Optimal Traction Forces for Four-Wheel Rovers on Rough Terrain

This paper addresses the minimization of the risk of wheel slippage for a popular class of rovers. In the absence of any constraints on the system (e.g., force/torque balance and maximum motor torques), the optimal traction solution is known to be that with equal “friction requirements” (ratios of tractive to normal force) for all wheels. Nevertheless, the current state of the art is to routinely perform computationally expensive constrained optimization because of the presumed importance of the constraints in a real system. The contribution of this paper is a thorough investigation of the configuration space for four-wheel rovers, driving straight over rough terrain, in search of configurations where the unconstrained optimal answer does or does not satisfy the constraints, and, thus, is or is not valid. Equal “friction requirements” are added to the four-wheel rover's system of quasi-static equations and a valid solution is sought to this augmented system of equations. It is found that the equal “friction requirements” solution is almost always valid, except for the case where two of the wheels are wedged against opposing vertical faces, a highly unusual and unlikely scenario. Therefore, we can conclude that computationally expensive constrained optimization is not required to achieve traction control for four-wheel rovers.