to stand mode. Both the Ninja legs and the RHex legs are shown Performance variation with effective arm length Two variants of tripod gait Comparing the performance of variants of Tripod gait Block diagram of Gait Adaptation Algorithm Effect of gait on data distribution x

11 5 3 RosNodes for simulating the Gait Adaptation algorithm Leg motor current and vertical acceleration (A z ) plotted as a function of Leg angle Plots showing terrain differentiability Plot showing variation in performance of the classifier with f c Classification results on data from four terrains Data simulating two terrains Robot traversing from terrain 1 to terrain 2 only once Terrain transition for every 20 steps (T s = 20) Terrain transition for every 2 steps (T s = 2) Terrain transition for every 3 steps Error in choosing right gait plotted against transition step length (T s ) Classification plotted against distance between the mean of Gaussian distributions Robot sensor dataset collected from two terrains : dry sand and grass Results of classification and gait adaptation plotted against time samples The step length is changed to 3 (T s =3) and this simulates a change in terrain for every 3 steps The step length is changed to 2 (T s =2) and this simulates a change in terrain for every 2 steps xi

12 CHAPTER 1 Introduction 1.1 Introduction In this thesis, we investigate the question of how a legged robot can walk efficiently, and take advantage of its ability to alter its gait. Autonomous terrestrial vehicles find applications in various fields including search and rescue operation, agricultural land survey, geological debris exploration, payload carriage on difficult terrains, outdoor surveillance, remote inspection, and security mission. These applications call for a robot that is able to walk effectively through challenging terrains (e.g., ice, sand, gravel, snow, and wooded lands), climb steep hills, walk over small obstacles (e.g., lumps of mud, logs, sand piles, and rocks), climb stairs, and achieve many other maneuvers. Legged robots are a kind of terrestrial robots which use legs for their locomotion. The mechanical ability of legged robots to navigate through different kinds of terrains is one of their major potential benefits over other wheeled or tracked mobile robots. Legged robots are highly capable of walking on rough, rocky, sandy, steep and undesired terrains. These robots can also use different kinds of leg movements to jump or step over an obstacle, climb stairs and crawl on highly inclined surfaces. Energy efficiency while walking, generation of an effective gait (a pattern of movement of limbs in animals, used for locomotion) to move efficiently on challenging terrains, maintaining static and dynamic stability of the system while walking are few of the challenges faced by legged robots. Energy efficiency, higher locomotion speeds, robust walking capabilities on difficult surfaces, versatility and adaptability to different walking environments are the key ingredients that will encourage a wide range 1

13 utilization of legged locomotion in autonomous systems. In this thesis, we try to address some of these challenges and strive to maximize the effectiveness of legged robots. We used an amphibious Aqua family robot [20] (Fig. 1 1a) for our experiments. This is a hexapod, built based on the design of RHex robot [57] (Fig. 1 1b). We recorded the proprioceptive measures from the robot using the inertial measurement unit and actuators aboard the robot. One of the important characteristics of Aqua class robots is their use of robust open-loop walking, which allows for robust walking across many terrain types with a very simple mechanical design and control mechanism. (b) RHex Robot [57] (a) Aqua robot [20] Figure 1 1: Hexapod robots 1.2 Problems Addressed In this work, we concentrate on some of the challenges in the mobility of legged robots. We investigate the walking efficiency and estimate the performance of legged robots when operated with different walking gaits and in varied environments. We also investigate the capacity of autonomous vehicles to sense their environment using proprioceptive measurements recorded during their interaction with the environment. We also assess the impact of mechanical changes on the walking performance of the robot. Through this 2

14 work, we address some of the mobility issues in legged robots, operating on challenging terrains, by building algorithmic and mechanical solutions. We decompose this problem into three sub-problems: a walking gait problem, physical adaptation problem, and terrain identification and gait adaptation problem. For example, considering the walking efficiency problem in humans: different gaits (e.g., walking, running, and jumping) affect their mobility, physical adaptations (e.g., shoes, slippers, and spikes) aid in effortless walking on different terrains, and finally, knowledge about the terrain will help in planning the walking style compatible to that terrain. The walking gait sub-problem aims at analyzing gaits and gait parameters and their effects on the performance of the robot. A walking gait is a combination of different movements of limbs to achieve locomotion and is defined by a set of properties, called gait-parameters, that alter the locomotion trajectories of the mobile system. For example, a human walking gait is defined by parameters, such as step length, stride length, speed, and foot angle. In this work, for our analysis of walking gaits in legged robots, we consider the gait parameter - leg rotation frequency. The robot is operated with varying leg rotation frequencies and its performance is estimated as a function of this frequency change, which turns out to have a profound effect on the robot s performance. For investigation, we quantize the performance into factors such as ground speed and energy efficiency of the robot. In this sub-problem, we also investigate the impact of the environment on the walking performance of the robot by driving the robot on different terrains. For our experiments, we chose terrains with varied properties including granular terrains like wet and dry sand, soft terrain like grass, and hard terrain like concrete surface. The second sub-problem is physical adaptation problem. A physical adaptation to the kind of terrain can enhance the walking experience. For example, 3

15 walking on ice surface is much easier with spiked shoes than with the flat sole boots. Thus, a good physical equipment can help one in achieving better performance as a walker. As an approach to this sub-problem, we inspected the effect of different kinds of limbs on the walking performance of the robot. We designed and verified the legs which enhanced the capabilities of the robot beyond walking. In this work, we explore different gaits that could be achieved with the newly designed Ninja legs and analyze the performance of the robot on various terrains, when equipped with these new legs. We look into few mechanical aspects of the robot legs that would help the robot walk efficiently and elegantly. (a) Ninja legs used for terrestrial locomotion. (b) Ninja legs used for swimming underwater. Figure 1 2: Amphibious Aqua robot equipped with Ninja legs [18]. The last sub-problem is terrain identification and gait adaptation in realtime. Identifying the terrain by tactile sensing has been an interesting problem for many years. Sensing the terrain and getting to know the terrain well in advance helps to plan one s walk on that terrain. If one knows that the terrain type is deep snow, then a gait - lifting the leg completely out of snow on every step - can be planned. This kind of planning improves the walking efficiency on the identified terrain. Similarly, in robots, good walking plan based on the knowledge about the terrain helps in improving the efficiency of the robot and aids the robot in choosing a terrain specific walking gait. Based 4

16 on our analysis in the walking gait sub-problem, we map walking gaits onto terrains by considering a trade-off between performance factors. Once the terrain is identified in real time, the robot looks up in this map to choose a near-optimal high performance gait for that terrain. We have designed an algorithm to identify the terrain in real time and autonomously change the walking gait to suit the terrain identified. We achieve this by initially classifying the proprioceptive measurements from different terrains using one of the cost-based unsupervised classification techniques. We also combine the sub-problems and investigate the interplay between the gait parameters and the terrain classification accuracy, and the effects of gait-parameters on the gait adaptation algorithm. 1.3 Motivation Walking robots are gaining importance in many critical applications including rescue mission, and exploring debris. All these applications pose difficult challenges for the robot to adapt to rough environments. A robot capable of walking only on flat indoor surfaces will be of limited utility on complex irregular terrains. Hence, it is important to endow the robot with the ability to infer terrain classes and thus moderate its behavior accordingly. A legged robot walking with high leg speed can get stuck in deep snow, but lower leg speeds allow the robot to walk without digging into the snow. For walking on hard concrete surfaces, however, the robot can be efficient and achieve better ground speeds at higher leg speeds. These observations motivated us to study gait and terrain relationships more deeply. Walking robots have the potential to function over a wide range of terrain types, such as sand, mud, grass, snow, and ice. But different terrains imply different optimal walking behaviors; a phenomenon well known to any person who has had to walk across an ice-covered sidewalk during a Canadian 5

