Robust control of Chat-PM: A switched singular system with mode-dependent bounded nonlinearity

This paper is concerned with the robust control of the composite hybrid aerial-terrestrial precise manipulator (Chat-PM), a quadrotor-based robot with aerial/terrestrial movement and payload transportation capabilities. Given the distinct dynamics between aerial and terrestrial locomotion modes, Chat-PM is modeled as a type of switched singular system. A nonlinear term is contained in the system to model the coupling between translational and rotational movements of Chat-PM, which is proven to be norm-bounded and mode-dependent. Besides, the estimation error of the robotic arm's interaction force/torque is treated as the disturbance of the system. By means of the mixed $H_2$/$H_{\infty }$ approach, numerically testable stability criteria are obtained, based on which the existence conditions for controllers with satisfactory transient and disturbance attenuation performance are provided. Compared to traditional studies assuming the nonlinearity term to be mode-independent, the conservatism in the controller design is reduced. Experimental results are provided to demonstrate the effectiveness of the proposed approach.