Real-time Motion-planning of Curvature-constrained AUVs under Steady Ocean Currents

In this paper, we propose a novel approach to obtain a real-time solution for the minimum-time motion-planning problem for curvature-constrained AUVs in the presence of ocean currents. The existing solution to this problem is obtained by solving the six Dubins path types (i.e., LSL, RSR, LSR, RSL, LRL and RLR) in the presence of currents, four of which involve a root-finding problem consisting of transcendental functions. Thus, the computational complexity of the exiting solution makes it infeasible for real-time applications, such as rapidly changing oceanic environments. The proposed approach utilizes only the LSL and RSR path types from the Dubins set, which provide analytical solutions as needed for real-time applications. It is shown that by extending the feasible range of circular arcs in these path types from 2 pi to 4 pi, full reachability is guarantee; i.e., a solution can be obtained for every pair of start and goal poses. Furthermore, it is shown that the proposed solution provides better time-costs with lower travel times as compared to the existing Dubins LSL and RSR paths. The proposed approach is validated by numerical studies through various examples to highlight its benefits for real-time applications.