Noninteracting constrained motion planning and control for robot manipulators

In this paper we present a novel geometric approach to motion planning for constrained robot systems. This problem is notoriously hard, as classical sampling-based methods do not easily apply when motion is constrained in a zero-measure submanifold of the configuration space. Based on results on the functional controllability theory of dynamical systems, we obtain a description of the complementary spaces where rigid body motions can occur, and where interaction forces can be generated, respectively. Once this geometric setting is established, the motion planning problem can be greatly simplified. Indeed, we can relax the geometric constraint, i.e., replace the lower-dimensional constraint manifold with a full-dimensional boundary layer. This in turn allows us to plan motion using state-of-the-art methods, such as RRT∗, on points within the boundary layer, which can be efficiently sampled. On the other hand, the same geometric approach enables the design of a completely decoupled control scheme for interaction forces, so that they can be regulated to zero (or any other desired value) without interacting with the motion plan execution. A distinguishing feature of our method is that it does not use projection of sampled points on the constraint manifold, thus largely saving in computational time, and guaranteeing accurate execution of the motion plan. An explanatory example is presented, along with an experimental implementation of the method on a bimanual manipulation workstation.