Path Planning for a Cooperative Navigation Aid Vehicle to Assist Multiple Agents Sequentially

This paper considers planning a path for a single underwater cooperative navigation aid (CNA) vehicle to sequentially aid a set of N agents to minimize average navigation uncertainty. Both the CNA and agents are modeled as constant-velocity vehicles. The agents travel along known nominal trajectories and the CNA plans a path to sequentially intercept them. Navigation aiding is modeled by a scalar discrete time Kalman filter. During path planning, the CNA considers surfacing to reduce its own navigation uncertainty. A greedy planning algorithm is proposed that uses a heuristic to schedule agents to the CNA that is based on the optimal time-to-aid, the overall navigation uncertainty reduction, and the transit time. The approach is compared to an optimal (exhaustive enumeration) algorithm through a Monte Carlo experiment with randomized agent trajectories and initial navigation uncertainty.