Decentralized utonomous Control of a Myriapod Locomotion Robot hmet Onat Sabanci University, Turkey onat@sabanciuniv.edu Kazuo Tsuchiya Kyoto University, Japan tsuchiya@kuaero.kyoto-u.ac.jp Katsuyoshi Tsujita Kyoto University, Japan tsujita@kuaero.kyoto-u.ac.jp bstract pplications such as demining and planetary exploration require locomotion over unstructured terrain. suitable approach to solve this problem is to use legged robots, because of the flexibility that they can offer, together with a compact size. Deciding on the gait patterns of the robot that optimizes such criteria as energy consumption, walking speed and providing a good stability margin against falling over, are important problems that need to be solved. myriapod robot is advantageous because the large number of legs contributes to the margin of stability and provides robustness against the failure of each individual leg. However, the choice of a suitable gait pattern becomes a more difficult task since more combinations of patterns arise. In this paper, we introduce a myriapod robot with ten legs, which was built with the purpose of investigating algorithms for generating gait patterns. The gait pattern generator contains nonlinear oscillators. Various gait patterns emerge through the mutual entrainment of these oscillators. The work presented here is preliminary and contains a small amount of experimental data. This paper is intended to give information about research that is planned on the subject.. Introduction Walkins one of the most efficient forms of locomotion over unstructured terrain, as demonstrated by most land based living creatures. In this paper we discuss the motion control strategy for a myriapod robot, present results of some experiments performed and go on to explain further research planned on the subject. considerable amount of research has been done on understanding the mechanics of walking and walking robots[,,3]. Initially a complete model based approach was favoured for controlling walking robots [] in which the real time control of the robot is based on a predetermined inverse kinematic and inverse dynamic model of the robot. However, this approach is not suitable when the geometric and kinematic conditions of the environment are not known or change, or there are variations in the parameters of the robot over time, as in the case of practical robots working on daily tasks. There are two main problems that must be solved: First, how to control a large number of elements with a large number of interactions, second how to determine the motion pattern for a given task [5,6]. Studies conducted on insects [] reveal that although the animal is made up of a large number of joints and muscles, for each specific task these elements function as one unit with less degrees of freedom. For another task, they can be organized in a different manner; still with less degrees of freedom, but arranged for doing another task efficiently. For example, the same leg can be controlled for fast locomotion over smooth surfaces, or for foothold search on rough surfaces. For walking on different types of terrain and at various velocities, it is necessary to use different gait patterns. Ethological studies show that both insects and larger animals employ different types of gaits, mainly for conserving energy. Insects for example, employ a method where each leg repeats a periodic forward and backward motion. Each leg has a contact sensor at its tip, conveyinnformation back to the nervous system whether that les in contact with the ground. s a result of processing this information, a gait pattern that is suitable for the velocity of the animal and the properties of the terrain emerges. myriapod robot has been built for assessing locomotion on rough and unstructured terrain. Such robots have a large number of legs and therefore offer both a high margin of stability against falling over in walking, and are robust against failure of each individual leg, making them suitable for use in such applications as demining and planetary exploration. This paper deals with such a control approach for a myriapod robot, summarizes some of the initial experiments performed, and explains future work planned. The control method devised by Tsuchiya et al.[4] is a hierarchical structure in which a leg controller controls the actuators of each leg at the lower level and a gait pattern controller coordinates the movement of the whole robot, at the higher level. t the highest level, a module produces the commanded
