Biomimetic Design and Optimal Swing of a Hexapod Robot Leg

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1 Journal of Bionic Engineering 11 (2014) Biomimetic Design and Optimal Swing of a Hexapod Robot Leg Jie Chen, Yubin Liu, Jie Zhao, He Zhang, Hongzhe Jin State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin , P. R. China Abstract Biological inspiration has spawned a wealth of solutions to both mechanical design and control schemes in the efforts to develop agile legged machines. This paper presents a compliant leg mechanism for a small six-legged robot, HITCR-II, based on abstracted anatomy from insect legs. Kinematic structure, relative proportion of leg segment lengths and actuation system were analyzed in consideration of anatomical structure as well as muscle system of insect legs and desired mobility. A spring based passive compliance mechanism inspired by musculoskeletal structures of biological systems was integrated into distal segment of the leg to soften foot impact on touchdown. In addition, an efficient locomotion planner capable of generating natural movements for the legs during swing phase was proposed. The problem of leg swing was formulated as an optimal control procedure that satisfies a series of locomotion task terms while minimizing a biologically-based objective function, which was solved by a Gauss Pseudospectral Method (GPM) based numerical technique. We applied this swing generation algorithm to both a simulation platform and a robot prototype. Results show that the proposed leg structure and swing planner are able to successfully perform effective swing movements on rugged terrains. Keywords: biomimetic design, legged robot, optimal control, biological movement principle, Gauss pseudospectral method Copyright 2014, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: /S (14) Introduction Animals ability to readily adapt to changing natural environment has attracted the attentions of engineers and roboticists in their quest to build functional mobile machines [1 7]. One of the fascinating subjects is the field of legged robots inspired by humans, mammals, insects and other arthropods. Indeed, legged systems theoretically offer the potential to better traverse rough terrains than traditional wheeled and tracked designs due to no need for paths of continuous contact with the ground, and also their bionic prototypes do reveal surprising ability in nature. Generally speaking, robots with more legs mean higher adaptability to irregular terrains, but inevitably lead to a more complicated control system. Of all the legged systems, six-legged robots seem to be a logical trade-off between adequate adaptability and control complexity, and therefore have been given great concern [8 10]. A powerful six-legged robot system strongly depends on both sophisticated mechanical structure and efficient motion planning algorithm, and as a result, various studies related to structures and movements of legs have been reported in the literature. In these designs, the legs mainly differ in number and form of Degrees of Freedom (DoF), drive and transmission systems, and sensors to be integrated. The overall trend has been toward higher power-to-weight ratio and stronger perception abilities [9 11]. Motion planning for an autonomous six-legged robot system has proven to be an intractable task. The robot has to sense its internal states as well as external environment continuously and generate feasible leg motions rapidly according to the sensory information. In our opinion, a layered control architecture consisting of a binocular stereo vision based navigation layer, a motion planning layer and a walking layer seems to be a promising strategy. The navigation layer allows the robot to recognize visual scenarios and plan proactively an approximately optimal path from the start to the goal; the motion planning layer is responsible for calculating sequences of footsteps and body posture, accounting for the influence of terrain shape; the task of the walking layer is to produce basic movements (swing and support) for Corresponding author: He Zhang 09B308015@hit.edu.cn

