In this paper 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 the dynamics of the object. The first approach employs linear programming techniques, and it allows us to obtain the timeoptimal execution of the given task utilizing the maximum torque capacities of the joint motors. The second approach is a sub-time-optimal method which is computationally very efficient. In the second approach we try to divide the given load into a share for each manipulator 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 which degenerate to a linear search algorithm for the case of two robots manipulating a common load, and this results in significant savings on the 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 under certain object trajectories the load distribution scheme yields truly time-optimal trajectories.

Date of this Version

January 1993