Kinematics of wheeled mobile robots on uneven terrain

This paper deals with the kinematic analysis of a wheeled mobile robot (WMR) moving on uneven terrain. It is known in literature that a wheeled mobile robot, with a fixed length axle and wheels modeled as thin disk, will undergo slip when it negotiates an uneven terrain. To overcome slip, variable length axle (VLA) has been proposed in literature. In this paper, we model the wheels as a torus and propose the use of a passive joint allowing a lateral degree of freedom. Furthermore, we model the mobile robot, instantaneously, as a hybrid-parallel mechanism with the wheel-ground contact described by differential equations which take into account the geometry of the wheel, the ground and the non-holonomic constraints of no slip. We present an algorithm to solve the direct and inverse kinematics problem of the hybrid-parallel mechanism involving numerical solution of a system of differential-algebraic equations. Simulation results show that the three-wheeled WMR with torus shaped wheels and passive joints can negotiate uneven terrain without slipping. Our proposed approach presents an alternative to variable length axle approach.