An algorithm to modify the trajectories of multiple robots in cooperative manipulation is developed. If a given trajectory results in joint torques that exceed the admissible torque range for one or more joints, the algorithm slows down or speeds up the trajectory so as to maintain all the torques within the admissible boundary. The proposed trajectory-modification algorithm uses the concept of time scaling developed by Hollerbach (1984) for single robots. The trajectory scaling scheme described in this paper requires the use of linear programming techniques and is designed to accommodate the internal force constraints and payload distribution strategies. The actuator torques may be found from the quadratic minimization that has the effect of lowering energy consumption for the trajectory. A scheme for generating a robust multirobot trajectories when the carried load mass and inertia matrix are unknown but vary within a certain range is described.
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