This research project investigates fundamental issues in the design, analysis, and real-time implementation of nonlinear control laws for underactuated mechanical systems. This class of systems is quite broad and encompasses balancing, brachiating, and walking robots, flexible structures of all kinds including flexible link robots, and flexible joint robots, airplanes and helicopters, underwater and space vehicles, electric motors, redundant robots, as well as mechanical system models that include actuator dynamics, and many of the classical control problems like the ball and beam and cart-pole systems. Global and semi-global stability and tracking results for classes of underactuated mechanical systems are investigated in this project. The tools used are Lagrangian and Hamiltonian methods of nonlinear dynamics, geometric nonlinear control theory, hybrid control, and saturation. The results also apply to a larger class of systems than have heretofore been investigated using these techniques. The unifying theme of this research is to exploit the underlying structure of the nonlinear dynamics to generate `natural closed loop motions` that make efficient use of passivity and energy. This work complements and extends existing energy and passivity methods and more recent backstepping methods, all of which attempt to exploit more fully the inherent nonlinearities of the system, by `shaping` rather than by `canceling` all of the nonlinearities in the system. On the experimental side, a number of testbed systems are used to test analytical research results. The laboratory includes several `gymnastic robots,` (Acrobots, Pendubots), a three degree-of-freedom air hockey playing robot, two direct drive robots, and a flexible joint robot. The experimental component of the research project is of vital importance both to the present project and to the ultimate goal of creating dextrous machines.
