Stability Analysis of Position and Force Control of Robot Arms

Stability issues involving the control of a robot arm under the influence of external forces are discussed. Several different scenarios are considered: position control with the external force as an unmodeled disturbance, compliant control for a bounded external force in some subspace, and compliant control for a force due to the interaction with an environment whose dynamical behavior can be modeled. In each of these cases, a stability analysis using the Lyapunov method is presented. An explanation of instability is suggested in the case that the environment has flexibility and the gains are inappropriately chosen. When the environment is stiff in the force control subspace, robust (in time delay) stability can be achieved via the integral force feedback. However, the integral feedback gain should be chosen sufficiently small to account for possible flexibility in the system.