Control design for a class of nonlinear systems using limited information and its application to robotics

Control theorists are continually pushing for a more accurate and robust design pedagogy utilizing nonlinear dynamics as part of system control design. In this work a general formulation for the stabilization of multiple planar systems, given only the measurement of one output state per subsystem is considered. Additionally, it is assumed uncertainty is inherent in the systems under consideration, where it is only required to know the bounding functions, Φ_i, of the nonlinear terms. Under this setting consider a class of systems whose nonlinear bounding functions are polynomially bounded in the unmeasurable states. A novelty of this method is the utilization of a dual observer approach, estimating linear and higher order states in parallel. Currently in the field of robotics control disturbance is largely a cause of unpredictable instability or singularity in N-degree-of-freedom manipulators with closed and open kinematic chains. With this system dominance technique, a tunable decentralized-control solution is derived providing semi-global-asymptotic-stability and robust closed loop tracking for the aforementioned class of robotic systems. In this work, an application of a motion control solution is shown, utilizing the aforementioned controller design, on a 2-DOF closed-link chain robot manipulator. In this application, an online trajectory tracking problem is solved for dual nonlinear subsystems achieving Semi-Global-Asymptotic-Stability.