A numerical approach for time-optimal control of double arms robot

Time-optimal nonlinear control of rest to rest maneuvers of a double arms robot is solved using Pontryagin´s minimum principle. A numerical non-optimal solution satisfying the state equations with the initial and the final boundary conditions is found and used to obtain a good approximation of the initial values of the costates. Then the corresponding nonlinear two-point boundary-value problem is solved by applying a shooting method. A good approximation of the initial costate is usually needed to make the shooting method converge. This initial guess is generated here by the forward-backward method. A strategy that combines the shooting method and the forward-backward method to time-optimal control of the double arms robot is illustrated by the numerical examples