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.

I. Introduction

Motion planning and control algorithms for robots interacting with the environment have been mostly studied separately. This separation of concerns typically sees first a motion planning phase for the constrained system, usually dealing with geometry and kinematics, followed by an execution phase, dealing with dynamics, where the planned trajectory is accurately executed possibly with some type of force control. This approach works well in cases where the robot-environment model is good enough, but it requires an extremely accurate (and time-consuming) planning phase. Also, there is no guarantee that errors in the constrained motion model will not generate unacceptable errors in the force interaction with the environment, nor that the force control execution will not interfere with the planned trajectory, causing violation of constraints and their consequences (e.g. bumping into obstacles, or loosing the grip on a manipulated object). This fact makes robot interactions dangerous and motivates the use of compliance in robot mechanisms.