Multiagent Gathering With Collision Avoidance and a Minimax Distance Criterion—Efficient Algorithms and Hardware Realization

Abstract

Multiple autonomous agents working cooperatively have contributed to the development of robust large-scale systems. While substantial work has been done in manufacturing and domestic environments, a key consideration for small hardware agents engaged in collaborative factory automation and welfare support systems is limited area and power on-board. When the agents attempt to meet for performing a task, it is natural for them to encounter obstacles and it is desirable for each agent to optimize its resources during its navigation. In this paper, we develop efficient geometric algorithms to find a point, termed as the gathering point (and denoted by $P_G$ ), for the agents that minimizes the maximum of path lengths . In particular, we present an $O(n \log _2 n)$ time algorithm for calculation of $P_G$ for an environment with two agents and $n$ static polygonal obstacles. We then use the notion of a weighted minimax point to derive an efficient algorithm (with complexity of $O(k^2 + kn \log _2 n)$ ) for computing $P_G$ for an environment with $k$ agents and $n$ obstacles. An enhancement to a dynamic environment is then presented. We also present details of an efficient hardware realization of the algorithms. Each agent, equipped with only an ATmega328P microcontroller and no external memory, executes the algorithms. Experiments with multiple agents navigating amidst static as well as dynamic obstacles are reported.