Dynamic stability of off-road vehicles: A geometric approach

Dynamic stability reflects the vehicle's ability to traverse uneven terrain at high speeds. It is determined from the set of admissible speeds and tangential accelerations of the center of mass along the path, subject to the ground force constraints and the geometric path constraints. This paper presents a geometric procedure for computing the set of admissible speeds and accelerations of a planar all-wheel drive vehicle. It first determines the boundaries of the set of resultant forces at the center of mass that satisfy the ground force constraints and the equations of motion along the path. This set is then mapped to the set of feasible speeds and accelerations along the path, from which the dynamic stability margin (DSM) is determined. A byproduct of this procedure is a static stability margin (SSM) that reflects the vehicle's ability to accelerate, or decelerate, at zero speed. Both stability margins are useful as cost measures for physics-based motion planning over rough terrain. The approach is demonstrated for a planar vehicle moving on a sinusoidal track.