Collision free trajectory planning and control of underactuated planar 3R manipulator

In this paper the problem of position control of underactuated planar 3R manipulator in the presence of obstacles is solved by tracking appropriated planned trajectories. A class of collision free trajectories is proposed to reach a desired configuration. The motion planning is formulated as an optimal control problem by incorporation final state errors and obstacle avoidance condition in cost function as penalty functions. Besides, a sliding mode control scheme is proposed to regulate the manipulator under error modeling and external perturbation. By using simulations, it is illustrated that if the coordinates of the underactuated system track the planned trajectories then the system reaches the desired configuration and can avoid obstacles Simultaneously.