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The paper considers a novel technique for manipulator motion in a constrained environment due to the presence of obstacles. The basic problem is that of avoiding collisions of the manipulator with the obstacles. The main idea is to cover the free space (i.e. the points of the configurations space in which no collisions are possible) by a connected family of polyhedral sets which are controlled-invariant. Each of these polyhedral regions includes some crossing points to the confining regions. The tracking control is hierarchically structured. A high-level controller establishes a connected chain of regions to be crossed to reach the one in which the reference is included. A low-level control solves the problem of tracking, within a region, the crossing point to the next confining region and, eventually, tracking the reference whenever it is included in the current one. The scheme assures that the reference is asymptotically tracked and that the transient trajectory is completely included in the admissible configuration space. A connection graph associated with the cluster of regions, and the high-level control is achieved by solving a minimum-path problem. As far as the low-level control is concerned, we consider both speed-control and torque-control. We propose two types of controllers. The first type is based on a linear stabilizing feedback which is suitably adapted to achieve a local tracking controller. Such a controller is computed by the plane representation of the sets which is more natural and useful then the vertex representation considered in previous work. The second is a speed-saturated type of controller which considerably improves the performance of linear-based control laws. Both these controllers have a speed-control and torque-control version. Experimental results on a laboratory Cartesian robot are provided.