Optimal Deployment of Multi-Robot Based Regional Positioning System Using Relative Bearing Measurement

Recently, the Multi-Robot based Regional Positioning System (MR-RPS) utilizing cooperative localization have emerged as a promising paradigm in Global Navigation Satellite Systems (GNSS)-constraint region: robots first localize themselves using extravagant sensors and then serve as anchors to propagate their noisy positions via cooperative localization and communication with users using accessible devices. However, research on the optimal deployment strategies for bearing-only sensor-based MR-RPS, such as using cameras, remains limited. The bearing-only approach provides a cost-effective and energy-efficient alternative to range-based solutions such as radio systems. This paper proposes a distributed optimal strategy for MR-RPS equipped with bearing-only sensors to provide effective positioning services to the GNSS-limited scenarios. We first employ the Fisher Information Matrix (FIM) and D-optimality as the localziation performance metric using the information received from the Multi-Robot System (MRS). Inspired by the coverage control problem from the Wireless Sensor Network, the optimal deployment of the MRS is then formulated into a locational optimization problem by integrating the value of D-optimality over the entire mission space. A distributed deployment strategy is thus developed, enabling each robot to iteratively compute optimal deployment strategies to enhance the overall performance for stochastically appearing users. Extensive simulations and physical experiments validate the resilience and effectiveness of the proposed method in delivering high-quality positioning services.