Coordinated Trajectory Tracking as an Inverse Problem with Applications to Collaborative Robotics

This paper develops a new approach to collaborative trajectory tracking for multiple robotic mechanical systems based on the notion of an inverse problem. The new method accounts for the path tracking accuracy of each individual system, the accuracy of their relative positions, and the physical limitations of the systems and their controls. This is accomplished by applying the theory of regularization of inverse problems, and integrating it into the variational approach to problems in control theory. The method is general enough that the problem of flocking (all systems weighted equally) and the leader-follower configuration are solved within the same framework. The method is applied to a problem of collaborative robotics, which demonstrates the capabilities of the method by solving the cooperative trajectory tracking problem for dual spherical pendulums with position control.