Data-Driven Passivity-Based Control of Underactuated Robotic Systems

Classical control strategies for robotic systems are based on the idea that feedback control can be used to override the natural dynamics of the machines. Passivity-based control (Pbc) is a branch of nonlinear control theory that follows a similar approach, where the natural dynamics is modified based on the overall energy of the system. This method involves transforming a nonlinear control system, through a suitable control input, into another fictitious system that has desirable stability characteristics. The majority of Pbc techniques require the discovery of a reasonable storage function, which acts as a Lyapunov function candidate that can be used to certify stability. There are several challenges in the design of a suitable storage function, including: 1) what a reasonable choice for the function is for a given control system, and 2) the control synthesis requires a closed-form solution to a set of nonlinear partial differential equations. The latter is in general difficult to overcome, especially for systems with high degrees of freedom, limiting the applicability of Pbc techniques. A machine learning framework that automatically determines the storage function for underactuated robotic systems is introduced in this dissertation. This framework combines the expressive power of neural networks with the systematic methods of the Pbc paradigm, bridging the gap between controllers derived from learning algorithms and nonlinear control theory. A series of experiments demonstrates the efficacy and applicability of this framework for a family of underactuated robots