Dynamic modeling and simulation of a wheeled mobile robot for traversing uneven terrain without slip

It is known in literature that a wheeled mobile robot (WMR), with fixed length axle, will undergo slip when it negotiates an uneven terrain. However, motion without slip is desired in WMR's, since slip at the wheel-ground contact may result in significant wastage of energy and may lead to a larger burden on sensor based navigation algorithms. To avoid slip, the use of a variable length axle (VLA) has been proposed in the literature and the kinematics of the vehicle has been solved depicting no-slip motion. However, the dynamic issues have not been addressed adequately and it is not clear if the VLA concept will work when gravity and inertial loads are taken into account. To achieve slip-free motion on uneven terrain, we have proposed a three-wheeled WMR architecture with torus shaped wheels, and the two rear wheels having lateral tilt capability. The direct and inverse kinematics problem of this WMR has been solved earlier and it was shown by simulation that such a WMR can travel on uneven terrain without slip. In this paper, we derive a set of 27 ordinary differential equations (ODE's) which form the dynamic model of the three-wheeled WMR. The dynamic equations of motion have been derived symbolically using a Lagrangian approach and computer algebra. The holonomic and nonholonomic constraints of constant length and no-slip, respectively, are taken into account in the model. Simulation results clearly show that the three-wheeled WMR can achieve no-slip motion even when dynamic effects are taken into consideration.