Time scaling of trajectories for cooperative multi-robot systems

The application of the time scaling method is extended to the multiple redundant robots in cooperative manipulation. The modification of the algorithm previously developed by the authors (Proc. 1990 IEEE Conf., Robotics and Automatio p.506-511, 1990) allows the use of the time scaling method without using the inverse of the Jacobian matrix. The trajectory scaling scheme described requires the use of linear programming techniques and is designed to accommodate the internal force constraints and payload distribution strategies. As the multirobot system is usually redundantly actuated, the actuator torques may be found from the quadratic minimization which has the effect of lowering energy consumption for the described trajectory. How to find the time scaling constant when the load is variable is described