An Equivalent Time-Optimal Problem to find Energy-Optimal Paths for Skid-Steer Rovers

A skid-steer rover's power consumption is highly dependent on the turning radius of its path. For example, a point turn consumes a lot of power compared to a straight-line motion. Thus, in path planning for this kind of rover, turning radius is a factor that should be considered explicitly. There is a lack of any analytical approach in literature for finding energy-optimal paths for skid-steer rovers. The key contribution of this work is an energy-time equivalency theorem, for skid-steer rovers on obstacle-free hard ground. The theorem converts the energy-optimal problem into an equivalent time-optimal problem. This non-intuitive result stems from the fact that with this model of the system the total energy is fully parameterized by the geometry of the path alone. Hence, instead of directly solving the energy-optimal path planning problem, which is highly nonlinear, the equivalent time-optimal problem can be solved. Furthermore, experimental results are provided to experimentally prove the equivalency theorem while using Husky UGV skid-steer rover.