Time-energy optimal control of articulated systems with geometric path constraints

The motions of articulated systems along specified paths are optimized to minimize a time-energy cost function. The optimization problem is formulated in a reduced two-dimensional state space and solved using the Pontryagin maximum principle. The optimal control is shown to he smooth, as opposed to the typically discontinuous time optimal control. The numerical solution is obtained with a gradient search that iterates over the initial value of one co-state. Optimal trajectories are demonstrated numerically for a two-link planar manipulator and experimentally for the UCLA Direct Drive Arm. The smoother time-energy optimal trajectory is shown to result in smaller tracking errors than the time optimal trajectory.