17 winter. Similarly, terrain-specific gait changes in legged robots are needed to optimize performance. The gait transition from walking to running in humans and other animals has been the subject of extensive prior research. There are several analyses of the transition from walking to running in biological systems as the speed of motion increases [19, 1]. One possible explanation for gait transitions is that the shift to a new mode of locomotion occurs at the mechanical limit of whatever locomotion mode is being used [2]. That is, once the mechanical limit of the legs, walking in particular gait, has been reached due to the speed of motion, the system must switch to a new gait to go any faster. Another explanation proposes that gait transitions occur in order to minimize the total metabolic cost, switching mechanism known as an energetic trigger. The transition can be predicted by observing when the rate of energy expenditure for walking surpasses that for running; this is equivalent to the speed at which running becomes more efficient than walking in terms of energy expenditure per unit distance. Human data indicates this speed to be m/s [45] [23]. These established observations suggested us to study the different gait parameters and their effects on energy efficiency and ground speed of the robot. The Aqua family robots are amphibious robots. As we work with an amphibious robot, we are also motivated by swimming to walking and walking to swimming problems. The problem of transition between swimming gait and walking gait poses several challenges - the robot should be capable of identifying the difference between the shore and the wave, it should be capable of deciding when to switch the gaits to have a smooth transition. These challenges motivated us towards concentrating our study on identifying the terrains and gait optimizations in real-time. 6

18 The walking robot gets a response back from the terrain. This response provides the proprioceptive measurement for our experiments. This response from the terrain depends on not only the terrain properties, but also the compliance and other properties of the robot s legs. Any changes in the properties of legs affect the performance of the robot and also the features measured for terrain identification. Hence, we considered studying different physical adaptations of the robot and measure their effects on the performance of the robot. 1.4 Contribution of this Work There is a vast literature available on legged robots and their walking behaviors, however, substantial study needs to be done on the impact of walking gaits on the robot s performance and adaptation of walking gaits to the terrain properties. In this study, we address few of the issues related to the efficient walking of legged robots. The major novel contribution of this work is an algorithm for on-line gait adaptation, in which the robot s behavior is altered as a function of observed terrain properties. We present an analytical study of the interplay between the gait parameters and the performance of the robot. Then, we add terrain variations to this problem to make it more interesting and investigate the response from the terrain to varying gait parameters. From the results, we try to develop a mapping between the terrains and near-optimal gait properties. Optimal gait properties are the set of parameters which yield optimal performance of the robot. In a continued study of interaction between terrain and robot, we try to take advantages of physical modifications to the robot. As an another novel contribution, we present the design of an amphibious robotic leg (Ninja leg), that enhances the capabilities of our robotic platform. These new legs 7

19 possess different properties and have an effect on the performance of the robot and proprioceptive measurements from the robot. We analyze the impact of physical alteration on the performance of our algorithm and terrain properties. 1.5 Thesis Outline The thesis is organized into key important chapters, one for each of the core sub-problems mentioned above. As a preliminary, however, Chapter 2 introduces the background to gait and terrain identification problems. We discuss some previous work related to walking gaits and performance in legged robots, tactile sensing and classification of the terrains. Chapter 3 presents a detailed discussion of the walking gaits we use, and the associated gait parameters. We describe the approach used to address our first sub-problem and discuss the results and observations of our experiments. In Chapter 4, we discuss the mechanical aspects of the newly designed legs for the robot. We also present a set of behaviors and observations of the robot equipped with different kinds of legs. Chapter 5 introduces the terrain identification and gait adaptation problem and discusses the algorithm to identify the terrain properties in real time and adapt to an optimal walking gait. In this chapter, we provide results with a simulated setup to verify the performance of our algorithm. We also discuss the possible interplay between the sub-problems and provide the related results. Finally, we conclude the thesis with Chapter 6, wherein we discuss the contributions of the work to the field of robotics and probable future work. 8

20 CHAPTER 2 Background and Related Work Since this thesis touches on different subjects including walking gaits, terrain clustering, gait transitions, performance of the robot, and physical adaptations, this chapter reviews some of the previous work done in these different areas. 2.1 Walking Gaits and Performance The details of a walking gait have a great influence on the overall performance of locomotive systems. Being able to select an effective combination of gait parameters benefits the mobile system by delivering better performance. Gait studies in terrestrial mammals show a species-specific bias for the speed these animals use, although they are capable of utilizing and sustaining a wide range of speeds [47]. Studies discovered that the domestic horse has a preferred speed within each gait [33], and many species have been observed to use certain speeds much more frequently than others [11, 32, 48]. Prior research shows that the preference for certain specific speeds associated with each gait is due to the fact that at these speeds, energy efficiency is maximized [33]. Studies also show that a particular locomotion mode can achieve only certain finite maximum speed within the system s mechanical limit [2]. That is, once the mechanical limit of the legs, walking in particular gait, has been reached due to the speed of motion, the system must switch to a new gait to go any faster. Thus the gait parameters in animals affect their mobility. There has also been a body of prior work on the walking capabilities and efficient gaits in legged robots. One of the earliest legged robots to demonstrate impressive obstacle climbing ability, and good mobility in difficult terrains is 9

21 GE Quadruped [62, 21]. Other notable early results are the speed evaluation tests on six legged robots such as Atilla [6] and Genghis [5]. The gait related properties including leg placement, and stride frequency are also discussed in these robots. Saranli et al. [57] proposed a speed analysis on a hexapod robot, RHex. In their work, the gait of the robot is split into slow and fast swings and the robot uses a tripod gait for locomotion. The parameters of the gait, such as stride angle, stance angle, and stride period, are varied and the speed achieved is estimated. The effects of the terrain properties on the velocity of the robot are considered as well. They also concentrate on evaluating the performance of the robot in terms of power consumption and specific resistance of the terrain. Another performance evaluation conducted by Cham et al. [13], on the Sprawlita hexapod, investigates the stride frequency optimization to achieve maximum performance. This study captures the effects of stride period on the performance measures such as hopping height and velocity. In a recent paper, Garcia Bermudez et al. [25] discuss the maximum velocity achieved by the OctoRoACH robot on distinct rough terrains. Here, the authors concentrate on the effects of stride frequency and measure the performance in terms of maximum velocity and vibrational terrain signatures. In our work, we quantify the performance in terms of ground speed and energy efficiency over different terrains. We conduct the performance evaluation over two variable spaces: the gait-parameters and the terrain properties. 2.2 Amphibious Adaptations in Robots Amphibious robots have the potential for many applications in coral reef studies, terrain mapping, and search and rescue operations. Amphibious legs equip the robot with a capability to explore diverse locations in the world encompassing those that are on the ground as well as underwater. 10

22 Recently, there have been amphibious robots designed to operate with legs to walk and swim effectively. The design by Boxerbaum et al. [9] has six propeller legs which can be used as wheels on land and propellers under water. The propeller legs in this design have 2DOF, to achieve translational and yawing motions of the robot underwater, increasing the complexity of the controller and probably have a negative impact on cost and robustness relative to the design proposed by us. An alternative design by Yu et al. [70] is equipped with four circular legs and two flippers for swimming. The circular legs are used as wheels for land locomotion and as propellers for underwater mobility. In these designs, the legs have more than one degree of freedom which is achieved by using multiple actuators per leg. Increased number of actuators in these designs complicate the robot s operations. A major drawback of propeller based legs is the plausible harm propellers could cause to delicate marine creatures. The amphibious six-legged AmphiHex-robot, in the study by Liang et al. [43], uses six adaptable legs which can adapt to both swimming and walking. This design has a limitation on the strength of the legs to support the weight of heavier robots. A good estimate of swimming capabilities of the robot in actual underwater environments is missing in their work. Also the strength of the legs is not discussed in detail. The Ninja leg [18], which we discuss in later chapter, is a mechanically simple design with 1 degree of freedom per leg and allows the Aqua robot to achieve complex maneuvers with 5DOF trajectories. Table 2 1 presents a comparison between different amphibious leg designs. The gait used for different maneuvers of the robot affects the power efficiency and range of physical speed of the robot. Several research groups have addressed the development of efficient tripod gait walking for legged robots [34, 15, 58, 26]. Several studies have also been conducted on swimming gaits 11

23 Table 2 1: Comparison of the amphibious leg designs. Platform Used Terrestrial Underwater Thrust Complexity Mode Mode (N) per Leg Alexander S Boxerbaum, Philip Werk, Roger D Quinn, and Ravi Vaidyanathan. [9] (2005) Whegs IV Wheel Propeller 34 2DOF Jiancheng Yu, Yuangui Tang, Xueqiang Zhang, and Chongjie Liu. [70] (2010). Wheel Propeller 30 2DOF Xu Liang, Min Xu, Lichao Xu, Peng Liu, Xiaoshuang Ren, Ziwen Kong, Jie Yang, and Shiwu Zhang. [43] (2012) AmphiHex Legged Oscillatory 27 1DOF Bir Bikram Dey, Sandeep Manjanna, and Gregory Dudek. [18] (2013) Aqua Legged Oscillatory 36 1DOF 12

