476094.fig.003a
(a)
476094.fig.003b
(b)
476094.fig.003c
(c)
476094.fig.003d
(d)
476094.fig.003e
(e)
Figure 3: Control and state variables of the optimal solution of problem 1, a boundary value problem for the planar robot manipulator with boundary conditions , , , , , , , and . The initial and final times are and , respectively. The corresponding sequence of configurations of the robot manipulator at times with is represented in Figure 2.