Sufficient Stability Conditions for Constrained Robot Maneuvers: Theory and Experiments

This work presents a nonlinear stability analysis for constrained robotic motion, which accounts for external disturbances, sensor noises, parameter uncertainties, and the dynamics of the total system comprised of the robot and the environment Manipulator control is implemented with both a Computed Torque [1] trajectory controller, which regulates the robot position, and a compliance controller, which modulates contact forces. Two sufficient conditions for stability are derived. The first condition guarantees stability of the robot and a finitely stiff environment when a compliance compensator (operating on the contact force) supplements the trajectory controller; this condition may be simplified for systems omitting force sensor feedback. This criterion shows that, for a fixed trajectory controller, the compliance controller´s L¿-gain must vary in inverse proportion to the environment stiffness to guarantee stability and that, in the vicinity of a singularity point, robot stability cannot be guaranteed. The second stability criterion shows that, for a robot contacting a very stiff environment, the compliance compensator´s gain must vary in inverse proportion to the trajectory compensator´s gain.