24 for legged robots. A study by Plamondon et al. [49] discusses the development and performance properties of swimming gaits, for Aqua-class vehicles, with names such as middle-off, hovering, sinusoid, alternate, each of which provides a trade-off between stability, speed, and other factors. We use middle-off swimming gait for our experiments in this work. One of the open questions in amphibious legged robots is the adaptive leg that enables the robot to run on terrestrial surfaces and swim underwater. We try to address this issue by presenting a design (Ninja legs) that amalgamates the walking abilities of legs and swimming abilities of the flippers. We evaluate our design not only for performance, but also for practical robustness, by posing challenging tasks like entering and exiting surf in the ocean. 2.3 Terrain Sensing and Identification Terrain identification has the potential to increase the efficiency of navigation in mobile vehicles. Once the terrain is identified, mobile vehicles can use this information to adapt their gaits based on prior knowledge about the terrain, avoid certain terrain types that would pose challenges, improve the walking abilities and performances. To be able to identify the terrain, one should be capable of sensing its properties. Many sensors like cameras, and range sensors, can be considered for terrain identification purposes, but tactile sensing provides information directly related to the mechanical properties of the terrain. Tactile sensing is an economical and robust solution for surveying the terrain properties. In this work, we sense and identify the terrain through tactile feedback. Similarly, many animals use tactile feedback for navigation through challenging environments. For example, whiskers on the body of some animals act as tactile sensors and aid them in functionalities including exploration, locomotion, gather information about surface textures and shapes [50, 63, 42]. 13

25 One of the earliest research to mention tactile sensors in robots is Grey Walter s study on tortoise robot [64]. The tortoise robot uses a touch sensor to avoid obstacles and navigate through the environment to reach its reward. Some of the popular ways to achieve tactile sensing are using artificial whiskers, tactile probes or vehicle-mounted sensors. In the literature, the deflections of artificial flexible whiskers, measured using a potentiometer, are used to estimate the distance to an obstacle [37, 16] or recognize an object [55]. These whiskers are not sensitive to the texture of the surface and thus are not very much suitable for terrain sensing. A study by Roy et al. [54] presents surface texture classification technique using the acoustic response obtained by tapping a probe against a surface. Another work using a tactile probe, presented by Giguere et al. [29, 26], analyzes the acceleration patterns induced at the tip of the probe while it is dragged over a surface. They present classification results over ten different surfaces including both indoors and outdoors. Yet another efficient way to sense a terrain is by considering the dynamics of overall system when the robot is traversing different terrains. This can be achieved by measuring the inertial estimations captured by inertial sensors mounted on the robot s body. In this model, wheels or the legs of the vehicle act as tactile probes. In [56], Sadhukhan proposed a terrain classification technique using the internal sensors on a wheeled vehicle. This technique relied on vertical acceleration of the chassis of the vehicle to perform terrain identification. DuPont et al. [22] present a terrain identification technique for wheeled vehicles by considering the vibration signatures represented by angular velocities such as pitching and rolling, and vertical accelerations. They make use of a probabilistic neural network to differentiate between three terrains such as grass, gravel and asphalt. Brooks et al. [10] use linear separator and Weiss et 14

26 al. [67] use support vector machines on the vibrational signatures produced by chassis vibrations when the vehicle traversed different terrains. The problem of terrain identification by legged vehicles was studied initially in the context of research on enhancing the mobility of planetary rovers. Krotkov et al. [40] proposed the modeling of terrain to plan the leg placements of the Ambler rover [7]. In their subsequent work, Krotkov et al. described the estimation of terrain characteristics from leg contact forces [39]. Giguere et al. [28, 26] proposed an unsupervised machine learning algorithm to classify the inertial sensor data from different terrains. This algorithm exploits the time-dependencies between the samples and is able to cluster data from fast-switching terrains. An advantage of this technique is that the method works by finding a set of parameter values for any user-specified classifier that minimizes a cost function. We use this elegant methodology [28] in our gait adaptation algorithm for on-line terrain identification. 2.4 Gait Adaptation Humans naturally adapt their gait to the environment they are walking on. For example, people are able to walk on both grass and ice, even though they require substantially different gaits to avoid falling. Thus, the subsystems in our brains adapt in order to achieve a stable gait on different terrains. Similarly, the legged robotic vehicles need to walk through difficult terrains without becoming unstable or painfully inefficient. There has been a body of prior work on achieving stable locomotion with legged vehicles on rough terrains. One of the approaches is to deliberately and carefully plan every footfall of the robot [68, 14]. A paper by Shih et al. [61] discusses the gait adaptation by modeling the states of the robot to maintain its stability. This approach divides the environment into permitted and nonpermitted cells for leg placement. This study presents three approaches such 15

27 as body motion adaptation, leg sequence adaptation, and leg position adaptation. Footfall planning algorithms are very difficult to achieve on a small mobile platform because of the need for accurate sensor information, accurate constraint modelling, and huge computation power. Another recent work on the BigDog robot [52] proposes a control system that adapts to terrain changes through terrain sensing and posture control. This control system determines the desired load on each leg and actuator, and the contact with the ground using joint sensor information. A posture algorithm coordinates the kinematics of legs with their ground reaction forces to produce a desired body position. An alternative approach for gait adaptation is to have explicitly designed gaits for specific purposes. These individual gaits are stored and activated based on the current purpose. For example, if the current purpose is to climb, then the gait with ability to climb stairs is selected from stored gaits. There are several studies conducted to improve the robustness and the performance of this approach by applying learning techniques [59]. Weingarten et al., in their study to achieve automated gait adaptation [66], use a modified version of Nelder-Mead descent to adapt the gait parameters of the robot. They also conclude that Nelder-Mead tuning yields better performing gaits as compared to those achieved by manual tuning. We use a similar approach to map the gait parameters against the terrain type. Instead of purpose, we have a terrain type based on which a suitable gait is picked. With a large set of possible gaits, the task to transition between the gaits becomes challenging. Haynes et al. [15] present acyclic feed-forward motion patterns that allow a robot to switch from one gait to another. As we have a limited set of gaits, we have not yet considered the complex gait transition challenges in this work. 16

28 In our work, we try to bridge the gap between terrain sensing and gait adaptation. We propose an algorithm to adapt the walking behavior of the robot based on the proprioceptive feedback received from the terrain. 17

29 CHAPTER 3 Gait and Performance of the Robot In this chapter, we discuss our approach towards the walking gait problem, wherein, we analyze the influence of gait parameters and terrain properties on the performance of walking robots. We evaluate our approach through a set of experiments on four different flat terrains: grass, dry sand, wet sand, and concrete surface. Some parts of this chapter are published in one of our publications [44]. 3.1 Walking gaits and Gait parameters Walking gait in terms of legged robots can be defined as a periodic pattern of leg movements that propel the body mass center of the mobile system. The repetition of this periodic pattern provides locomotive ability to the robot. Besides stable locomotion, another important aim of a stable gait is to provide balance or stability to the system. Walking gait of the legged system depends on various factors, such as the physical structure of the system, number of legs it has, its center of mass, the environment, and the constraints of the current task. Some of the legged vehicles like SIL04 [17], Athlete [69], and humanoid HRP-3 [38] compute the trajectories for their legs and feet to achieve a stable locomotion [31, 40]. These trajectories depend on the properties of the terrain, the vehicles are planning to navigate through. Hence, the computation of these trajectories need many sensory feedback from the environment. These vehicles should use sensing equipments, such as visual sensors, stereo vision cameras, laser range finders, to estimate the terrain properties along with lot of computing resources to compute actual trajectories. Some motion planners 18

