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.
Highlights
Our multi-time model extends the single-time case formulated and solved by T
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 in vogue for micro-scale and nano-scale robotic systems
Summary
Our multi-time model extends the single-time case formulated and solved by T. We refer to a microrobotic system consisting of n planar robots which evolve in multi-temporal sense. The control of this system is hard, at least from an algorithmic point of view. The tensor fields are written via their components etc
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