Path following control of planar snake robots using virtual holonomic constraints

This paper considers path following control of planar snake robots using virtual holonomic constraints. We first derive the Euler-Lagrange equations of motion of the snake robot. Moreover, we integrate the effects of friction forces into these equations. 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. In particular, we show that the constraint manifold can be made invariant by a suitable choice of feedback. Furthermore, we analytically design a smooth feedback control law to render the constraint manifold exponentially stable for the controlled system. We show that enforcing the appropriately defined virtual holonomic constraints implies that the robot converges to and follows a desired geometric path. Numerical simulations are presented to support the theoretical design.