gait pattern to the gait pattern controller. This module plays back a suitable gait pattern blindly. The interactions between these modules are set in such a way that during locomotion, the actual gait pattern can be different from the commanded gait pattern. The actual pattern that emerges would be one, which is more suitable for the environmental constraints such as the type of terrain, and performance requirements such as the velocity of the robot. The method has already been tested on a quadruped type robot, both on simulations and experiments on a real robot [4]. It was observed that a gait pattern can emerge which is quite different from the commanded gait pattern because of the environmental constraints. Similarly, the gait pattern can even change within a short period of time during walking.. Definition of the robot schematic representation of the robot can be seen in Fig.. It consists of ten legs, five base units to which two legs each are attached, and a rigid backbone. Each leg consists of two links, connected together with a one degree of freedom joint. The legs are connected to the base units through a one degree of freedom joint. They can move in the vertical plane parallel to the long axis of the backbone. Figure : Schematic representation of the myriapod robot. The inertial coordinate frame is defined as: [ a ] = [ a, a, a3 ] where [ a ] coincides with the long axis of the backbone and the direction of a is in the vertically upward direction. motion and [ ] 3 Body fixed coordinate system is represented by and r [ a ] r [ ] a ω a = is the position vector and = is the angular velocity vector from the origin of a to ( 0) = a. Similarly, i ( i,,3) are defined as the components of Euler angle from [ a ] to [ a ]. lthough the robot has ten legs, the legs on each base unit are controlled such that their tips follow the same trajectory on the two parallel planes that they move in. Therefore we can say that the robot has five compound legs, for the work presented here. The compound legs are enumerated as shown in Fig.. The joint closest to the body on each les joint, and the outer is joint. The base units are attached to the backbone through a two degree of freedom sliding joint, constrained with springs on each axis. Therefore, each base unit can move with respect to the backbone in the vertical plane, applying or absorbing a force determined by the force that the other legs, as well as itself, are applying to the ground. This force is the physical coupling between the legs. lthough each base unit can move with respect to the backbone, we consider the motion of the robot to be represented by that of the backbone. The angles ( θ j are defined as the joint angle of link j on le. We can define the state variable as follows: T q = r ω θ where i = (,...5 ) j = (, ) [ ] k k j k = (,,3). We assume that there is no slip between the tips of the legs and the ground. 3. The control method schematic representation of the architecture of the control system is shown in Fig.. It has a hierarchical structure with a commanded gait pattern generator at the top, gait pattern controller at the mid level, and leg controllers at the lowest level. The commanded gait pattern generator supplies the gait pattern controller with a predefined gait pattern. One leg controller exists for each leg and includes conventional feedback control mechanisms to drive the actuators of the tip of the leg on a predefined trajectory, which can be modified during locomotion. The position of the tip on this trajectory is directly related to a single variable that is handed down from the gait pattern controller. Contact sensors are attached to the tip of each leg, the output of which are connected to the gait pattern controller. The gait pattern controller forms the main part of the algorithm. It consists of nonlinear oscillators; one controlling each leg. The oscillators run at the same frequency, and are coupled to each other such that their phases interact. The commanded gait pattern and the signal from the contact sensors also effect the phase of each oscillator. The position of the tip of each leg on its trajectory corresponds to the phase of its respective controller. The properties of each module will be explained in detail next.
Figure 3: Swing and support phases of leg. ef rˆ e F ˆ ˆ r e S ˆ ( φ ) ( φ ) r ˆ = () r ˆ = () Figure : Overview of the control method. 3. The leg controller In a walking robot, the legs generally have two phases during each step cycle: The support phase and the swing phase (Fig.3). During the support phase, the tip of the les in contact with the ground and is supporting part of the weight of the robot. The tip is moved in the opposite direction to the direction of motion of the whole robot. During the swing phase, the les not supporting the robot but is lifted clear from the ground, brought forward, and lowered on the ground for the next support phase. The position of the tip with respect to the base unit at the time of transition from the swing phase to the support phase is called the anterior extreme position (EP), and the position where transition occurs between the support phase to the swing phase is called the posterior extreme position (PEP). Nominal PEP and EP are defined on [ a ] as r ep e r and respectively, where the superscript xˆ denotes the nominal value. The swing phase trajectory is a closed curve given as the nominal trajectory r and the support phase is a linear trajectory given by ef r. Both nominal trajectories include r e and r ep. The position of the tip of each leg on these trajectories is determined by the phase of the oscillator that governs the leg. The nominal phase dynamics of the leg are governed by a constant, single frequency ˆ oscillation: φ = ω and the nominal trajectories of each phase are functions of the phase of the oscillator: Each trajectory can be alternately used at each transition through EP and PEP, to generate the desired trajectory of the leg: ( φ ) φ < rˆ 0 φ ef r ˆe φ = (3) ˆ ( φ ) φ r φ < π We define phases where ˆ φ = φ at EP and ˆ φ = 0 at PEP. Finally, we define the nominal duty ratio of the tip trajectory as: ˆ φ β = (4) π The normalized ratio between the time elapsed during the nominal supporting phase and the time required for one period of the step cycle. In this scheme, the tip of each leg describes the swing phase trajectory if the tip never touches the ground. If contact with the ground is made the trajectory switches to the support phase at EP and describes until PEP. The speed of the tip during the support phase can be different from the speed during the support phase r. This difference is dictated by the nominal duty ˆ ratio, and realized by eq.