Minimum-time control laws for robotic manipulators

The problem of minimum-time control (MTC) for rigid robotic manipulators with point-to-point motion subject to hard constraints on the control torques is addressed. A Hamiltonian canonical formulation of the robotic dynamic equations is used. A perturbation-based transformation algorithm is applied to solve this category of the MTC problem. In this algorithm, the original MTC problem, possibly a partially singular one, is converted into a totally nonsingular optimal control problem by introducing a perturbed energy term into the original objective functional. It is shown that, in the limiting case, the solution to the transformed problem is convergent to that of the original MTC problem. The numerical solutions to several example manipulators are presented to verify the theoretical result on the structure of the MTC law. Some of the characteristics of the resulting optimal trajectories are analyzed by using a dynamic scaling approach. The result provides new insight into the dynamic characteristics of robot arms, pertaining to both path planning and design specifications