2 Chen et al.: Biomimetic Design and Optimal Swing of a Hexapod Robot Leg 27 each leg according to the footsteps from upper planning layer and external environment from sensory readings. Support movement of a leg involves motions of the robot body and must be in coordination with other supporting legs. Whereas leg swing is comparatively free and needs to be planned deliberately to enhance obstacle avoidance ability of the robot and smoothen the actuator torques. Some researchers utilize fixed curves or composite curves such as polynomials [9] and sinusoids [11] to predefine the leg swing trajectories. While this is conceptually straightforward and computationally efficient, there is a disadvantage that could lead to a waste of energy in level ground or a collision in rugged terrains. Erden optimized the leg protraction to minimize the integral of torque squares which is used as an index of energy consumption [12]. By introducing a modified version of gradient descent, many unfeasible and inefficient local optima are jumped over to some extent. However, this approach might suffer from a drawback of long duration, which is seriously terrible in the situation where rapid responses are required. In addition, this work ignores the complexity of terrains surrounding the robot, limiting the mobility and usable range of operation. Lewinger and Quinn proposed a neurobiologically-based method to produce stepping actions for a multi-jointed robot leg [10]. The basic movements of each joint were generated by one neural oscillator network located at the corresponding joint and coordinated by sensory feedback such as joints angles and leg load. Despite considerable efforts in swing movements of a walking robot leg, these works are either using a onefold engineering approach or partially imitating animals nerve-muscle control mechanism. In this study, we focus on an alternate method, which combines both engineering solution and reasonably achievable principles distilled from biology, to plan swing movements for a small six-legged robot leg over extreme terrains. First, biomimetic design of the leg mechanism is proposed. The design inspiration is taken from the musculoskeletal structure of insect legs with necessary approximations and extensions. As with swing movements, we formulate the problem as an optimization procedure that minimizes a biologically-inspired objective function under the premise that the robot has obtained surrounding terrain models and accurate localization. Finally, we demonstrate the swing generation algorithm on both a simulation platform and a robot prototype. 2 Biomimetic design of the walking robot leg 2.1 Biological inspiration from hexapods Insects are considered as ideal models on which to base robot designs owing to their spectacular locomotivity and agility. This pronounced trait relies to a relatively large extent on their sophisticated musculoskeletal system in legs. Typically, each insect leg is made up of five basic segments connected by joints and these are, from proximal to distal: coxa, trochanter, femur, tibia, and tarsus, as depicted in Fig. 1. Among them, trochanter is a small part of femur connecting to coxa, and tarsus is used for helping hold onto walking surfaces [13]. Motions of each segment are imparted through contracting and relaxing muscles, which involve complex biomechanics, neural control and muscle characteristics. It seems impractical to directly copy the anatomical arrangement of insect legs due to the complexity of biological system itself and technical limitation in materials, actuators, sensors and processor. To this end, the key elements that are contributed to the desired agility on insects must be identified and implemented using available and mature technology. According to the results of biological studies [14,15], four key elements for the artificial legs are listed, taking accounting of the technical availability. They are, 1) kinematic structure; 2) effective leg length; 3) actuation system; 4) compliance characteristics. 2.2 Biomimetic design of the robot leg Kinematic structure Simply copying the 5-DoFs anatomical arrangement of insect legs may increase the cost of both mechanisms and control. From the perspective of mechanism theory, 3-DoFs have been proven the minimum number for a leg of walking robots capable of omnidirectional walk [11]. As an eventual compromise, trochanter and tarsus are neglected due to their functions and small size, and the robot leg with three segments, Fig. 1 Anatomical structure of a typical insect leg [13].