30 also use force transducers to assess the characteristics of interactions between the robot s feet and the terrain surface [24]. The gait generated by this kind of computed trajectories and foot-placement strategies can be referred to as closed-loop gait. It is called closed-loop because the trajectories depend on the sensory feedback from the environment. Thus, to operate with a stable gait, the system requires a robust and detailed profiling of the ground surface. This increases the complexity and potentially makes the system fragile. Contrary to closed-loop gait, open-loop gait provides predetermined foot trajectories for navigation of the mobile system. Here, the trajectory is independent of the environment. Many legged robots use open-loop strategies for land locomotion [12, 51, 53]. As Aqua robot is built based on RHex design, similar to Rhex, Aqua s land locomotion is inspired by the principles of cockroach locomotion. Biological studies on the locomotion of cockroaches suggest that the lag between neural signal propagation from cockroach s brain to its leg and the speed of its gait is relatively large. This lag forces high speed cockroach runners to employ an open-loop feed-forward gait [36]. Following this model, even Aqua employs open-loop gait mechanism. In Aqua robot, the PD controller regulates the hip actuators and thus controls the torque to its leg shaft. The controller aims at eliminating the differences between its clock signal and actual shaft position, and the velocity. The local hip feedback does not provide any information about the true state of the leg or the body, thus making the robot to operate in a task open-loop manner [65]. In our experiments, we use a forward alternating tripod gait [57]. In this mode of walking, the three legs, two on one side and one on the other side of the robot, form a stable tripod. While one tripod formation is in contact with the ground and propelling the robot forward, the other tripod formation is circulated rapidly around to be ready for the next support phase [66] (Fig. 3 1). This quick 19

31 alternation of support, coupled with the compliant nature of the legs, results in a complex dynamic interaction between the robot and the ground. Figure 3 1: Graphical representation of Tripod Gait. The triangle represents the tripod support produced by three legs in the tripod gait. Every gait has a set of variables which define the physical trajectory followed by components of the system. These properties are referred to as gait parameters. For example, walking gait of a human is characterized with gait parameters such as step length, stride length, speed, and foot angle. Similarly, even the tripod gait is defined by gait parameters such as total stride period, stance period, and stance angle. Before introducing the details of parameters for the tripod gait, here is a brief introduction to the Buehler clock, which is an essential part of walking gait of the Aqua robot. Buehler clock is a computational analog of the central pattern generator [8, 35] in animals. The Buehler clock was originally developed for RHex [57, 4] and is based on a study which shows that cockroach legs are excited by a strongly stereotypical clock reference signal [41]. As the Aqua is based on RHex, it follows a similar pattern for walking. To achieve the tripod-gait, this clock uses a piece-wise linear angle vs. time reference trajectory characterized by four parameters[60]: the total stride or cycle period t c, the duty factor (the ratio of a single stance period over the cycle period) t s /t c, the leg angle swept during the stance Φ s and an angle offset to break symmetry in the gait Φ 0. Fig. 3 2 depicts the feed-forward clock signal that is fed into the robot s legs to achieve the stable gait. In the alternating tripod mechanism, this same 20

32 Figure 3 2: Plot showing the parameters of the tripod gait. Angular signals are plotted against the clock signals of the rotation of a leg. reference signal is supplied to each leg, except that the left tripod is out of phase with the right tripod. The grey region in Fig. 3 2 represents the part of the leg rotation at which the leg is touching the ground, i.e., the stance phase of the gait. As it can be seen, there are several parameters to this simple gait. Optimizing the gait refers to optimizing all the gait parameters. It gets complex and non-converging if all the parameters are considered at once. Hence, for the initial set of studies, we consider the performance of the robot over varying cycle frequency (f c ). Cycle frequency is the frequency of the robot s leg rotation (i.e. number of leg rotations per second). In our experiments, we record the walking data at various cycle frequencies and estimate the performance of the robot over different terrains. 3.2 Performance Factors One of the significant aims of a gait is to provide balance or maintain stability of the system and robustness for walking through different environments. It does not seem feasible to analyse the effects of gait changes on the stability or robustness of the system. Hence, we need to derive measurable quantities which will affect the stability, fitness and robustness of the robot. 21

33 We chose to assess the performance factors that increase the overall capabilities of the robot and thus provide better robustness and stability to the robot for operating on different terrains. We considered few of the performance factors such as: ground speed (actual speed achieved by the robot on a walk), on-spot rotation capabilities (ability to rotate on the spot when operating on different terrains), energy efficiency (power consumed by the robot per unit distance walk), alignment to a straight path (measure of deviation of path from straight line), and terrain tear (measure of tear caused to the terrain). Among these factors, with a constraint on equipment and test environment, we considered measuring two performance factors, ground speed and energy efficiency. We had to reject the on-spot rotation factor as the robot failed to rotate on certain surfaces (e.g., grass and sand) because of a high back emf on the robot s leg when operated in reverse mode. We also dropped the straight path factor as the test environments (e.g., beach areas) were not perfectly flat to consider the deviation from straight path. Measuring the terrain tear was difficult due to the lack of equipment, however, we would like to consider these factors in future studies. The ground speed gives the actual speed that the robot is able to attain on a particular terrain. Analyzing this performance factor will give an estimation of capabilities of the robot when operated in different environments. This factor facilitates us to estimate a near-optimal cycle-frequency per terrain, at which the robot can cover maximum distance in given time. Secondly, the energy efficiency of the robot gives a measure of sustainability of the robot on difficult environments. This performance factor will help us investigate the energy efficient cycle frequency for operations on a particular terrain. Thus, we estimate the performance of the robot by evaluating its ground speed and energy efficiency on various terrains. 22

34 In specific terms, the problem is to optimize the cycle frequency - for a particular terrain - at which the robot achieves either highest ground speed, or power efficient operations, or a trade-off between both. 3.3 Experiments We investigated this problem by conducting walking trials of the robot on four different terrains with five different cycle-frequencies. We computed the ground speed of the robot by measuring the time from recorded videos and the distance between the flag posts. We also recorded the battery current and battery voltage during the trials and computed the power consumed by the robot for every run. Thus, we have an estimate of the ground speeds and power consumption of the robot on different terrains, when operated with different cycle-frequencies (f c ) Experimental Setup The experiments were conducted on four terrains (Fig. 3 3a), namely dry sand, wet sand, grass, and concrete floor. The setup as seen in Fig. 3 3b was used on these terrains and Aqua was made to walk from the start point till the end point. Video of all the trials was recorded from a fixed distance as shown in Fig. 3 3a. This video was used to compute the time taken by the robot to cover the experimental path distance. This time is precise and is used for computing the ground speed of the robot Data Collection The cycle-frequency (f c ) is controlled by changing the speed levels in the graphical interface of the Aqua robot. Five different values of f c , 1.187, 1.332, and 2.05 Hz, are achieved by changing the speed control setting to five levels - 0.1, 0.2, 0.4, 0.6 and 0.8, on the graphical speed bar of the interface. For each speed control setting and every terrain, five trials were conducted. 23

35 (a) Different terrains and graphical representation of experimental setup. (b) The field setup indicating the robot s path and the markers. Barbados. Taken at Bellairs lab, Figure 3 3: Experimental Setup The data collected is a mixture of many sensor measurements. The relative leg rotations are measured using optical encoders attached to the motor shafts and a MSI-P400 quadrature decoder card is used to decode the signals from light receivers. Leg motor electrical current are estimated using carefully calibrated motor models [46]. These models compute an electrical current estimate based on physical parameters of the motors, voltage commands to the motors and their angular velocities. The robot is equipped with a 3-axis 24

36 Inertial Measurement Unit (3DM-GX1TM), which carries 3 Micro-Electro- Mechanical Systems (MEMS) acceleration sensors, 3 MEMS rate gyroscopes and 3 magnetometers. Accelerometers measure the accelerations of the robot s body, in m/s 2 and rate gyroscopes measure the angular velocities of the robot s body in rad/s. The data is collected from these sensors at a rate of 50 Hz, i.e. 50 sensor readings per second. 3.4 Results and Observations This set of experiments was conducted to investigate the effects of changing leg cycle frequency (f c ) on the performance of the Aqua robot. As discussed in previous sections, in this work, the performance is measured in terms of ground speed and power consumed per unit distance of walk. In Fig. 3 4, we see that the ground speed of the robot increases with cycle-frequency for soft-granular terrains (dry sand and wet sand), whereas the ground speed of the robot on hard terrains (grass and concrete surface), decreases at higher f c value of 2.05 Hz. We suspect that the robot s legs start to slip from the surface of the terrain, when rotated at very high speeds on hard terrains. On soft granular terrains, the granularity of the terrain provides grip to the legs and helps the robot achieve higher ground speeds even at an increasing cycle frequency. Thus, the results show that, to achieve higher ground speeds on hard terrains, the f c value should be capped to the range Hz to 2.05 Hz and to achieve the same on soft granular terrains, the robot needs to operate at its highest f c values. Results of these experiments clearly show that the terrain type has a strong influence on the velocity of the robot, at fixed gait parameters. 25

