Inverse Force/End-Point Control, Zero Dynamics and Stabilization of Constrained Elastic Robots

We treat the question of position and force control of three-axis elastic robotic systems on a constraint surface based on nonlinear inversion of an input-output map and linear feedback stabilization. Unlike the rigid robots, the feedback linearizing control of end point motion gives rise to unstable zero dynamics. Instability of zero dynamics is avoided by controlling a parameterized output vector corresponding to a point close to the end point of the arm. Zero dynamics are stable or almost stable as long as the parameter in the output vector does not exceed a critical value. Using the inverse controller the position and force control of the end point is possible while the end effector moves on the constraint surface, however, this excites the elastic modes. For the final capture of the terminal state and vibration suppression, a linear stabilizer is designed. Simulation results are presented to show that in the closed-loop system trajectory and force control on the constraint surface is accomplished