3 28 coxa, femur and tibia, was developed Effective leg length Generally, for walking insects, femur and tibia are the longest leg segments but variations in the lengths and robustness of each segment relate to their functions and living environment. Taking consideration of the fact that the robot designed in this study is intended to walk on extreme terrains, relative proportion of leg segment lengths was optimized to maximize robot body flexibility, and optimization results showed that 1:4:3 (coax : femur : tibia) is the best. More details about the relative proportion of leg segment lengths can be obtained in Ref. [16]. Journal of Bionic Engineering (2014) Vol.11 No.1 (a) Coxa BC joint CF joint Femur Tibia FT joint Actuation system Insects impart motions via contracting and relaxing pairs of agonistic and antagonistic muscles that attach to the cuticle, which is related to the complex biomechanics and muscle functions. In contrast to the hardware compensation method of adding elastic elements, such as torsional springs, in series between the actuator and the load to imitate natural muscles, we attempt to introduce a more flexible and exact scheme of active compensation through feedback of actuator system output torque and angle with a certain transfer function G, where G is designed on the basis of muscle function and can be expediently modified according to new study from scientists. With this regard, each joint of the leg was designed to be actuated by a DC servomotor combined with a synchronous belt drive and a harmonic drive for speed reduction and toque amplification, and a position sensor based on Hall effect as well as a torque sensor based on strain gauge was integrated into the joint. Following the valuable guidelines mentioned above, the robot leg with three revolute joints was developed, proximal to distal: Body-Coxa (BC) joint for protraction and retraction, Coxa-Femur (CF) joint for elevation and depression, and Femur-Tibia (FT) joint for extension and flexion, as shown in Fig. 2a. The leg s dimensions were scaled up taking into consideration the desired mobility as well as the intended terrain to walk on. Table 1 displays the final dimension and weight data Compliance characteristics Biologists have pointed out that animals ability to rapidly adapt to perturbations from the environment Locating pin Joint link Spring (b) Linear bearing 3D force sensor Fig. 2 Biomimetic design of the robot leg. (a) CAD drawing of the leg; (b) diagram of the spring mechanism in tibia. Table 1 Dimension and weight parameters of the robot leg Segment Length (mm) Weight (kg) Coxa Femur Tibia relies largely on their musculoskeletal structures, which can provide enhanced compliance through neural and mechanical feedback. Neural feedback produces active compliance according to the sensory information, whereas mechanical feedback uses visco-elastic structures to offer passive compliance [17,18]. Moreover, the distal part of the robot leg is usually in direct contact with the ground. In this regard, a spring mechanism was introduced in the tibial leg segment to respond to ground impact and small irregularity of terrain on touchdown, as illustrated in Fig. 2b [19]. In this case, the tibia segment was composed of FT joint link, spring, linear bearing,

4 Chen et al.: Biomimetic Design and Optimal Swing of a Hexapod Robot Leg 29 locating pin and force sensor link, whose bottom half is able to sense ground reaction forces simultaneously. A brushed DC motor mounted at femur distal end turns the FT joint link, at the bottom of the FT joint link is a fixed linear bearing, the linear bearing is passed through by top half of the tibial link as a rod with a spring wrap around it, which results in a spring damping model from the mechanical vibration point of view. The linear bearing constrains the tibial link sliding linearly, and the travel is limited by a combination of a locating slot and a pin. When contacting, a load is transferred to the joint link due to ground impact, leading to the joint link sliding linearly. At the same time, the spring is compressed and as a result the impact force is mitigated to a certain degree. 2.3 Kinematics and dynamics During walking of a six-legged robot, there must be some of the legs performing swing movements in the air, and the rest supporting and propelling forward the body on the ground. That is to say, the movements of swing legs are coupled with those of support legs through the body. In order to fully understand the movement mechanism of swing legs rather than focusing on complex leg coordination and body trajectory generation schemes, we hypothesize that body of the robot keeps stationary while leg swinging. Under this hypothesis, each swing leg can be considered to be a 3-DoFs open kinematic chain attached to a stationary base. As a matter of fact, the outcomes can be applied on a practical robot just via composing motion of the body caused by movements of support legs. Fig. 3 illustrates the kinematic model of the robot leg under the hypothesis, with the