Time-optimal control of gripper motion in a two-link manipulator with allowance for the terminal configuration

We consider a time-optimal control problem for the motion of a point gripper of a plane two-link manipulator with linear links of equal length, the second link being statically balanced. Domains of attainable configurations are constructed on the plane of generalized manipulator coordinates. These domains permit one to determine which of the two final point configurations corresponding to a given gripper terminal position, together with the manipulator control method, ensures the gripper motion from the initial rest position to a given final rest position in minimum time. It is established by numerical calculations that the optimal choice of the final configuration can significantly improve the response speed.