Stability Investigations into the Force Control of Robots with Nonlinearities

In this paper, several practical issues related to the force control of manipulators are investigated. The main issue studied is instability due to the non-linearity introduced by control signal saturation. By using phase-plane portrait analysis, it is shown that this non-linearity can drive the manipulator system which uses a discrete proportional-type feedback force control structure into a limit cycle, even for a very small sampling period that by far satisfies Shannon\´s sampling theorem. All studies were performed by using a plant model appropriately developed for force control applications. The main feature of this plant model is that the nonlinear slip-stick friction is conveniently described in terms of a "dead-zone" torque instead of the sign of rotational speed (as usually done in position control). In order to support the theoretical conclusions, preliminary experiments were performed with the PUMA 560 industrial robot testbed facility developed at Colorado State Univ.