corresponding Denavit-Hartenberg parameters in Table 2 [20]. Following this model, the foot end position with respect to body reference frame (considered as inertial reference frame) from joint angles was derived as follows px c( lc 1 1+ lc 2 1c2+ lc 3 1c23) s( ls 2 2ls 3 23) cx, (1) p l s lsc lsc c (2) y y, pz s( lc 1 1+ lc 2 1c2+ lc 3 1c23) c( ls 2 2ls 3 23) cz, (3) where (p x, p y, p z ) is foot end position in the body reference frame; (c x, c y, c z ) describes the position of the origin Body O Z 0 1 Y 0 Z 1 X 0 Y 1 3 X 2 2 X 1 Z Walking direction O X Fig. 3 Kinematic model of the robot leg. Table 2 D-H parameters of the leg model Joint i i a i d i BC 1 /2 l 1 0 CF 2 0 l 2 0 FT 3 0 l 3 0 of the reference frame X 0 Y 0 Z 0 in the body reference frame; i (i=1,2,3) is i-th joint angle numbered from BC to FT joint; l i is segment length of the robot leg from coxa to tibia; c and s mean cosine and sine functions; and expression ijk stands for ( i + j + k ). Similarly, the dynamic equations for the swing leg can be written in following form M( +C ) ( +G, ) ( ) =, (4) where corresponds to the joint position vector, M() is the inertia matrix, C and G represent respectively the Coriolis/centrifugal and gravitational terms [21]. Both the kinematics and dynamics discussed above will be used to impose restrictions on the movements of swing legs. 3 Optimal swing of the robot leg As stated previously, natural swing of legs can make the robot more capable and more agile. It is universally acknowledged that human and animals typically perform motions in a highly optimized and rational way through evolutionary pressure, following some specific rules or criteria [22,23]. This implies us that it seems working to use mathematical models and optimization algorithms integrating biologically-based objectives extracted from human and animal motions to plan robot movements. In this section, a procedure for correctly formulating the problem of planning swing movements for a six-legged robot leg as an optimal control problem is described, with a Gauss Pseudospectral Method (GPM) based efficient numerical solution technique. Z 2 Y 2 Z 3 X 3 Y 3

5 Formulation of the optimal control problem State-space model The most forthright choice for control or input variables of the state-space equation may be joint torques, with corresponding positions and velocities as state variables deriving from the dynamics model of the leg. While conceptually straightforward, such choice would complicate subsequent solving process in terms of computation. As an alternative, we use the angular joint jerks, defined as the time derivative of the acceleration, as control inputs, and joint positions, velocities and accelerations as state variables. This results in the following state-space model describing the leg system [24] x Ax+ Bu, (5) where x = x1, x2, x3, x4, x5, x6, x7, x8, x 9= 1, 1, 1, 2, 2, 2, 3, 3, 3 is state variable, u [ u1, u2, u3] [ 1, 2, 3] is input variable and A, B are coefficient matrixes Choice of biologically-based objective The goal of this section is to choose an adequate objective function based on the principles of biological motions. To the best of our knowledge, there are no studies presented in the literature yet which clearly address what is the basic principle underlying the insect movements. Fortunately, neurophysiologists have pointed out that an optimization criterion linked to minimum-jerk is followed in the movements of human arms, which are exactly analogous to insect legs from the points of both anatomy and mechanisms [25,26]. Owing to such similarity, it may be inferred that the optimality criterion of human arm movements is applicable to the robot leg swing. Moreover, limiting jerk can contribute to Journal of Bionic Engineering (2014) Vol.11 No.1 improve trajectory tracking accuracy and reduce actuator wear. These ideas lead to the objective function C t f t0 uu T d, t (6) where t 0, t f are initial and final time of the swing interval Constraints For a six-legged robot walking on rough terrains, there are mainly three categories of constraints imposing restrictions on leg swing: physical constraints, initial and final state constraints, and terrain constraints. I. Physical constraints The final required torques must be within the limits of those actuators are able to produce, and additionally mechanical structures also impose restrictions on joint range of motion. That is to say, the following inequalities should be met 1 max, 2 max, 3max; 1min 1 1max, 2min 2 2max, 3min 3 3max. (7) II. Initial and final state constraints At initial time t 0, the robot foot is located at its current position and it is not moving, i.e. ( t ), ( t ) 0. (8) Also at final time t f, the foot gets to the desired foothold; likewise, the constraint inequalities should be satisfied ( t ), ( t ) 0. (9) f f f III. Terrain constraints Insects acquire terrain models surrounding them through eyes in advance when planning footsteps and leg movements. This is particularly important in situations where locomotion cannot be accomplished by employing simple reactions to the ground contact information. Likewise, the HITCR-II six-legged robot presented in this paper is designed to incorporate a binocular stereo vision system to recognize external environment. To concentrate on leg movements, we assume that the model of the terrain to cross is already obtained and represented by a series of quadratic surface patches which are fit by an elevation map in z associated with a regular grid in (x,y). So terrain elevation h(x,y) at any point (x,y) can be obtained uniquely. In practice a set clearance height h c is used so that the foot maintains a safe tolerance above the terrain to

