AUV Rendezvous Online Path Planning in a Highly Cluttered Undersea Environment Using Evolutionary Algorithms Somaiyeh MahmoudZadeh· Amir Mehdi Yazdani· Karl Sammut· David M.W Powers Centre for Maritime Engineering, Control and Imaging, School of Computer Science, Engineering and Mathematics, Flinders University, Adelaide, SA 5042, Australia somaiyeh.mahmoudzadeh@flinders.edu.au amirmehdi.yazdani@flinders.edu.au karl.sammut@flinders.edu.au david.powers@flinders.edu.au Abstract- In this study, a single autonomous underwater vehicle (AUV) aims to rendezvous with a submerged leader recovery vehicle through a cluttered and variable operating field. The rendezvous problem is transformed into a nonlinear optimal control problem (NOCP) and then numerical solutions are provided. A penalty function method is utilized to combine the boundary conditions, vehicular and environmental constraints with the performance index that is final rendezvous time. Four evolutionary based path planning methods namely particle swarm optimization (PSO), biogeography-based optimization (BBO), differential evolution (DE) and Firefly algorithm (FA) are employed to establish a reactive planner module and provide a numerical solution for the proposed NOCP. The objective is to synthesize and analysis the performance and capability of the mentioned methods for guiding an AUV from loitering point toward the rendezvous place through a comprehensive simulation study. The proposed planner module entails a heuristic for refining the path considering situational awareness of underlying environment, encompassing static and dynamic obstacles overwhelmed in spatiotemporal current vectors. This leads to accommodate the unforeseen changes in the operating field like emergence of unpredicted obstacles or variability of current vector filed and turbulent regions. The simulation results demonstrate the inherent robustness and significant efficiency of the proposed planner in enhancement of the vehicle’s autonomy in terms of using current force, coping undesired current disturbance for the desired rendezvous purpose. Advantages and shortcoming of all utilized methods are also presented based on the obtained results. Keywords- Rendezvous, NOCP, reactive path planning, autonomous underwater vehicles, evolutionary algorithms 1 Introduction AUV rendezvous with a mother ship, mobile recovery station or submerged vehicle has been an area of interest in recent underwater surveys and oceanic exploration [1-3]. It provides a facility for updating the mission, refueling, data transferring and results in increasing AUV’s endurance and extension of underwater operation. To do so, the vehicle needs to have a certain level of autonomy chiefly tied-up with the path planning procedure. The path planner should be capable of generating geometric path and corresponding traj ectory for at least relevant states such as vehicle’s heading and velocity profile to safely guide the vehicle form loitering pint to the target of desired rendezvous area, while optimizing a performance index like flight time or energy expenditure. However, the AUV’s operation through a non-characterized and cluttered undersea environment adds some difficulties for reliable and optimal rendezvous process [4] On one side, existence of moving obstacles may lead to change the rendezvous conditions, as time goes on, and on the other side, variability of ocean current components has considerable impact in drifting the vehicle from target of interest [5]. In such a situation, adaptability of the path planner to a strong environmental variability is a key element to carry out the mission safely and successfully. An efficient trajectory produced by the path planner enables an AUV to cope with adverse currents as well as exploit desirable currents to enhance the operation speed that results in considerable energy saving. The first step toward having a satisfactory rendezvous mission is to find out a suitable and efficient method of path planning. This needs to technically analysis the available methods in the state of the art. In general, the challenges associated with the path planning can be considered form two perspective; firstly, the mechanism of the algorithms being utilized, and secondly the competency of the techniques for real-time applications. A plethora of research suggested deterministic methods for solving unmanned vehicle’s path planning problem [6-9]. Path planning based on deterministic methods is carried out on repeating a set of predefined steps that search for the best fitted solution to the objectives [6]. For instance, a non-linear least squares optimization technique is employed for AUV path planning through the Hudson River [7] and sliding wave front expansion algorithm is applied to generate appropriate path for AUVs in presence of strong current fields [8]. In [9], level set methods are exploited to provide an energy-efficient optimal path for AUV considering the benefit of current vectors. All abovementioned deterministic methods are criticized for their weak performance and expensive computational cost in high- dimensional problems. For a group of problems in which the deterministic techniques and classic search methods are not capable of finding exact solutions, the heuristic-grid search approaches are good alternatives with fast computational speed, specifically in dealing with multi-objective optimization problems. Some heuristic search methods such as Dijkstra's, A*, and D* algorithms have been provided and applied to the AUV path planning problem in recent years [10-12]. In [13,14] A* method is utilized to provide a time optimal path with minimum risk for a glider path planning according to an offline data set. D* algorithm