Numerical Nonlinear Robust Control with Applications to Humanoid Robots

Robots would be much more useful if they could be more robust. Systems that can tolerate variability and uncertainty are called robust and the design of robust feedback controllers is a difficult problem that has been extensively studied for the past several decades. In this thesis, we aim to provide a quantitative measure of performance and robustness in control design under an optimization framework, producing controllers robust against parametric system uncertainties, external disturbances, and unmodeled dynamics. Under the H1 framework, we formulate the nonlinear robust control problem as a noncooperative, two-player, zero-sum, differential game, with the Hamilton-Jacobi-Isaacs equation as a necessary and sufficient condition for optimality. Through a spectral approximation scheme, we develop approximate algorithms to solve this differential game on the foundation of three ideas: global solutions through value function approximation, local solutions with trajectory optimization, and the use of multiple models to address unstructured uncertainties. Our goal is to introduce practical algorithms that are able to address complex system dynamics with high dimensionality, and aim to make a novel contribution to robust control by solving problems on a complexity scale untenable with existing approaches in this domain. We apply this robust control framework to the control of humanoid robots and manipulation in tasks such as operational space control and full-body push recovery.