Motion Control and Coupled Oscillators

applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical, heterogeneous and dynamic problems of engineering technology and systems for industry and government. Abstract It is remarkable that despite the presence of large numbersof degrees of freedom, motion control problems are eeectively solved in biological systems. While feedback, regulation, and tracking have served us well in engineering, as useful solution paradigms for a wide variety of control problems including motion control, it appears that nature gives prominent roles to planning and coordination as well. There is also complex interplay b e t ween sensory feedback and motion planning to achieve eective operation in uncertain environments, for example, in movement on uneven terrain cluttered with obstacles. Recent investigations by neurophysiologists have brought to increasing prominence the idea of central pattern generators, a class of coupled oscillators , as sources of motion scripts" as well as a means for coordinating multiple degrees of freedom. The role of coupled oscillators in motion control systems is currently under intense investigation. In this paper we examine some unifying themes relating movement in biological systems and machines. An important insight in this direction comes from the natural groupings of degrees of freedom and time scales in biological and engineering systems. Such grouping and separation can be treated from a geometric viewpoint using the formalisms and methods of diierential geometry, Lie groups, and ber bundles. Coupled oscillators provide the means to bind degrees of freedom either directly through phase locking or indirectly through geometric phases. This point of view leads to fresh ways of organizing the control structures of complex technological systems.