Path constrained motion optimization for rigid and flexible joint robots

For rigid robots, a time-optimal velocity profile can be computed using available methods. An approach which is applicable to both rigid robots and flexible joint robots is to use polynomial approximation to obtain a parametric optimization problem. A method based on this idea is presented. The method is implemented, and it is illustrated by numerical examples. An optimality result on the structure of the time-optimal solution is presented, showing that the minimum time solution for flexible joint robots has properties similar to the rigid solution in the sense that at least one torque is at the limit