37 Concrete Dry Sand Grass Wet Sand Ground Speed (m/s) Cycle frequency (Hz) Figure 3 4: Ground speed of the robot plotted against f c. The plot shows the variation found over different terrains. Plot also displays the errors occurred during different trials. Another result in Fig. 3 5 shows the variation of power consumed by the robot per unit distance of walk against varying cycle-frequency. The power consumed by the robot is measured by recording the battery current and battery voltage over the robot s run. From the results, it is evident that the robot reacts differently to hard and soft granular terrains. We take a trade-off between the performance factors, ground speed and power consumption, as an optimal performance. The f c value at which the robot consumes less power yet achieves acceptable ground speeds is considered as near-optimal f c value. For example, on wet sand, the robot operating at high f c value of 2.05 Hz achieves highest ground speed, yet maintain low power consumption compared to other terrains. On dry sand, however, it is very power inefficient to operate at high f c values. 26

38 RMS Power consumed per meter (J / ms) Concrete Dry Sand Grass Wet Sand Cycle frequency (Hz) Figure 3 5: Root mean square of power consumed per unit distance walk of the robot plotted against f c. The plot shows the errors in the readings over five trials for each speed and terrain. Using both the ground speed results and the energy efficiency results, we build a table (Table 3 1), presenting the f c values at which optimal performance can be achieved by the robot. Here, we consider optimal performance as a trade-off between the ground speed and the power consumption, higher ground speeds achieved at not very expensive power consumptions. The Table 3 1 presents a mapping of the terrain and f c values at which the highest ground speed is achieved and f c values at which an acceptable measure of power is consumed. The fourth column presents the f c values at which an optimal performance can be expected. 27

39 Table 3 1: Tabular representation of the experimental observations. The table presents a f c at which optimal performance is achieved on different terrains. Terrain f c f c Optimal Performance (max Ground Speed) (acceptable Power Consumption) Concrete Hz Hz < f c < Grass Hz Hz f c = Dry Sand 2.05 Hz Hz < f c < 2.05 Wet Sand 2.05 Hz 2.05 Hz f c = Summary In this chapter, we introduced walking gaits and gait parameters of the robot. We also discussed the performance factors that will be affected by the gait used for walking. Through experiments, we analyzed the effects of gait parameters and terrain properties on the performance of the robot. Finally, we estimated the optimal gait settings in the Aqua robot to achieve better performance on various challenging terrains. One of the limitations of our analysis in this chapter is the study over only one gait parameter (f c ). We would like to enhance our analysis by considering different gait parameters in future. We would also like to explore the cyclefrequency domain thoroughly, instead of just five frequency values. We also have plans to incorporate other performance factors mentioned in Section

40 CHAPTER 4 Physical Adaptation In this chapter, we address the problem of improving the walking performance of the robot by physically adapting to the environment. One of the ways to improve the mobile efficiency is to employ physical modifications suitable to the environment. This chapter introduces a physical adaptation of the Aqua robot in the form of new robotic legs called Ninja legs. 4.1 Ninja Legs Ninja legs are a class of robotic legs that enable amphibious operation, both walking and swimming, of the Aqua class hexapod robots. We refer to these amphibious legs as Ninja legs as the design resembles a spinning ninja star. Fig. 1 2 shows the Aqua robot equipped with the Ninja legs. The mechanical design for these legs was developed by Bir Bikram Dey and Gregory Dudek. A detailed discussion on the mechanical aspects of this design can be found in our recent paper [18]. As discussed before, legged mobility has often been envisioned as the most versatile locomotion strategy possible for terrestrial robots. Likewise, the use of actuators with flippers can provide an exceptionally large degree of mobility and versatility in the underwater domain. What has proven elusive to date, however, is a simple leg design that exhibits the advantages of terrestrial walking legs as well as the motile efficiency of flippers when underwater. It is this type of hybrid that we discuss and evaluate in this chapter. The leg design and associated assembly we propose has the attributes of flippers, legs as well as wheels. 29

41 Several different classes of leg design have been previously developed for Aqua-class vehicles, including both robust all-terrain legs for walking, and efficient flippers for swimming. Notably, however, the walking legs have extremely poor efficiency and limited thrust when used for swimming in the water, and the flippers are completely unsuitable for terrestrial locomotion since they are unable to bear the physical load of the robot due to the flexibility they require for efficient swimming. A long standing problem is to develop robust robotic legs designed to perform both effective terrestrial and efficient underwater maneuvers. With the design of Ninja legs, we have attempted to address the problem of adapting to different modes of locomotion. We also evaluated the qualitative performance of the robot using Ninja legs in terms of entering and exiting the open ocean, through surf with a wave height of roughly 1 m (Fig. 4 1). Under these circumstances, we observed that the robot was able to swim to shore, switch (under manual controls) to walking mode upon contact with the beach, and walk onto the shore. It was similarly able to walk into the surf, enter the water, and swim out in the open water. Executing this maneuver depends critically on a sequence of gait transitions to time various actions relative to wave action, and this challenging behavior was executed under manual control. The legs, however, were clearly sufficient to perform this activity. In the scope of this thesis, the rest of the chapter concentrates only on evaluating Ninja legs and their properties for terrestrial locomotion. As the thesis concentrates on the terrestrial mobility of legged robots, we will not discuss further the swimming efficiency and capabilities of Ninja legs. More on swimming abilities of Ninja legs can be found in [18]. 30

42 (a) Surf Entry-Aqua walks to the ocean and starts swimming once it is in water. (b) Surf Exit-Aqua swims to the shore and starts walking on the beach Figure 4 1: Surf entry exit experiment with Ninja legs Design Approach As discussed before, our aim is to design a set of legs with properties suitable for both terrestrial walking and underwater swimming. We propose a 31

43 design in which a structure encloses the flipper, in order to protect the flipper during terrestrial operations. The enclosing structure also performs as the walking legs for terrestrial locomotion. Figure 4 2: Ninja leg behaving as an offset wheel. An enclosure of circular shape is designed to contain the flippers used for generating thrust underwater (or on the water surface). This whole structure, consisting of a circular enclosure along with the flippers, will rotate at an offset from the center as seen in Fig This allows us to have the advantages and some disadvantages of an offset wheel. This offset-wheel design of the enclosure is effective as it provides the advantages of traditional semi-circular walking legs in both forward and backward directions. Since the enclosure is a cage-like structure, with an extensive open area for water to flow through, the flippers inside can still generate enough thrust for the robot s swimming Mechanical Properties The Aqua robot, while using tripod gait for walking, needs three legs to be able to support the weight of the robot. The robot weighs about 16 kg to 18 kg, with the batteries. For safety and robustness, we fabricated Ninja legs with enough strength so that one leg can take the weight of the whole robot. The property of a material to undergo elastic deformation is called the compliance. Compliance of the leg is a critical property for an efficient walking of a robot, hence, we need the Ninja legs to be compliant. The enclosure is 32

44 the part which acts as leg when the robot is in walking mode. Hence, we used bent spring steel rods to make the circular shaped enclosure. Carbon fiber plates are used to reinforce the structure as they increase the strength of the legs and are light-weight and slender. Fig. 4 3 shows the detailed structure of the Ninja legs. Figure 4 3: Illustrated diagram of the Ninja Leg. As shown by the arrow in Fig. 4 4, Ninja legs have shorter effective arm length due to the increase in their diameter. Shortening of arm length reduces the leg motor current required for the robot to go from sit mode to stand mode. We will verify this claim in our results section. Figure 4 4: Comparison of the effective arm length between the semi-circular walking legs and the Ninja legs. The arrows represent the effective arm length. The semi-circular walking legs have compliance for of the motor rotation (Fig. 4 5a). Whereas, Ninja legs have compliance for about

