Optimal trajectories of robot arms minimizing constrained actuators and travelling time

Dynamic optimization of the motion of a robot arm is carried out using the Pontryagin maximum principle. A mixed performance index involving travel time and bounded actuators is minimized to obtain a near-minimum traveling time and continuous output. One can avoid, in that case, actuating effort jumps and arm jerks. A full dynamic model formulated with Hamiltonian variables is used. This model, together with the optimality conditions, leads to a two-point boundary value problem which is solved by combining a gradient algorithm and a shooting method