Trajectory planning of tracked vehicles

The motions of planar tracked vehicles are governed by three force and moment equations, but driven by only two independent control variables. The force equation perpendicular to the tracks represents a dynamic nonholonomic constraint which is explicitly dependent on vehicle speed. It couples path planning with trajectory planning, that is, solving for vehicle kinematic motions requires specifying vehicle speeds. In contrast, wheeled vehicles are governed by kinematic nonholonomic constraints, allowing separate planning of the path and the trajectory. In this paper, we determine the nominal track forces required to follow a specified path at desired speeds. The problem is reduced to computing vehicle orientations along the path that are consistent with the nonholonomic constraint. The computation of vehicle orientations is formulated as a parameter optimization that minimizes the violation of the equality constraint. The method is demonstrated for planar motions along a circular path on flat and inclined planes.