Mathematical Theory of Learning with Applications to Robot Control

  • Suguru Arimoto


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.


Nonlinear Dynamical System Robot Manipulator Learning Control Iterative Learning Control Gain Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Suguru Arimoto
    • 1
  1. 1.Faculty of Engineering ScienceOsaka UniversityOsakaJapan

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