45 of the motor rotation (Fig. 4 5b). The remaining of rotation does not permit compliance because of presence of the carbon fibre plate. (a) Compliance span for Ninja legs. (b) Compliance span for semi-circular walking legs. (c) Effective arm lengths of the Ninja legs on granular terrain. Figure 4 5: Mechanical properties of Ninja legs One of the major concerns was the capability of the robot to walk on granular terrains (e.g., sand, and snow) with the Ninja legs. As the rods are thin, there is a chance of digging into the terrain. Hence, we added the walking supports to increase the area of contact between the legs and the terrain. The placement of walking supports on the rods determines the effective arm lengths (Fig. 4 5c). 4.2 Experimental Results and Observations We conducted three sets of experiments to evaluate the effectiveness of the Ninja legs for terrestrial locomotion. The first set of experiments were to evaluate the performance of the robot equipped with Ninja legs. We also conducted experiments to evaluate the claim regarding advantages of a shorter arm length (Fig. 4 4). We compare the performance of the Ninja legs against the RHex legs as these are widely used in legged robots for terrestrial locomotion [57, 4, 58, 3] and provide a combination of simplicity, load bearing 34

46 capacity, compliance and robustness. Finally, we use a variant of standard tripod gait and compare the performance of the robot Performance Evaluation In this section, we present the results of performance evaluation experiments on the Aqua robot equipped with both RHex semi-circular legs and Ninja legs. The experiments conducted are similar to those explained in Section 3.3, with the difference being that the data was collected with both RHex legs and Ninja legs. We conducted experiments on one terrain so that we can compare the two leg designs, keeping the terrain constant. The terrain used is a tiled surface (Fig. 4 6). The performance factors measured are ground speed and energy efficiency. (a) Aqua is equipped with Ninja legs. (b) Aqua is equipped with RHex legs. Figure 4 6: Trial runs of the Aqua robot on tiled surface. The plot in Fig. 4 7 shows the ground speeds achieved by the robot when operated with varied leg-cycle frequencies (f c ). Ninja legs, due to the reduced compliance of their building materials, achieve better physical speeds at higher values of f c. The semi-circular walking legs, however, make the robot s motion irregular (i.e. bumpy) at higher values of f c because of higher compliance of their component materials. 35

47 RHex Legs Ninja Legs Ground Speed (m/s) Cycle Frequency (Hz) Figure 4 7: Ground speeds for both RHex legs and Ninja legs plotted against cycle frequency of leg rotation RHex Legs Ninja Legs RMS Power Consumed per unit walk (J/ms) Cycle Frequency (Hz) Figure 4 8: The Power consumed per unit distance walk plotted against the cycle frequency of the leg rotation. The plot shows the readings for both RHex legs and Ninja legs. 36

48 Fig. 4 8 represents the power consumed per unit distance of walk plotted against varying cycle frequency (f c ) of the robot legs. The plot indicates that the robot consumes more power when walking with the Ninja legs than with the RHex walking legs. We suspect this is because of the added weight of the Ninja legs. Even though the power consumption is slightly higher than the usual semi-circular RHex legs, the Ninja legs achieve higher ground speeds. In future, we plan to reduce the weight of Ninja legs by replacing the heavy spring steel rods with other light weight and more compliant material. Reducing the weight of the legs will definitely have an impact on the power consumption as we will be reducing the load on the motors Effective Arm Length Effective arm length is the length measured from the arm-joint on the body till the contact point of the arm with the ground. With respect to our robot, the effective arm length is the distance between the leg-hip joint of the robot and the leg-ground contact point. The arrows in Fig. 4 4 depict the effective arm lengths of both Ninja legs and semi-circular RHex legs. This experiment was conducted to justify our claim in Section shortening of arm length reduces the current through the leg motors when the robot transits from sit mode to stand mode (Fig. 4 9). Fig. 4 4 shows that the effective arm length of Ninja legs is shorter than that of semi-circular RHex legs. The robot was made to go from sit mode to stand mode and current through the leg motors was recorded. Four trials were conducted with both RHex legs and Ninja legs. From the average of four trials, we found that Ninja legs draw 0.65 Amperes of current which is significantly lesser than 1.96 Amperes drawn by RHex legs. Plot in Fig shows the peaks in the leg motor current. It can be observed that the RHex legs draw a significant load of current to attain the stand position. 37

49 Figure 4 9: Depiction of Aqua robot going from sit mode to stand mode. Both the Ninja legs and the RHex legs are shown RHex Legs Ninja Legs 3 Leg Motor Current (A) Time (Sec) Figure 4 10: The robot was made to go from sit mode to stand mode with both RHex legs and Ninja Legs. Figure shows leg motor current plotted against the clock. Also the plot shows that the RHex legs consume a sustained current even when the robot is idle. This can be attributed to the semi-circular shape of these legs which do not permit a completely stable static stance, and thus a torque is applied continuously. Ninja legs, however, achieve a stable static standing because of their circular wheel shape. Thus Ninja legs draw zero current as long as the robot is idle Linear Variant of Tripod Gait As discussed in Section 3.1, to achieve the tripod gait, the central pattern generator of Aqua robot uses a piece-wise linear angle vs. time reference 38

50 trajectory. For the first two experiments, we used a tripod gait, in which the angular velocity of the leg varies accordingly whether the leg is in aerial phase or stance phase, demonstrating the salient features of Buehler clock. Hence, we refer to this kind of tripod gait as Buehler clock based tripod gait (B c -tripod). In this experiment, we tried a variant of the tripod gait by making the angle vs. time reference trajectory linear. This variant is called wheel mode tripod gait because the legs rotate with constant angular velocity similar to wheels. Since the stance is still a tripod, three legs rotate out of phase with the remaining three legs as in standard tripod gait. Fig shows a comparison between the angular trajectories of B c -tripod and wheel mode tripod gait. As it is seen in the plot, B c -tripod gait has a stance phase in which the angular velocity of the leg is slower, whereas the angular velocity of the leg is constant over period in wheel mode tripod gait. As before, we recorded the current through leg motors in both B c -tripod gait and wheel mode tripod gait. Fig shows leg motor current plotted against the clock time. We can see that the B c -tripod gait has large current spikes. This peak in current arises due to the forceful impact of the robot leg onto the ground after a fast aerial phase. In wheel mode, however, there is no different aerial and stance phase, thus preventing a high impact at the legground contact. We would like to further analyze this new variant of tripod gait in future. 39

51 4 3 2 Leg Angle (Radians) Clock (sec) (a) Trajectory plot for Beuhler-clock based tripod gait Leg Angle (Radians) Clock (sec) (b) Trajectory plot for wheel mode tripod gait. Figure 4 11: Two variants of tripod gait. 40

52 8 6 Wheel Mode Beuhler Mode 4 Leg Motor Current (Amp) Time (Sec) Figure 4 12: Leg motor current peaks recorded on the robot when operated with both B c -tripod and wheel mode tripod. 4.3 Summary This chapter introduced a new physical adaptation of the robot which enhances the capabilities of the robot. We demonstrate experimentally that the Ninja legs have clear advantages in terms of their ability to achieve high ground speeds as well as their reduced power consumption in standing mode. We also investigated the behavior of the robot when operated in several variants of the tripod gait. Some of the limitations of our design are the weight of the legs resulting in high power consumption, rigidity of the legs affecting the leg motor current peaks, and the material used for walking supports in the legs that is responsible for slipping of the robot on smooth surfaces. We plan to address these issues by looking in depth into the materials used in manufacturing the legs. We would like to get valid inputs from experts in the field of material composition to have a clear idea on the materials to be used. In future, we would like to 41

53 analyze the response from different terrains when the robot is operated with Ninja legs (similar to our experiments in Section 3.3). 42

