用数学方法优化不同能力机器人对多目标的追踪分配

This paper addresses the challenge of assigning heterogeneous sensors (i.e., robots with varying sensing capabilities) for multi-target tracking. We classify robots into two categories: (1) sufficient sensing robots, equipped with range and bearing sensors, capable of independently tracking targets, and (2) limited sensing robots, which are equipped with only range or bearing sensors and need to at least form a pair to collaboratively track a target. Our objective is to optimize tracking quality by minimizing uncertainty in target state estimation through efficient robot-to-target assignment. By leveraging matroid theory, we propose a greedy assignment algorithm that dynamically allocates robots to targets to maximize tracking quality. The algorithm guarantees constant-factor approximation bounds of 1/3 for arbitrary tracking quality functions and 1/2 for submodular functions, while maintaining polynomial-time complexity. Extensive simulations demonstrate the algorithm's effectiveness in accurately estimating and tracking targets over extended periods. Furthermore, numerical results confirm that the algorithm's performance is close to that of the optimal assignment, highlighting its robustness and practical applicability.