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Time-Optimal Motions of a Mechanical System with Viscous Friction

Author

Listed:
  • Dmitrii Kamzolkin

    (Department of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, International University Park Road 1, Shenzhen 518172, China
    These authors contributed equally to this work.)

  • Vladimir Ternovski

    (Department of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, International University Park Road 1, Shenzhen 518172, China
    These authors contributed equally to this work.)

Abstract

Optimal control is a critical tool for mechanical robotic systems, facilitating the precise manipulation of dynamic processes. These processes are described through differential equations governed by a control function, addressing a time-optimal problem with bilinear characteristics. Our study utilizes the classical approach complemented by Pontryagin’s Maximum Principle (PMP) to explore this inverse optimal problem. The objective is to develop an exact piecewise control function that effectively manages trajectory control while considering the effects of viscous friction. Our simulations demonstrate that the proposed control law markedly diminishes oscillations induced by boundary conditions. This research not only aims to delineate the reachability set but also strives to determine the minimal time required for the process. The findings include an exact analytical solution for the stated control problem.

Suggested Citation

  • Dmitrii Kamzolkin & Vladimir Ternovski, 2024. "Time-Optimal Motions of a Mechanical System with Viscous Friction," Mathematics, MDPI, vol. 12(10), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1485-:d:1391866
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