Optimal Virtual Tube Planning and Control for Swarm Robotics
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This paper presents a novel method for efficiently solving trajectory planning problems for swarm robotics in cluttered environments. While recent research has demonstrated high success rates in real-time local trajectory planning for swarm robotics in cluttered environments, optimizing every trajectory for each robot is computationally expensive, with a computational complexity of O(n^2) to O(n^3). To address this issue, we first propose the concept of the optimal virtual tube, which includes infinite optimal trajectories. Under certain conditions, any optimal trajectory in the optimal virtual tube can be expressed as a convex combination of a finite number of optimal trajectories, with a computational complexity of O(1). Afterward, a planning method of the optimal virtual tube is proposed. In simulations and experiments, we show that the proposed method efficiently reduces calculation and is validated by comparison with traditional methods.
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