Nonlinear Control Problems for Underactuated Mechanical Systems

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This proposal describes a research program to investigate control problems for underactuated mechanical systems, that is for mechanical systems with fewer independent control variables than degrees of freedom. We propose a mathematical model that provides a framework for (1) developing a conceptual synthesis for control of the many examples of underactuated mechanical systems that have been studied in the published literature and (2) constructing new control analysis and design tools that are specific for underactuated mechanical systems. Our first research objective is to develop a synthesis or unification of the disparate results in the existing literature on control of underactuated mechanical systems, thereby providing new insights into the applicability of various nonlinear control approaches. Our other research objective is to develop new nonlinear control results that are specific to the class of underactuated mechanical systems. This research direction would build heavily on the successful results developed under our current NSF research grant (on supervisory and hybrid control of nonlinear systems) as well as on the relevant nonlinear control results developed by many of our research colleagues. We identify specific research directions that we believe are likely to be successful and we suggest that the expected results are likely to provide important advances beyond the existing knowledge base for control of underactuated mechanical systems.