A concept for manipulator trajectory planning

Following a prescribed trajectory with a manipulator tip in an ideal manner results in a one DOF overall motion whatever the configuration of the manipulator and of the path might be. Thus, a transformation of the equations of motion from joint coordinates to path coordinates leads to a set, which cannot only be solved by formal quadrature but defines as well the phase space of admissible motion constrained by path geometry and joint torques. Time optimal solution representing the maximum mobility of the path-manipulator-configuration can be determined by a field of extremals bounded by a maximum velocity curve, which acts as a trajectory source or sink. Its properties lead to an algorithm for evaluating the time-minimum-curve from a sequence of accelerating/decelerating extremals. Additional optimizing criteria are regarded applying Bellman´s principle.