Dynamic frictional constraints in translation and rotation

Active constraints and virtual fixtures are popular control strategies used within human-robot collaborative manipulation tasks, particularly in the field of robot-assisted surgery. Recent research has shown how active constraints, which robotically regulate the motion of a tool that is primarily manipulated by a human, can be implemented in dynamic environments which change and deform throughout a procedure. In a dynamic environment, movement of the constraint boundary can cause active forcing of the surgical tools, potentially reducing the surgeon's control and jeopardising patient safety. Dynamic frictional constraints have been proposed as a method for enforcing dynamic active constraints which do not generate energy of their own, and simply dissipate or redirect the energy of the surgeon to provide assistance. In this paper, dynamic frictional constraints are reformulated to allow formal proof that they are indeed dissipative, and hence also passive. This new formulation is then extended such that dynamic frictional constraints can simultaneously constrain the position and orientation of a tool. Experimental results show that the method is of significant benefit in performing a dynamic task when compared to cases without any assistance; with position and orientation constraints individually and with a conventional frictional constraint without energy redirection.