Path Following for Mechanical Systems Applied to Robotic Manipulators

Abstract

Many applications in robotics require faithfully following a prescribed path. Tracking controllers may not be appropriate for such a task, as there is no guarantee that the robot will stay on the path. The objective of this thesis is to develop a control design method which makes the “output” of a robot get to, and move along the prescribed path without leaving the path. We consider the class of mechanical systems, which encompasses robotics. Various techniques exist for designing pah following controllers. We base our approach on a technique called “transverse feedback linearization”. Using this technique, if feasible, we decompose the dynamics of a mechanical system into a transversal subsystem and a tangential subsystem using a coordinate and feedback transformation. The transversal subsystem is linear, time-invariant and decoupled from the tangential subsystem. Stabilizing the origin of the transversal subsystem is equivalent to stabilizing a set corresponding to the output of the mechanical system being on the desired path, thereby partly achieving the control objective. Given a mechanical system and a path, we provide conditions under which this is possible. The tangential subsystem describes all of the motions of the mechanical system, when the output is on the path. Some tangential dynamics may move the output along the path, and thereby meet the design objective. In order to move the output of the mechanical system along the path, we further decompose the tangential subsystem into a subsystem which moves the output along the path, and a subsystem which does not, if feasible, using partial feedback linearization. The subsystem which governs output motions along the path is linear, time-invariant and decoupled. The remaining tangential dynamics have no special structure. We provide conditions under which such a decomposition of the tangential dynamics is possible. We show that a five-bar robotic manipulator has dynamics which may be transversely feedback linearized, and the tangential dynamics may be partially linearized. Given a circular path, we experimentally implement our path following design, and observe that our control objective is indeed met. Inherent advantages of path following over trajectory tracking are illustrated. Standard feedback linearization of a five-bar robotic manipulator with a flexible link has been shown to fail. We show that this system is transversely feedback linearizable, and its tangential dynamics may be partially linearized, under mild restrictions. Simulations illustrate path following applied to this complex system.