54 CHAPTER 5 Terrain Identification in Real-time And Gait Adaptation Terrain identification and gait adaptation to suit the terrain are some of the important qualities that help the robot walk efficiently in its environment. In this chapter, we propose an algorithm to enable the robot to adapt its open-loop walking gait to the terrain. The algorithm consists of terrain classification, terrain identification in real-time and gait adaptation. We will discuss the overview of the algorithm followed by a detailed description. In the experiment section, we analyze the effects of gait parameters on terrain sensing and terrain classification. At the end, we evaluate our algorithm with both semi-synthetic data and robot sensor data. 5.1 Overview The block diagram in Fig. 5 1 shows the data flow and processes in our gait adaptation algorithm. The whole process is divided into two phases: a training phase and an execution phase. The training phase is indicated by the dotted line rectangle in the block diagram (Fig. 5 1). In the training phase, we collect proprioceptive data from different terrains and build classifiers using an unsupervised cost-based learning technique [28]. At the end of training phase, we have classifier parameters and classes with labels. In the execution phase, we classify the data coming from the robot s sensors in real-time and identify the terrain class. Once we know the terrain, we make the decision on appropriate gait for that terrain and feed the gait into the robot. Thus, the algorithm enhances the robot s abilities by making it capable of adapting its gait in real-time. Each block in the diagram (Fig. 5 1) and the data flow between the blocks is discussed further in this section. 43

55 Figure 5 1: Block diagram of Gait Adaptation Algorithm Sensor Data The robot is made to walk on different terrains and multiple sensors onboard are used to collect proprioceptive data. We record the leg positions, current through the robot s legs, linear accelerations, angular velocities, battery current and voltage drawn. The leg positions of the robot are obtained by relative leg rotations measured using optical encoders attached to the motor shafts. Leg motor electrical current are estimated using carefully calibrated motor models [46], that compute an electrical current estimate based on the 44

56 physical parameters of the motors, the voltage command to the motors and their angular velocities. The robot is equipped with a 3-axis Inertial Measurement Unit (3DM-GX1TM), which houses 3 Micro-Electro-Mechanical Systems (MEMS) acceleration sensors, 3 MEMS rate gyroscopes to measure angular velocities and 3 magnetometers. The data is collected from these sensors at a rate of 50 Hz, i.e. 50 readings of sensor data are recorded per second Feature Selection The feature selection block is responsible for generating the vector x t as an input to the classifier. The data vector x t represents the data from one complete leg cycle. Thus, data vector x t consist of data collected by sampling 13 sensors - comprising of 3 accelerometers, 3 rate gyroscopes, 1 leg angle encoder and 6 motor current estimators - at a rate of 30 samples per one cycle of the leg. Thus, each feature vector x t is of size 13x30. In this work, the dimensionality of the dataset is reduced by applying Principal Component Analysis and only the top N f = 2 main features are selected for the classification. It was shown by Giguere et al. [27, 26], that the two main components are sufficient to discriminate between the terrain classes. We plan to consider other components to achieve more discrimination in our future work. The features selected in this step are fed into the classifier Classification Methodology We use an elegant methodology developed by Giguere et al. [28] for unsupervised clustering of proprioceptive data samples. These samples represent sequences of consecutive measurements from the robot as it traverses the terrain. Since the samples are generated through a physical system interacting with a continuous or piece-wise continuous terrain, time-dependency will be present between consecutive samples. The clustering algorithm [28] explicitly 45

57 exploits this time-dependency. It is a single-stage batch method, eliminating the need for a moving time-window. The algorithm works by minimizing a cost function which minimizes the variation of classifier posterior probabilities over time, while simultaneously maintaining a wide distribution of posterior probabilities. The aim of the algorithm is to search for the parameters θ that minimizes the following cost function, N c arg min θ i=1 T 1 t=1 (p(c i x t+1, θ) p(c i x t, θ)) 2 var(p(c i X, θ)) 2 The dataset needed for the algorithm are, A sample set X = { x t }, generated by a Markovian process with N c (No. of Classes) states, where x t is a feature vector produced at some time t ϵ {0, T }. A classifier with parameters θ used to estimate the probability P (c i x t, θ), that the sample belongs to class c i C, where C is a set of all possible N c classes. A set of parameters θ that is able to classify the data set X reasonably well. The classifier is fed with the data vector x t from feature selection step. The advantage of this algorithm is that it can be evaluated with different kinds of classifiers, such as k-nearest neighbors (k-nn), linear separator and mixture of Gaussian, based on the knowledge about the class distributions. In this work, we use linear separator and k-nn classifier with this unsupervised learning technique. At the end of this step, we have a vector of classifier parameters θ that define the classes. Once we have the classifier parameters, we make use of true labels of the data to produce classes with labels and the classifier. 46

58 5.1.4 On-line Terrain Identification The objective of the training phase is to (efficiently) produce a classifier and an associated small set of class labels. Next, the aim is to identify the terrain using the real-time data from the robot when it is walking. Initially, a random gait is selected for the robot to walk. The sensor data from the robot is split into feature packets, each packet comprising of data samples from one complete leg rotation as mentioned in Section The feature packets are then fed into the classifier. The classifier classifies each feature packet to its terrain class and generates a list of class labels representing all the feature packets. The terrain identification block identifies the terrain by employing decision making strategies on the list of class labels. Different decision strategies, such as maximum appearance strategy (a class label that appears most frequently in the list is decided to be the terrain class), certainty of the class strategy (a class with least uncertainty is chosen as the current terrain class), and consecutive similarity strategy (a class with maximum consecutive appearances will be chosen as the terrain class), could be employed in making the decision about the terrain class. Due to its simplicity and efficiency, in this work, we employ maximum appearance strategy Gait Switch This algorithm selects a gait based on the identified terrain. Initially a mapping of terrains against walking gaits is built from the information available about the effectiveness of different gaits on the terrains. We build such a map from the results of our experiments in Chapter 3. By considering a trade-off between ground speed and energy efficiency, we create a terrain vs. cycle-frequency (f c ) mapping as shown in Table

59 Table 5 1: Mapping of terrain types and optimal gaits Terrain Label Terrain Gait Label Optimal Cycle-frequency (Hz) A Concrete Gait A f c = ( )/2 B Grass Gait B f c = C Dry Sand Gait C f c = ( )/2 D Wet Sand Gait D f c = 2.05 Once we have identified the terrain, the task is to look up this table and pick the corresponding gait. The decision to change the gait has to be taken with a strategy such as the cost of switching strategy (switch the gait only if the cost is minimal), and the value of switching strategy (compute the value in terms of a utility function). For example, if we consider the ground speed achieved as a utility function, then the value of switch is the ratio of ground speed achieved by right gait on the terrain (Gait B on Terrain B) to that achieved by wrong gait on the terrain (Gait D on Terrain B). If this ratio is more than certain threshold, then the gait will be switched. The Table 5 2 shows an example for value of switching gaits between terrain B (Grass) and terrain D (Wet Sand), using ground speed as the utility function. Table 5 2: An example for value of switching gaits with ground speed as utility function. The speed data is taken from the results of Chapter 3 Terrain Class / Gait Class Gait B Gait D Value of Switch Terrain B (Grass) m/s m/s : = Terrain D (Wet Sand) m/s m/s : = As the robot changes its walking style, the response from the terrain changes and this affects the data collected by the robot s sensors. Thus, every gait will give different readings from the terrains. For example, Fig

60 shows similar features sampled from two terrains with two different gaits. The feature values are clearly different for both the gaits. It is evident from the plots that different classifiers are needed for different gaits used. Consider the data in Fig. 5 2, an advanced classifier, such as k-nn, trained with the Dataset1, will fail to classify the data samples from Dataset2. For example, a data-point (-1, -0.6) will be classified as Terrain B by a classifier trained with Dataset1, whereas the same data-point will be classified into Terrain C by a classifier trained with Dataset2. Hence, we use gait-specific classifiers. That means, if we have n gaits, we will repeat the training phase of the algorithm n times with the data generated by each of these n gaits to generate n classifiers. Feature Dataset 1 : fc = Hz Feature 1 Feature Dataset 2 : fc = Hz Feature 1 1 Terrain 0.5 C (Dry Sand) 0 Terrain B (Grass) Figure 5 2: Plot showing the effect of gait on data distribution. It shows the difference in the sample space of the data collected by the robot running on two terrains with different gaits. This makes it necessary to have a classifier trained for each of the gaits. 5.2 Semi-supervised Gait Adaptation In the previous section, we discussed a detailed overview of the gait adaptation algorithm. Different strategies and decision making mechanisms were 49

