Control of manipulators in a constrained workspace by means of linked invariant sets

We propose a new technique for controlling manipulators in constrained environments. Based on recent developments on constrained control theory, our approach basically consists in covering the admissible region of the configuration space by partially overlapping convex polyhedra arbitrarily fixed and forming a connected family. Each of these polyhedra, defined in the configuration space, is suitably extended in the state-space (i.e. configuration-plus-velocity space) in order to maintain all the original connections among regions and to be a tracking domain of attraction for the system, i.e. a set of initial states from which a reference signal can be asymptotically approached without constraints violation during the transient. The connection path is not generated a priori, but it is automatically produced on-line by a hierarchical feedback controller. A high-level controller selects the confining polyhedron, to which the current state has to be transferred, which is the closest to the one containing the target reference. A low-level controller solves the problem of locally tracking a suitable crossing point to the desired new region under constraints. The robustness of the scheme as well as the control effort constraints are also taken into account. Copyright (C) 2004 John Wiley Sons, Ltd.