New class of control laws for robotic manipulators Part 2. Adaptive case

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Abstract
A new class of asymptotically stable adaptive control laws is introduced for application to the robotic manipulator. Unlike most applications of adaptive control theory to robotic manipulators, this analysis addresses the non-linear dynamics directly without approximation, linearization, or ad hoc assumptions, and utilizes a parameterization based on physical (time-invariant) quantities. This approach is made possible by using energy-like Lyapunov functions that retain the non-linear character and structure of the dynamics, rather than simple quadratic forms, ubiquitous in adaptive control literature, which have bound the theory tightly to linear systems with unknown parameters. It is a unique feature of these results that the adaptive forms arise by straightforward certainty equivalence adaptation of their non-adaptive counterparts found in Wen and Bayard (1988)—i.e. by replacing unknown quantities by their estimates—and that this simple approach leads to asymptotically stable closed-loop adaptive systems. Furthermore, it is emphasized that this approach does not require convergence of the parameter estimates (i.e. via persistent excitation), invertibility of the mass matrix estimate, or measurement of joint accelerations.

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