Stability analysis of an online algorithm for torque limited path following

A secondary controller for online time scaling of nominal high-performance trajectories has been proposed to handle path following with torques close to the limits. Such nominal reference trajectories are typically available from an offline optimization. The stability properties of a closed-loop system including a robot, a primary controller, and a new secondary controller are studied. The analysis shows that if the nominal velocity profile is within certain limits, the result is a bounded actual velocity profile. The stability of the closed-loop system is then obtained by requiring a specified tracking performance for the primary controller