Time-Optimal Cooperative Path Tracking for Multi-Robot Systems

Abstract: Robotic systems are nowadays the key technology in a wide variety of applications. The increasing demand for performance of robotic systems is often met by employing a team of cooperating robots for a specific task.When the task carried out by the robots involves manipulation of an object, the multi-robot system is said to perform a cooperative manipulation task.Cooperative manipulation is an important capability for extending the domain of robotic applications.This thesis studies the time-optimal path tracking problem for a cooperative manipulation scenario where an object is rigidly grasped by multiple manipulators. The goal is to move the object along a predefined geometric path in minimum time while satisfying the imposed constraints on the motion. First, it is shown that the time-optimal path tracking problem for cooperative manipulators can be cast as a convex optimization problem. A fundamental property of convex optimization problems is that any locally optimal solution is also a globally optimal one. Furthermore, by recognizing and formulating a problem as a convex optimization problem, it can be solved very reliably and efficiently using interior-point or other methods for convex optimization.These results are presented in two separate studies. In the first one which is a preliminary study, the manipulation setup is a particular setup comprised of two planar manipulators and a bar. Furthermore, the load distribution among the manipulators is considered to be equal. The second study extends the results in the preliminary study to a general scenario with $N$ generic manipulators and an object with a desired orientation during the motion. Here, the load distribution among the manipulators is determined via a generic pseudo-inverse of the grasp matrix that can be chosen by the user.The freedom in the choice of the pseudo-inverse allows to consider different load distributions which can be exploited to account for the potential differences in the capabilities of the manipulators.The second part of this thesis is devoted to finding load distributions that are free of internal forces. A drawback of using multiple manipulators in a cooperative manipulation task is that internal forces can be introduced.Internal forces are forces exerted by the end-effectors at the grasping points that do not contribute to the motion of the manipulated object. While a certain amount of such forces can be useful in some cases, in general they must be avoided to prevent object damage and unnecessary effort of the manipulators.This thesis proposes a new approach to obtain internal force-free load distributions.The proposed approach results in a new pseudo-inverse of the grasp matrix parameterized by coefficients that have the meaning of the inertial parameters of some parts of the object. The freedom in the choice of the parameters of the pseudo-inverse allows to assign different loads to the manipulators. This can be exploited to account for the differences in the power capabilities of the manipulators.The results are further explored for scenarios where the object is three-dimensional and convex and has uniform mass density. Finally, the proposed pseudo-inverse is combined with the results in the first part of the thesis to solve the problem of time-optimal cooperative path tracking subject to zero internal forces during the motion.

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