(,). If β is close to, then the tip spends most of its time in the support phase and ˆ vice versa. The value of β is, in turn, related to the commanded gait pattern, walking speed of the robot and the number of legs that must be on the ground at the same time for stability or supporting the weight of the robot. In the real world, the nominal EP and even the PEP may not be realizable. Because of the attitude of the backbone with respect to the ground, and the irregularity of the terrain, the tip of a leg might not contact the ground at EP (or even not contact at all) or might leave the ground before PEP; a scheme is
necessary to respond to these irregularities. This is one of the goals of the gait pattern controller. 3. Gait patterns Since there are five compound legs on the robot, numerous gait patterns can be conceived. The ˆ metachronal gait is one where β = 0. 8 and the phase difference between each consecutive oscillator is π 5, such that at any given time, one les in the swing phase and all the others are in the support phase. The number of the len the swing phase follows the ordering of,,3,4,5, Gait patterns similar to the metachronal but with coupling of the phases of some of the oscillators is also possible. For example, the phases of oscillators and 5 may be coupled so that they work as one compound leg. Metachronal gaits offer stability and less pitching movements of the backbone, but result in slow speed. nother possible gait is called alternating gait. Here, ) 3) 5) () φ = φ = φ and ˆ φ = 4) φ, but ˆ () φ = ) φ + π. ˆ lso, β = 0. 5 or higher. There are two compound legs in this gait, which alternately support the robot during locomotion. higher locomotion speed can be achieved. Other gaits can also be conceived or emerge, with different amounts of stability against falling over. ll ten legs of the robot can also be commanded separately. For example a ten leg metachronal walk ˆ would require β = 0. 9 and a nominal phase difference of π 0 between each consecutive oscillator. For the experiments discussed here, five compound legs were used. Each gait pattern can be represented by a matrix (m) Γ denoting the phase differences, such that j) φ = φ + Γ, where the index m is assigned ij arbitrary numbers to represent the type of gait. 3.3 Gait pattern controller The gait pattern controller [4] contains one oscillator governing the movement of each leg. The phase dynamics of the oscillators are given by: φ = ω + g + =,...,5 (5) where is the term coupling the commanded gait pattern with the oscillator and incorporates the signals from the contact sensors. The first term is based on a potential function intended to regulate the phase differences between each oscillator to the commanded gait pattern: ( j) (, Γ ) = K ( φ φ Γ ) V φ ij (6) g i, j From the potential function V, ( j) ( Γ ) ij can be derived as = K φ φ (7) Function is intended to make discontinuous changes to the phases of the oscillators by changing the phase instantaneously as the tip contacts the ground. t the instant of contact, three events take place:. Phase of the oscillator is changed from φ to φ.. The leg trajectory transitions from the swing phase to the support phase. 3. Since it is not possible to move the tip of the leg ( discontinuously, r e is used instead of r e and the trajectory ep r. r is recalculated as a straight line to Based on item above, can be defined as: φ at the instant leg touches ground g = φ (8) 0 otherwise. Therefore, besides ω, the two terms g and g change the phases of the oscillators in two ways; g is a continuous interaction based on the commanded gait pattern and g is an instantaneous, discontinuous interaction. Through these interactions, the oscillators generate gait patterns that satisfy the requirements imposed on the robot. 4. The experimental robot The control mechanism of the robot hardware used in the experiments has three layers. The control method discussed so far runs on a personal computer and calculates the phases of the nonlinear oscillators and the joint angles of the robot in real time. microcomputer on board the robot receives this information through a serial link, converts it into a form suitable for sending to the joint actuators and produces the necessary signals. It also manages the timing for sampling the tip contact sensors, and sends the information to the personal computer. Finally, high feedback-gain servomotors drive each leg joint. The main control program is not in the hardware control loop. photograph of the experimental set up is shown in Fig.[4].
