Minirobots Moving at Different Partial Speeds

Constantin Udrişte and Ionel Ţevy
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Constantin Udrişte: Faculty of Applied Sciences, Department of Mathematics-Informatics, University Politehnica of Bucharest, Splaiul Independenţei 313, 060042 Bucharest, Romania
Ionel Ţevy: Faculty of Applied Sciences, Department of Mathematics-Informatics, University Politehnica of Bucharest, Splaiul Independenţei 313, 060042 Bucharest, Romania

Mathematics, 2020, vol. 8, issue 6, 1-17

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.

Keywords: multi-time motion planning; multi-time multi-robot systems; multi-time optimal control; multi-time Hamilton-Jacobi-Bellman PDE (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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