6 Chen et al.: Biomimetic Design and Optimal Swing of a Hexapod Robot Leg 31 compensate for control errors or other disturbances. Therefore we have the following constraint at any given time t during swinging z hxy (, ) h, t t t f. (1) c Solution of the optimal control problem The aforementioned optimal control problem can be stated formally: to find an optimum control trajectory u(t) that drives the robot leg from its current position to the desired foothold while minimizing the objective function (6) subject to the physical constraints (7), initial and final state constraints (8) and (9), and terrain constraints (10). To solve the above problem, an efficient solution algorithm simple enough to perform on-board is required in that the robot must plan its leg trajectories extremely fast even real-time in unstructured application scenarios. As such, a direct transcription method called GPM is employed thanks to its advantage of fast convergence rates and high computational efficiency [27]. The basic idea of GPM is to discretize the control variable u [ 1, 2, 3] and state variables x [ 1, 1, 1, 2, 2, 2, 3, 3, 3] simultaneously at Legendre-Gauss (LG) points and then to approximate them using a basis of globally orthogonal Lagrange polynomials. With that the state-space Eq. (5) is transcribed into algebraic constraints. Also the objective function (6), physical constraints (7), initial and final state constraints (8) and (9), and terrain constraints (10) can be approximated using the values of the state variable, control input, and time at the LG points via a Gauss quadrature and differentiation matrix, respectively. This results in a Nonlinear Programming Problem (NLP). For the generated NLP, it can be solved by Sequential Quadratic Programming (SQP) method. The SQP is a well-known iterative method in which search direction and step are obtained by solving a QP sub-problem. Through the above solving process, the corresponding joint positions, velocities, accelerations and jerks can be obtained. The overall solution path is shown in Fig. 4. More details about GPM and SQP can be obtained in Ref. [27]. 4 Results and discussion 4.1 Simulation study A six-legged robot on simulation platform was built to verify the availability of the aforementioned leg swing generating method, as shown in Fig. 5. Configuration and dimension of the platform were modeled strictly on the robot leg designed in section 2. For ease of exposition, we consider the situation in which only one leg performs swing movements and the body is supported by the rest legs as a stationary base. As such, we can bypass the complex leg coordination as well as body trajectory generation issues and concentrate our efforts on intra-leg motion. Without loss of generality, we assumed right-middle leg as the swing one. Several test cases, which differ in terrains that the robot has to step over while swinging, were chosen to evaluate the algorithm roundly. In addition, initial and final footholds of the tip point of the leg are also different in these test cases. Table 3 shows the specific initial-final positions with respect to the reference frame O'X'Y'Z' (projection of body reference frame OXYZ on the ground plane, as shown in Fig. 5) and some typical terrain features of two of these test cases. For each of the two cases, collision-free and terrain-matching swing trajectories for the robot leg were obtained through the planning methods, as shown in Fig. 4 Flow diagram of GPM based numerical technique O O Z O Walking direction 0.2 X Swing trajectory Rugged terrain Fig. 5 Simulation platform of the six-legged robot. Table 3 Initial-final positions and terrain features for the test cases Current foothold (mm) Desired foothold (mm) Maximum height of the terrain (mm) Maximum height difference of the terrain (mm) Case 1 (260,50,5) (275,75,10) Case 2 (260,50,0) (280,65,20) 50 57

