Redundancy Resolution in Minimum-Time Path Tracking of Robotic Manipulators

Minimum-time trajectories for applications where a geometric path is followed by a kinematically redundant robot's end-effector may yield economical improvements in many cases compared to conventional manipulators. While for non-redundant robots the problem of finding such trajectories has been solved, the redundant case has not been treated exhaustively. In this contribution, the problem is split into two interlaced parts: inverse kinematics and trajectory optimization. In a direct optimization approach, the inverse kinematics problem is solved numerically at each time point. Therein, the manupulator's kinematic redundancy is exploited by introducing scaled nullspace basis vectors of the Jacobian of differential velocities. The scaling factors for each time point are decision variables, thus the inverse kinematics is solved optimally w.r.t. the trajectory optimization goal, i.e. minimizing end time. The effectiveness of the presented method is shown by means of the example of a planar 4R manipulator with two redundant degrees of freedom.