Kinematics of wheeled mobile robots on uneven terrain

This paper deals with the kinematic analysis of a wheeled mobile robot (WMR) moving on an 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. 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 constrain of no slip. We present an algorithm to solve the direct and inverse kinematics problem of the hybrid-parallel mechanism. 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