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Missions across a variety of disciplines require the interception of multiple targets. In defence scenarios, targets may pose a threat to sites, while in agriculture the targets may be invasive pests or fruit ready to harvest. This paper focuses on the cooperative control of a robot swarm for interception missions of multiple static and dynamic targets while avoiding collisions. We formulate two modifications of the classical Navigation-Function for a swarm interception mission which are suitable for deterministic and stochastic scenarios: the Swarm Navigation Function (S-NF) for the deterministic case, and the Swarm Probabilistic Navigation Function (S-PNF) for the stochastic case. Both functions provide a simultaneous solution for the problems of target assignment and motionplanning as opposed to the classical approaches that solve each problem independently. We demonstrate the effectiveness of these functions through extensive simulations and real-world experiments, comparing their performance with optimal solutions and human decision-making in similar scenarios. We show analytically that by following the Swarm-Navigation-Function gradient, the swarm will intercept all static targets while avoiding agent-agent and agent-obstacle collisions and similarly following the gradient of the Probabilistic-Navigation-Function will almost surely converge to a target in finite time, while the probability for agent-agent and agent-obstacles collisions is limited to a predefined value. The complexity of both schemes is linear with the number of targets and robots, and therefore it is scalable. Although not optimal, these solutions are simple and efficient, making them suitable for an extended set of real-time and real-life applications. We compare the resulting Swarm-Navigation-Function trajectories to that of a human in a catch game and an interception virtual game, the comparison indicates that as the trajectories are similar, human decision-making performs better. We conclude the paper with a set of simulated experiments and real-world experiments demonstrating the efficiency of the proposed scheme for dynamic targets.

Navigation function for Multi-Agent Multi-Target Interception Missions