The Control of Natural Motion in Mechanical Systems

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Abstract
This paper concerns a simple extension of Lord Kelvin’s observation that energy decays in a dissipative mechanical system. The global limit behavior of such systems can be made essentially equivalent to that of much simpler gradient systems by the introduction of a “navigation function” in the role of an artificial field. This recourse to the mechanical system’s natural motion helps transform the open-ended problem of autonomous machine design into the more structured problem of finding an appropriate “cost function” in the many situations that the goal may be encoded as a setpoint problem with configuration constraints.

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