We present two schemes for planning the time-optimal trajectory for cooperative multi-manipulator system (CMMS) carrying a common object. We assume that the desired path is given and parameterizable by an arclength variable. Both approaches take into account the dynamics of the manipulators and object. The first approach employs linear programming techniques, and it allows us to obtain the time-optimal execution of the given task utilizing the maximum torque capacities of the joint motors. The second approach is a sub-time-optimal method that is computationally very efficient. In the second approach the given load is divided into a share for each robot in the CMMS in a manner in which the trajectory acceleration/deceleration is maximized, hence the trajectory execution time is minimized. This load distribution approach uses optimization schemes that degenerate to a linear search algorithm for the case of two robots manipulating a common load, and this results in significant reduction of computation time. The load distribution scheme not only enables us to reduce the computation time, but also gives us the possibility of applying this method in real-time planning and control of CMMS. Further, we show that for certain object trajectories the load distribution scheme yields truly time-optimal trajectories.

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.>

An algorithm is developed to modify the trajectories of multiple robots in cooperative manipulation. If a given trajectory results in joint torques which exceed the admissible torque range for one or more joints, the trajectory speed is scaled so as to maintain all the torques within the admissible boundary. 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 can be found from the quadratic minimization, which has the effect of lowering energy consumption for the trajectory. Several examples are given to show the effectiveness of the multirobot trajectory scaling scheme.>