Controllability and Stability Analysis of Planar Snake Robot Locomotion

Abstract

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.

Virtual holonomic constraint based direction following control of planar snake robots described by a simplified model

“…Thus, (61) indicates that the friction coefficient c n needs to be sufficiently large for the system to be stable. This complies with the results concerning controllability of snake robots presented in [19].…”

“…[14][15][16] for various examples), we consider (25) as a VHC for the body shape variables of the snake robot. Furthermore, these VHC will be enforced through the control inputū in (19). In particular, (25) is a dynamic VHC in that it depends on the state-evolution of two dynamic compensators.…”

“…Our control design approach for the snake robot is given in the following two steps: 1. In the first step, we use the control inputū in (19) to stabilize the constraint manifold (26) for the fully-actuated shape variables of the robot. This induces a forward motion based on the gait pattern lateral undulation for the robot.…”

“…This implies that joint angle errors converge exponentially to zero, i.e. the constraint manifold is a globally exponentially stable manifold for (10,19), and the control objective (20) will be achieved.…”

Two new design concepts for snake robot locomotion in unstructured environments

“…This alternative approach simplifies the development of the physical coverage of a snake robot since the coverage can be developed more or less independently of the contact force sensor system. To verify that the external forces on a snake robot indeed can be determined from the joint constraint forces, we investigate the force balance for a single link of the robot based on the model formulation considered in [32]. As shown in Figure 4a, we consider a planar snake robot with N links interconnected by N − 1 motorized revolute joints, where the links are influenced by the forces and torques illustrated in Figure 4b.…”