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

This paper considers direction following control of planar snake robots for which the equations of motion are described based on a simplified model. In particular, we aim to regulate the orientation and the forward velocity of the robot to a constant vector, while guaranteeing the boundedness of the states of the controlled system. To this end, we first stabilize a constraint manifold for the fully-actuated body shape variables of the robot. The definition of the constraint manifold is inspired by the well-known reference joint angle trajectories which induce lateral undulatory motion for snake robots. Subsequently, we reduce the dynamics of the system to the invariant constraint manifold. Furthermore, we design two dynamic compensators which control the orientation and velocity of the robot on this manifold. Using numerical analysis and a formal stability proof, we show that the solutions of the dynamic compensators remain bounded. Numerical simulations are presented to validate the theoretical design.