(a) ,
(b) ,
(c) ,
Figure 2: Sequence of configurations of the robot manipulator at times with corresponding to the optimal solution of problem 1, a boundary value problem for the planar robot manipulator with boundary conditions ,  [rad], , , , , , and , obtained with a discretization of into subintervals. The initial and final times are and , respectively. The corresponding control and state variables are represented in Figure 3.