Path following control of planar snake robots using virtual holonomic constraints: theory and experiments

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.

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

“…Furthermore, in [10] it is shown that the fundamental properties of the simplified model such as stabilizability and controllability, are essentially the same as the more complex models presented in several previous works, see e.g. [4,5,12].…”

“…The simplified dynamic model (10)(11)(12)(13)(14)(15)(16)(17) is suitable for the model-based direction following control design which will be presented in the following sections.…”

“…Kinematic and dynamic models of snake robots are previously derived in several works (see e.g., [4,5,10,12]). The snake robot is modelled using a series of prismatic joints which move the robot forward by translational displacements.…”

“…[14][15][16]. It was used for snake robot locomotion in [12] to control the orientation of a wheel-less snake robot, but the velocity of the snake robot was not controlled. Using the VHC approach, we confine the state evolution of a mechanical system to an invariant constraint manifold.…”

“…In [10,11], cascaded systems theory is employed to achieve path following control of a wheel-less snake robot described by a simplified model. In [12], a dynamic feedback control law is used to control the orientation of the robot to a reference angle defined by a path following guidance law.…”