61 also discussed. Here, we present pseudo code for the algorithm and discuss the implementations made for validating this algorithm Algorithm We present a semi-supervised gait adaptation algorithm to aid the robot achieve better walking on rough and varying terrains. We call it gait adaptation because this algorithm enhances the robot with an ability to adapt its walking gait according to the terrain. The algorithm is deemed semisupervised because we use the true class labels in training phase to build the classifiers and terrain classes. The pseudo code in Algorithm 1 presents stepwise details for the computational stages in the block diagram ( Fig. 5 1), presented in the previous Section. Here, the training phase can be executed off-line or on-line, however, the execution phase is always run on-line Implementation For this work, we have implemented the simulation version of the gait adaptation algorithm. This is the initial phase of the algorithm validation which serves to permit more controlled and rigorous analysis than the real system, and to allow pre-configuration before deployment on the real system. As part of initial implementation, we use ROS nodes to replace the actual robot sensors. The real-time data from on-board sensors is simulated by a publisher node which publishes the data on to a ROS topic. The gait adaptation node, representing our algorithm, subscribes to this ROS topic and processes the data vectors that are published. Fig. 5 3 shows the ROS publisher and subscriber nodes, and the ROS topic used to stream data. Node robotsensors publishes the sensor data onto topic DataStream. GaitAdaptation node, subscribed to DataStream topic, 50

62 Algorithm 1 Semi-supervised Gait Adaptation Algorithm Input: Set of n terrain classes, T = {t 1, t 2,...t n }. Set of n gaits, G = {g 1, g 2,...g n }. Data collected with every gait g i in G, X G = { X g1, X g2,... X gn }. Where, X gi = { X t1, X t2,..., X tn }, Data from each terrain t i. X ti = { x 1, x 2,..., x m }, m data samples in every vector. x i = {s 1, s 2,...s 13 }, Readings from 13 Sensors. Output: t curr : Current terrain identified. g new : Optimal gait chosen for terrain t curr Training Phase: 1: Map {T G} A map of Gaits to Terrains 2: for each g i in G do 3: classifier parameters: θ gi UnsupervisedCostBasedClassifier( X gi ) 4: c gi Classifier ( θ gi,t ) 5: g i {g i,c gi } Every gait is assigned with its own classifier 6: end for Execution Phase: 7: initialize current gait: g curr Random(G) 8: define: switchthreshold 9: while (T rue) do 10: online sensor data from terrain: Xti = { x 1, x 2,..., x m } k data samples belong to one complete cycle of leg rotation. Each feature packet is made of k samples 11: feature packets: F : {f1, f 2,..., f m/k } sampling( X ti ) 12: terrain labels: t : {t 1, t 2,..., t m/k } classify( F ) 13: current terrain: t curr max( t) 14: g new lookup(map{t G},t curr ) 15: if (valgaitswitch(g new, g curr, t curr ) switchthreshold) then 16: g curr g new 17: end if 18: end while 51

63 processes the sensor data. For validation of the algorithm, we use both synthetically generated data and real data collect by the robot over multiple runs on different terrains. Figure 5 3: RosNodes for simulating the Gait Adaptation algorithm. 5.3 Experimental Results and Observations We present three sets of experiments to evaluate the interplay between walking gaits and terrain sensing ability of the robot. These experiments were conducted with the Aqua robot equipped with semi-circular legs. Initially, we investigate the effects of gait parameters on the terrain differentiability. In this problem, we define terrain differentiability as the distance between terrain classes in the feature space. If the terrain classes are farther apart, then those classes are more differentiable. In our second experiment, we evaluate the performance of the classification methodology with the data collected by the robot operated with different walking gaits. Lastly, we validate the semisupervised gait adaptation algorithm proposed in this chapter Terrain Differentiability and Gait Parameters In this subsection, we analyze the effects of cycle-frequencies on the differentiability of the terrain classes. We created a feature set by considering the leg motor currents (I 0 ) and vertical accelerations (A z ), as these features are most affected by physical interaction with the terrains. The dimensionality of the feature set is reduced by sampling the data at one particular angle of the leg rotation cycle, at which the separation between the terrain classes is the highest [30]. In Fig. 5 4, the features I l and A z are plotted as a function of leg angle. The plot also shows the optimal angle (1.25 radians) at which the classes are well separated. The optimal angle is computed by considering the 52

64 angle at which the average distance between the classes is maximum. Then the data is sampled at leg angle of 1.25 radians and used for further results. 8 Leg motor current Leg Angle = 1.25 rad Leg Angle (radians) Vertical acceleration Grass Concrete Dry Sand Wet Sand Leg Angle (radians) Figure 5 4: Leg motor current and Vertical acceleration (A z ) plotted as a function of Leg angle. The plot also shows the angle (1.25 radians) at which the data sets collected from different terrains are well classifiable. The results in Fig. 5 5 show the data from different terrains, sampled at the leg angle of 1.25 radians. The data samples were collected over all five f c values. In Fig. 5 5, the data samples are plotted on the same scale. It is observed that the terrain samples collected at different f c values are distributed differently in the feature space. Moreover, this class separation is terrain-dependent. For example, the terrains grass and dry sand are well separated at the f c setting of Hz, but not separated at an f c value of 2.05 Hz. Similar observations can be made for different pairs of terrains. This again stresses the impact of terrains on the robot s dynamics. These results exemplify how difficult it is to distinguish the classes at different f c values. They can also be used to verify the terrain identified by the robot. For example, if the robot identifies a terrain to be concrete surface while walking with f c set to Hz, it can switch the f c value to 2.05 Hz 53

65 Vertical Acceleration (Az) fc = Hz Leg Current (I0) Vertical Acceleration (Az) fc = Hz Leg Current (I0) Vertical Acceleration (Az) fc = Hz Leg Current (I0) Vertical Acceleration (Az) fc = Hz Leg Current (I0) Vertical Acceleration (Az) fc = 2.05 Hz Leg Current (I0) 1 Wet Sand Concrete Dry Sand Grass Figure 5 5: Terrain Differentiability : Distribution of sensor measurements in feature space (motor current I l, vertical acceleration A z ) sampled at leg angle 1.25 rad, with changes in f c. The data shows four terrain classes. and re-run the identification to more reliably estimate the terrain. Thus, these results are useful in real-time gait adaptation Performance of the Classifier One of the critical parts of our algorithm is the classifier. In these experiments we try to evaluate the performance of the classifier and the effect of changing f c on the classifier. The results indicate that there are specific cycles-frequencies (f c ) at which the discrimination between different sets of 54

66 terrains becomes more accurate. As illustrated in Fig. 5 6, a f c value of Hz is optimal for many pairs of terrains; however, for dry sand and grass, f c of 2.05 Hz gives better classification success rates and for grass and concrete, f c of Hz gives better classification success rates. The classifier performs better when the speed factor is taken into account. The success rate for twoclass classifier is estimated around 90% at the optimal speed. This is more efficient than the success rate of 73.75% in [28]. Figure 5 6: Plot showing variation in performance of the classifier with f c. It shows a comparison between different pairs of terrains. The previous results suggest that the f c value of Hz is optimal for classification of most of the terrains we examined. Hence, we classified the data from four different terrains collected at the f c of Hz. The top 2 (N f ) PCA features from the data were used. We see from Fig. 5 7 that the performance is very good and comparable to the similar experiments conducted by Garcia et al.[25] with an overall success rate of 92.11%. Our advantage is that by using unsupervised machine learning we have only a weak dependence on the 55

67 availability of training data. The training was achieved with unlabeled data and the feature set used is also very small. Feature Labeled Data Wet Sand Concrete 0.5 Dry 0 Sand Grass Feature 1 Feature Labels comming from Clusering Algorithm Wet Sand Concrete Dry Sand Grass Feature 1 (a) Results of classification algorithm run on data collected from four terrains. (b) Confusion matrix of the classification results. Figure 5 7: Classification results on data from four terrains On-line Terrain Identification and Gait Adaptation We validated our gait adaptation algorithm with two types of datasets - semi-synthetic dataset: data samples are generated by two Gaussian distributions, and robot sensor dataset: data samples collected by running the robot through different terrains. The samples in these data are segmented 56