Adaptive control of holonomic constrained systems: a feedforward fuzzy approximation-based approach

This paper proposes a novel adaptive fuzzy control scheme for the motion/force tracking control of holonomic constrained systems with poorly understood models and disturbances. Some disadvantages of traditional adaptive fuzzy controllers are removed here. In comparison to typical state-feedback fuzzy approximation, the uncertainties are compensated based on a feedforward fuzzy approximation (FFA), which takes desired commands as the premise variables of fuzzy rules. In detail, a unified control model is introduced for representing well-known holonomic systems with an environmental constraint or a set of closed kinematic chains. Then, the FFA-based fuzzy system, adaptation mechanism, and auxiliary-compensating control are derived to ensure robust motion and force tracking in a global manner. Furthermore, a feasible solution for the derived linear matrix inequality guarantees the attenuation of both disturbances and fuzzy parameter errors in an L₂-gain sense. Finally, two applications are carried out on: 1) a two-link constrained robot and 2) two planar robots transporting a common object. Numerical simulation results show the expected performance.