Exact Optimal Trajectories for Robots
Prof. Devin Balkcom
Robot control algorithms, like computer algorithms, allocate resources to accomplish tasks; resources include time, energy, degrees of freedom, steps of computation, and precision. A fundamental problem is to determine the minimum resources required -- the physical complexity of of the task. The optimal trajectories provide insight into the capabilities of a mechanism, independent of compromises introduced by particular planning or control techniques.
The exact optimal trajectories were previously known for two vehicles: the Dubins car, and the Reeds-Shepp car. We have discovered the optimal trajectories for a third vehicle; the common differential-drive (wheelchair-like) robot, and work on two more vehicles is nearing completion.