Game-Theoretic Distributed Sensor Tasking in Earth Observation Satellite Constellations

This paper presents a game-theoretic sensor selection for coordinating multiple satellites, where each satellite adjusts its roll angle to observe multiple targets. The main objective is to find a joint sensor schedule for the satellite constellation over a finite time horizon that minimizes both mean square error (MSE) and slew costs, which is a challenging combinatorial optimization problem. Standard MSE-based sensor scheduling problems typically involve optimizing non-submodular functions, which introduces computational complexity in designing algorithms that achieve provable performance guarantees. To address this issue, we propose a submodular surrogate objective function that is monotonic under specific conditions for the weights on MSE and slew cost terms. This reformulation enables the problem to be modeled as a potential game, facilitating the use of a distributed algorithm to find a Nash equilibrium that provides a bounded efficiency. The proposed solution is compared with an alternative game-theoretic solution using a different performance metric, as well as with a centralized greedy solution, to demonstrate the performance of the surrogate approach, particularly in the presence of isolated subgraphs and stochastic communication delays. Additionally, the versatility of the proposed scheme is highlighted, as it is applicable to heterogeneous satellites and sensors with disconnected communication graphs.