Mathematical Theory of Learning with Applications to Robot Control

Suguru Arimoto
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Suguru Arimoto: Osaka University, Faculty of Engineering Science

A chapter in Adaptive and Learning Systems, 1986, pp 379-388 from Springer

Abstract: Abstract Fundamental forms of learning control law are proposed for linear and nonlinear dynamical systems which may be operated repeatedly at relatively low cost. Given a desired output y d (t) over a finite time duration [0, T] and an appropriate input u 0(t) for such a system, a general proposed law of learning control is described by a PID-type (Proportional, Integration, and Differentiation) iterative process: u k +1(t) = u k (t) + {Φ + Γd/dt + Ψ ∫ dt}(y d (t) − y k (t)), where u k denotes the input at the kth trial, y k the measured output when u k excites the system, and Φ, Γ and Ψ are constant gain matrices. For a class of linear mechanical systems where x and y(= dx/dt) stand for position and velocity vectors respectively, it is shown that a P-type or PI-type iterative learning control law with appropriate gain matrices Φ and Ψ is convergent in a sense that y k (t) approaches y d (t) pointwisely in t ∈ [0, T] and x k (t) does x d (t) uniformly in t ∈ [0, T] as k → ∞. In case of using a D-type or DP-type iterative learning control law, an analogous conclusion is also proved for a class of nonlinear dynamical systems. Finally, proposed learning methods are applied to some problems of trajectory or path tracking control of robot manipulators.

Keywords: Nonlinear Dynamical System; Robot Manipulator; Learning Control; Iterative Learning Control; Gain Matrice (search for similar items in EconPapers)
Date: 1986
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DOI: 10.1007/978-1-4757-1895-9_27

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