Fermat’s spiral smooth planar path planning under origin-departing and corner-cutting transitions for autonomous marine vehicles

Abstract This research investigates the planar path planning method, particularly where straight survey line in ocean exploration is required. The smooth transition path between multiple straight survey segments in origin-departing and corner-cutting transition modes is studied. First, different transition modes of autonomous marine vehicles (AMVs) in practical ocean survey navigation are realized and distinguished. Based on the definition of different transition modes, the waypoints can be pre-assigned, generated online, or compatible with online and offline assignments. Second, to avoid wiggles of vehicles, zigzags of the tracking trajectory, and to satisfy the requirements on second-order parametric and geometric continuities, the Fermat’s Spiral (FS) having advantages of low computational load and engineering practicability is selected to design the transition path between multiple straight segments. The scaling of FS segments is optimized by considering the maneuverability of AMVs. Besides, the FS is parameterized in both transition modes to simplify the subsequent guidance and control scenarios. Thirdly, the closed-form analysis on geometric and parametric continuities of spliced transition path are derived. Finally, based on the parameterized smooth path and a slender underactuated AUV, numerical simulation demonstrates the effectiveness of the FS-based path planning method under integrated origin-departing and corner-cutting transition modes.