Figure 4: Photograph of the experimental set up. 5. Hardware experiments limited number of hardware experiments have been conducted on the robot. These involve a modified form of the control algorithm where the g term was g ( i ) = not employed (ie. 0 ). The leg trajectories were updated using a constant frequency ω and the g term only. The aim was to investigate whether the dynamics of the robot and the control system using the tip contact sensors are sufficient to converge into a constant gait pattern. The desirable gait pattern is one where the pitching of the backbone is small and the phase difference between the oscillators is even. In the other extreme case, the phase difference between all of the oscillators might converge to zero, which means that all of the tips contact the ground at the same time, and the robot cannot move forward. This pattern is called synchronized gait. In the hardware experiments, the dominant free ˆ parameter is the nominal duty ratio β. This parameter was varied from 0.85 to 0.5 and the robot was allowed to walk on a hard, flat and horizontal surface. The duration of the experiments were between two and three minutes which was observed to be sufficient for the robot to converge into a constant gait pattern. t the start of each experiment, the phases of the oscillators were initalized to the values of the metachronal gait. Our results show that for larger values of βˆ, no constant gait pattern emerges. Figure [5] shows the number of iterations of the algorithm versus the phase ˆ angle of each len radians for β = 0. 85, after two minutes of walking. During this experiment random gaits appeared and changed into other gaits, but no constant gait emerged. ˆ However, as β was reduced to values between 0.65~0.5 the robot converged into constant gait patterns that were also smooth and stable. Figure [6] shows the ˆ initial pattern for β = 0. 60 at the beginning of the experiment, and Fig.[7] shows the pattern after convergence. In this experiment, the phases of the oscillators are initially close to each other, which is not desirable. However, the final pattern shows that the phases have evened out and converged into a constant gait pattern dictated by the dynamics of the robot and the control algorithm. The phases of compound legs and 4 are very close in the emerged gait pattern. fter a constant gait pattern emerged, disturbances were introduced by pushing at various parts of the backbone from various angles. However, the gait pattern did not dissolve. Figure 5: Phase differences fail to converge for large values of nominal phase ratio ˆ β = 0. 85. Figure6: Phase differences at the onset of experiment for ˆ β = 0. 60
References [] K. kimoto, S. Watanabe, and M. Yano, n Insect Robot Controlled by Emergence of Gait Patterns, Proc. Intl. Symposium on rtificial Life and Robotics, Vol. 3, No., 999, pp. 0-05. [] R.. Brooks, Robust Layered Control System for a Mobile Robot, IEEE Journal of Robotics and utomation, Vol., No., 985, pp. 4-3. [3] R.. Brooks, Robot that Walks; Emergent Behaviour from Carefully Evolved Networks, Neural Computation, Vol., 989, pp. 53-6. Figure 7: Phase differences after two minutes, for ˆ β = 0.60 6. Conclusion The control method proposed by Tsuchiya et al. was applied to a myriapod walking robot, with five compound legs. commanded gait pattern term was not utilized in the algorithm. constant gait pattern did not emerge for large values of the nominal duty ratio βˆ. However, a gait pattern emerged that was stable both in the sense that the pitching of the backbone is less and also in the sense that the pattern does not change over time. The touch signals provided by the leg contact sensors, together with the dynamics of the robot mechanism were sufficient to cause a stable phase relationship between the oscillators such that smooth locomotion is accomplished. lso, the pattern did not dissolve as long as the robot was in motion or under disturbances from the environment, such as uneven loading while the robot was in motion. In further tests planned with the robot, the commanded gait pattern will be incorporated. Checks will be made whether the robot can converge to a constant gait pattern and also if the actual gait pattern of the robot changes due to external constraints such as terrain type and speed commands. [4] K. Tsuchiya and K. Tsujita, Principle of Design of an utonomous Mobile Robot, Proc. 4 th Intl. Symposium on rtificial Life and Robotics, Vol., 999, pp. 30-33. [5] K. Tsujita,. Onat, K. Tsuchiya et al., utonomous Decentralized Control of a Quadruped Locomotion Robot using Oscillators, Proc. 5 th Intl. Symposium on rtificial Life and Robotics, Vol., 000, pp. 703-70. [6] K. Tsujita, K. Tsuchiya,. Onat, et al., Locomotion Control of a Multipod Locomotion Robot with CPG Principles, Proc. 6 th Intl. Symposium on rtificial Life and Robotics, Vol., 00, pp. 4-46.