Energy-Optimal Trajectory Planning for Planar Underactuated RR Robot Manipulators in the Absence of Gravity
Figure 6
Sequence of configurations of the robot manipulator at times with corresponding to the optimal solution of problem 3, an initial value problem for an underactuated planar robot manipulator with boundary conditions , , , , , , , 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 7.
