The Control of Natural Motion in Mechanical Systems
This paper concerns a simple extension of Lord Kelvin's observation that energy decays in a dissipative mechanical system. The global limit behavior ofsuch systems can be made essentially equivalent to that of much simpler gradient systems by the introduction of a "navigationfunction" 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.
This paper offers a unified exposition of some recent results [13, 12, 15] heretofore scattered throughout a more mathematically oriented literature that strengthen our original suggestion [8, 9] concerning the utility of controlling natural motion as a means of simultaneously encoding, planning and effecting tasks in mechanical systems. The chief theoretical insight, Theorem 2, is a global global version of Lord Kelvin's century old result on the dissipation of total energy. Establishing this extension yields a rather general design principlethe notion of a navigation function-that seems to have useful application in a variety of settings. Roughly speaking, it offers a checklist of criteria for achieving the strongest possible convergence properties allowed on a configuration space by a smooth and bounded force/torque control strategy. Some simple examples introduced here may aid the exposition of these ideas. A sequel  to this paper illustrates how the ideas may be applied in more realistic settings.
Daniel E. Koditschek. "The Control of Natural Motion in Mechanical Systems" Departmental Papers (ESE) (1991).
Available at: http://works.bepress.com/daniel_koditschek/51