Robust H_∞ control of a tendon–driven elastic continuum mechanism via a systematic description of nonlinearities

This work treats the pose control of an underactuated elastic continuum mechanism via a linear H_∞ approach. To incorporate the nonlinearities into the linear design method, a systematic framework is proposed that describes the nonlinear part of the system as uncertainty in a parameter-affine state-space description. With the established description of the nonlinear system, a robust H_∞ controller is synthesized applying the structured singular value framework. The designed controller is evaluated in simulation and hardware experiments on the Elastic Continuum Mechanism (ECM) used as a robotic neck of DLR's humanoid robot David. The robust controller designed under consideration of the systematic treatment of nonlinearities is able to stabilize the system for a reference step with negligible inaccuracy which is superior to a comparable conventional mixed synthesis H_∞ controller or a simple PD design.