7 32 Fig. 6. Three-dimensional components (vertical, forward and lateral component) of the trajectories in time are included in the figure. We can see that, all the components of both cases are relatively smooth and natural; furthermore, the vertical components are no less than 15 mm above corresponding terrain elevations to make up for mechanical deformations, sensory errors and any other position disturbances, as a result, it is guaranteed that the robot wouldn t collide with the ground. Journal of Bionic Engineering (2014) Vol.11 No Application to the HITCR-II robot Robot prototype In order to assess the performance of the designed robot leg in section 2 and further verify the swing planner in section 3, a six-legged robot prototype HITCR-II, which was made of six identical legs so as to possess favorable interchangeability, was currently developed, as depicted in Fig. 7. The six legs were elliptically distributed for reducing the possibility of motion interference between legs as well as improving the walking stability. The robot body was hollowed out with the aim of decreasing its own weight. All the mechanical links in the robot prototype were manufactured in aluminum alloy. Control system of the robot consisted of a host computer for giving motion tasks, an ARM LPC2294 and DSP TMS320DM642 based main controller for motion planning and six isolated DSP TMS320F2812 based leg controllers for generating leg movements and controlling the motors. The size of the prototype is nearly 430 mm 529 mm 244 mm (length width height), and the robot weighs nearly 3.26 kg including actuators and circuits. (a) 3D leg swing trajectories in case 1 (b) 3D leg swing trajectories in case 2 Fig. 6 Three-dimensional swing trajectories of the robot leg in test cases Experimental results and discussion In this section, we discuss the hardware implementation of our swing generating method on the HITCR-II robot over an irregular artificial terrain. The robot requires two walking steps to traverse the terrain. For the first step, the maximum terrain height to walk over is 55 mm and the step length is approximately 130 mm. For the second step, the maximum terrain height to walk over is 35 mm and the walking stride is about 110 mm. Before the start of execution, foothold positions and terrain information were given to the DSP based leg controller in advance. Then the controller executed the whole planning algorithm autonomously and produced corresponding leg swing trajectories. Fig. 7 Prototype of the HITCR-II six-legged robot. Additionally, we need to guarantee that the leg moves along the desired trajectories as closely as possible, especially over the challenging terrains we consider in this study. In this regard, a PD based closed-loop

8 Chen et al.: Biomimetic Design and Optimal Swing of a Hexapod Robot Leg 33 control mechanism was introduced to realize accurate leg movements. Furthermore, the robot must have sufficient compliance to accommodate slight position deviations and respond to unexpected impacts. Once again inspired by biology, additional active compliance was added through impedance control, which can be understood as attaching a virtual spring-damper system to the leg [17,28]. The control block diagram for the robot leg is depicted in Fig. 8. The impedance controller consists of the inner loop of position control and the outer loop of impedance control. According to the impedance control function and the deviation F between desired force F desired and actual force F actual, the outer loop of the impedance control generates a foot position correction X, X is then converted to joint position correction correction to correct the reference position d. The compliance control law is implemented based on the following expression M X B X K X F, (11) d d d where M d, B d, K d are target inertia matrix, target damp matrix and target stiffness matrix of the impedance model respectively. The virtual mechanical impedance is capable of adapting to diverse ground by choosing desired M d, B d and K d. The experiment was carried out with the above described control schemes. The swing leg was firstly moved from initial position to final position A; then all of the six legs together propelled the body forward to the next swing posture; the leg executed the second swing cycle from final position A to final position B. Consecutive snapshots of the swing leg are shown in Fig. 9. The experimental results show that the robot leg can step over the artificial terrain successfully. That is to say, the leg system we presented has the ability to traverse rugged terrains whose maximum height is within 55 mm and whose maximum distance between adjacent footholds is within 130 mm. Fig. 10 shows the vertical ground reaction force during leg movements. The desired contact force with the ground is set to 15 N, which is approximately half of the robot weight. As can be seen from the figure, at initial time 0, all of the six legs together support the robot and the reaction force is one-sixth of the robot weight; at time 0 to 3 s, the reaction force reduces to zero because the leg is swinging in the air; at time 3 s, the leg starts contacting with ground and the impact happens, at the moment the impedance controller is activated and adjusts the reaction force to the desired force; at time 3 s to 6 s, fluctuation of the reaction force appears due to the fact that the leg has to propel the robot and support its weight; at time 6 s to 12 s, the leg starts implementing Fig. 8 The control block diagram of the robot leg. Fig. 9 Consecutive snapshots of the swing leg.

