Controllability and Stability Analysis of Planar Snake Robot Locomotion
ABSTRACT This paper contributes to the understanding of snake robot locomotion by employing nonlinear system analysis tools for investigating fundamental properties of snake robot dynamics. The paper has five contributions: 1) a partially feedback linearized model of a planar snake robot influenced by viscous ground friction is developed. 2) A stabilizability analysis is presented proving that any asymptotically stabilizing control law for a planar snake robot to an equilibrium point must be time-varying. 3) A controllability analysis is presented proving that planar snake robots are not controllable when the viscous ground friction is isotropic, but that a snake robot becomes strongly accessible when the viscous ground friction is anisotropic. The analysis also shows that the snake robot does not satisfy sufficient conditions for small-time local controllability (STLC). 4) An analysis of snake locomotion is presented that easily explains how anisotropic viscous ground friction enables snake robots to locomote forward on a planar surface. The explanation is based on a simple mapping from link velocities normal to the direction of motion into propulsive forces in the direction of motion. 5) A controller for straight line path following control of snake robots is proposed and a Poincaré map is investigated to prove that the resulting state variables of the snake robot, except for the position in the forward direction, trace out an exponentially stable periodic orbit.
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ABSTRACT: This paper considers path following control of planar snake robots using virtual holonomic constraints. In order to present a model-based path following control design for the snake robot, we first derive the Euler-Lagrange equations of motion of the system. Subsequently, we define geometric relations among the generalized coordinates of the system, using the method of virtual holonomic constraints. These appropriately defined constraints shape the geometry of a constraint manifold for the system, which is a submanifold of the configuration space of the robot. Furthermore, we show that the constraint manifold can be made invariant by a suitable choice of feedback. In particular, we analytically design a smooth feedback control law to exponentially stabilize the constraint manifold. We show that enforcing the appropriately defined virtual holonomic constraints for the configuration variables implies that the robot converges to and follows a desired geometric path. Numerical simulations and experimental results are presented to validate the theoretical approach.Robotics and Biomimetics. 08/2014;
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ABSTRACT: We consider a class of multilink mechanical systems arising from undulatory locomotion of multisegmental slender animals. All the body joints are assumed to have actuators, but the system is underactuated because of the lack of direct control over the position and orientation within the inertial frame. Yet, the system is controllable through interactive forces from the environment, just like in animal locomotion. It is systematically revealed that the motion behavior is composed of three fundamental actions: 1) oscillation; 2) orientation; and 3) locomotion. Through rigorous theoretical analyses and numerical simulations, feedback laws are developed to achieve effective control for the aforementioned three actions, exploiting the natural dynamics of body-environment interactions.IEEE Transactions on Control Systems Technology 01/2013; 21(5):1537-1548. · 2.52 Impact Factor
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ABSTRACT: Mammals such as dogs and cheetahs change their gait from trot to gallop as they run faster. However, lizards always trot for various speeds of running. When mammals run slowly with trot gait, their fore leg and hind leg generate the required force for acceleration or deceleration such that the yaw moments created by these forces cancel each other. On the other hand, when lizards run slowly, their fore legs and hind legs generate the forces for deceleration and acceleration, respectively. In this paper, the yaw motion of a lizard model is controlled by the movement of their waist and tail, and the reaction moment from the ground produced by the hind legs in simulation. The simulation uses the whole body dynamics of a lizard model, which consists of 4 links based on the Callisaurus draconoides. The results show that the simulated trotting of the model is similar to that of a real lizard when the movement of the model is optimized to minimize the reaction moment from the ground. It means that the body of a lizard moves in such a way that the reaction moment from the ground is minimized. This demonstrates our hypothesis on how lizards trot using body motion.Journal of Institute of Control, Robotics and Systems. 01/2013; 19(7).