Adaptive motion/force tracking control of holonomic constrained mechanical systems: A unified viewpoint

This paper proposes a robust adaptive motion/force tracking controller for holonomic constrained mechanical systems with parametric uncertainties and disturbances. First, two types of well-known holonomic systems are reformulated as a unified control model. Based on the unified control model, an adaptive scheme is then developed in the presence of pure parametric uncertainty. The proposed controller guarantees asymptotic motion and force tracking without the need of extra conditions. Next, when considering external disturbances, control gains are designed by solving a linear matrix inequality (LMI) problem to achieve prescribed robust performance criterion. Indeed, arbitrary disturbance/parametric error attenuation with respect to both motion and force errors along with control input penalty are ensured in the L₂-gain sense. Finally, applications are carried out on a two-link constrained robot and two planar robots transporting a common object. Numerical simulation results show the expected performances.