9 34 Journal of Bionic Engineering (2014) Vol.11 No.1 Acknowledgement Force (N) This work was supported by the National Natural Science Foundation of China (Grant no ) and the self-managed project of State Key Laboratory of Robotics and System in Harbin Institute of Technology (SKLRS200901A01). References Fig. 10 The vertical ground reaction force during leg swing. the second step, which is analogous to the first cycle. As the experimental results show, the use of the impedance controller helps mitigate the impact forces and adjust the ground reaction force to a desired level. For a robot system walking in severe challenging terrains, more effective and capable control schemes are still needed. This will be our future research focus. 5 Conclusion In this study, a three-joint leg mechanism for the HITCR-II six-legged robot was developed, taking account of leg morphology in insects as well as desired mobility. We successfully mimicked the musculoskeletal structures of biological systems by using a spring based passive compliance mechanism in the distal segment of the leg to offer certain mechanical softness and, as a result, avoid destroying the leg structure on touchdown. In addition, a leg locomotion planner for producing optimal swing on rough terrains was presented. The planner generated desired movements via executing an optimization procedure that satisfies a number of task terms while minimizing an objective function distilled from biology. The swing generating strategy has been demonstrated both on a simulation platform and a six-legged robot prototype which were constructed based on the proposed leg structure. Compared to previous work, our leg swing generating scheme achieves much natural and graceful foot trajectory. Such superior performance is attributed to the optimization procedure, which chooses a biologically-based objective function. Future work will involve dynamic control schemes of legs, further exploring different optimality criteria proposed by biologists, and gait planning for the walking robot. [1] Mahardika N, Viet N Q, Park H C. Effect of outer wing separation on lift and thrust generation in a flapping wing system. Bioinspiration & Biomimetics, 2011, 6, [2] Viet N Q, Park H C. Design and demonstration of a locust-like jumping mechanism for small-scale robots. Journal of Bionic Engineering, 2012, 9, [3] Zhang W P, Hu T J, Chen J, Shen L C. BioDKM: Bio-inspired domain knowledge modeling method for humanoid delivery robots planning. Expert Systems with Applications, 2012, 39, [4] Dai Z D, Sun J R. A biomimetic study of discontinuous-constraint metamorphic mechanism for gecko-like robot. Journal of Bionic Engineering, 2007, 4, [5] Li H K, Dai Z D, Shi A J, Zhang H, Sun J R. Angular observation of joints of geckos moving on horizontal and vertical surfaces. Chinese Science Bulletin, 2009, 54, [6] Ren L, Jones R K, Howard D. Predictive modeling of human walking over a complete gait cycle. Journal of Biomechanics, 2007, 40, [7] Liu A, Howard D. Kinematic design of crab-like legged vehicles. Robotica, 2001, 19, [8] Li Y, Ahmed A, Sameoto D, Menon C. Abigaille II: Toward the development of a spider-inspired climbing robot. Robotica, 2012, 30, [9] Görner M, Wimböck T, Hirzinger G. The DLR crawler: Evaluation of gaits and control of an actively compliant six-legged walking robot. Industrial Robot: An International Journal, 2009, 36, [10] Lewinger W A, Quinn R D. Neurobiologically-based control system for an adaptively walking hexapod. Industrial Robot: An International Journal, 2011, 38, [11] Klaassen B, Linnemann R, Spenneberg D, Kirchner F. Biomimetic walking robot SCORPION: Control and modeling. Robotics and Autonomous Systems, 2002, 41, [12] Erden M S. Optimal protraction of a biologically inspired robot leg. Journal of Intelligent & Robotic Systems, 2011, 64, [13] Gullan P J, Cranston P S. The Insects: An Outline of Entomology, 3nd ed, Wiley-Blackwell, Oxford, USA, 2005,

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