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Minirobots Moving at Different Partial Speeds

Author

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  • Constantin Udrişte

    (Faculty of Applied Sciences, Department of Mathematics-Informatics, University Politehnica of Bucharest, Splaiul Independenţei 313, 060042 Bucharest, Romania
    Academy of Romanian Scientists, Ilfov 3, 050044 Bucharest, Romania)

  • Ionel Ţevy

    (Faculty of Applied Sciences, Department of Mathematics-Informatics, University Politehnica of Bucharest, Splaiul Independenţei 313, 060042 Bucharest, Romania)

Abstract

In this paper, we present the mathematical point of view of our research group regarding the multi-robot systems evolving in a multi-temporal way. We solve the minimum multi-time volume problem as optimal control problem for a group of planar micro-robots moving in the same direction at different partial speeds. We are motivated to solve this problem because a similar minimum-time optimal control problem is now in vogue for micro-scale and nano-scale robotic systems. Applying the (weak and strong) multi-time maximum principle, we obtain necessary conditions for optimality and that are used to guess a candidate control policy. The complexity of finding this policy for arbitrary initial conditions is dominated by the computation of a planar convex hull. We pointed this idea by applying the technique of multi-time Hamilton-Jacobi-Bellman PDE. Our results can be extended to consider obstacle avoidance by explicit parameterization of all possible optimal control policies.

Suggested Citation

  • Constantin Udrişte & Ionel Ţevy, 2020. "Minirobots Moving at Different Partial Speeds," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1036-:d:375912
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    References listed on IDEAS

    as
    1. C. Udrişte & I. Ţevy, 2010. "Multitime Dynamic Programming for Curvilinear Integral Actions," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 189-207, July.
    2. Constantin Udrişte & Ionel Ţevy, 2011. "Multitime dynamic programming for multiple integral actions," Journal of Global Optimization, Springer, vol. 51(2), pages 345-360, October.
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