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Open AccessArticle

Minirobots Moving at Different Partial Speeds

1
Faculty of Applied Sciences, Department of Mathematics-Informatics, University Politehnica of Bucharest, Splaiul Independenţei 313, 060042 Bucharest, Romania
2
Academy of Romanian Scientists, Ilfov 3, 050044 Bucharest, Romania
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(6), 1036; https://doi.org/10.3390/math8061036
Received: 25 May 2020 / Revised: 20 June 2020 / Accepted: 23 June 2020 / Published: 24 June 2020
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
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. View Full-Text
Keywords: multi-time motion planning; multi-time multi-robot systems; multi-time optimal control; multi-time Hamilton-Jacobi-Bellman PDE multi-time motion planning; multi-time multi-robot systems; multi-time optimal control; multi-time Hamilton-Jacobi-Bellman PDE
MDPI and ACS Style

Udrişte, C.; Ţevy, I. Minirobots Moving at Different Partial Speeds. Mathematics 2020, 8, 1036.

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