Consistent task speci cation for manipulation systems with general kinematics

Although most part of the literature on manipulation systems deals with systems with as many degrees of freedom as the dimension of their task space, or even with more (redundant manipulators), kinematically defective manipulation systems are often encountered in robotics, in particular when dealing with simple industry{ oriented grippers, or when the whole surface of the manipulator limbs is exploited to constrain the manipulated object, as in \whole{arm" manipulation. Kinematically defective systems di er from non{defective and redundant manipulation systems under many regards, some of which have been addressed in the literature. In this paper, we focus on one of the central problems of manipulation, i.e., controlling the manipulator in order to track a desired object trajectory, while guaranteeing that contact forces are controlled so as to comply with contact constraints (friction bounds, etc.) at every instant. We attack this problem by an uni ed approach that is appropriate for manipulation systems with general kinematics. When dealing with kinematically defective systems, it results that it is not possible to assign arbitrary trajectories of object motions and contact forces. To understand what restrictions position and force reference trajectories should exhibit in order to be feasible by a given system, is the central issue of this work.