Time Scaling of Cooperative Multi-Robot Trajectories

In this paper we develop an algorithm 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 algorithm slows down or speeds up the trajectory so as to maintain all the torques within the admissible boundary. Our trajectory modification algorithm uses the concept of time scaling developed by Hollerbach[10] for single robots. A multiple robot system in cooperative manipulation has significantly different dynamics compared to single robot dynamics. As a result, time scaling algorithm for single robots is not usable with multi-robot system. The trajectory scaling schemes described in this paper requires the use of linear programming techniques and is designed to accommodate the internal force constraints and payload distribution strategies. As the multi-robot 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 trajectory. A scheme for generating a robust multi-robot trajectories when the carried load mass and inertia matrix are unknown but vary within a certain range is also described in this paper. Several examples are given to show the effectiveness of our multi-robot trajectory sealing scheme

Time-Optimal Trajectories for Cooperative Multi-Manipulator Systems

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