Forwarding-based dynamic surface control for antagonistic actuated robots

Implementation of immersion and invariance theorem for antagonistic actuated robots becomes increasingly difficult as non-linearity of elastic torque exists. This inherent difficulty is mainly driven by the need to solve the partial differential equations (PDEs) in the immersion conditions. In this work, forwarding-based dynamic surface control (DSC) for designing asymptotically tracking control laws is developed for a tendon-driven joint with mismatched external disturbances. At each step of the design, by defining a lower-order target system, the required mappings can be transformed into the virtual control inputs so that the prescribed transient performance is realised. Based on forwarding combined with DSC, all virtual controls are connected in sequence and high-frequency noises can be suppressed. This technique not only avoids solving the PDEs, but also avoids computing mappings and their analytic derivatives. In particular, global boundedness of all signals in the robotic systems can be ultimately guaranteed by the internal stability of filters. Controller performances are demonstrated by simulating an actuated robot with one joint.