# Event-Based Path-Planning and Path-Following  
in Unknown Environments for Underactuated Autonomous Underwater Vehicles  
[PERSON]  
1 Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, 134, Lemontova str., Irkutsk 664033, Russia; [EMAIL_ADDRESS] (I.B. ); [EMAIL_ADDRESS] (N.M.)1 Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, 134, Lemontova str. implementation. Real-time path planning can be achieved while using artificial potential field method [8], rapidly-exploring random trees [9; 10], Voronoi diagrams [11], bioinspired meta-heuristics [12], method based on interfered fluid dynamical system [13], and waypoint guidance method [4; 14; 15]. Additionally, AI-based optimization algorithms are actively applied to path-planning of AUVs in an unknown environment. Among them are particle swarm optimization (PSO) algorithm [5; 16; 17], ant colony algorithm [18], and differential evolution algorithm [19]. Many approaches are combined in order to provide the best solution. For example, in [4], PSO determines the best direction to avoid obstacles, and the waypoint guidance algorithm generates a sequence of points that provide a way around the obstacle in the selected direction. Almost all of the mentioned methods indirectly or directly use iterative procedures in order to obtain a locally optimal path. However, when dealing with an unknown environment, extensive optimization requiring significant computing resources is meaningless in many cases, since the resulting local path may not be optimal in the global sense. It should be noted that optimization-based methods do not always guarantee obtaining a near-optimal solution in a reasonable time. Thus, approaches that generate feasible paths in a short time are still in demand. It is known that AUVs operate in fairly harsh underwater environments and they are designed to be underactuated to reduce their costs. All of this imposes additional requirements to path planning algorithms; the planner must produce paths that meet the kinematic and dynamic constraints of the vehicle. In order not to take the AUV model explicitly into account when planning the path, kinematic constraints are often set by the minimum turning radius [4; 5; 14; 16]. In this case, the obtained path, which usually consists of straight lines and circular arcs, is only first-order differentiable or smooth. The degree of smoothness of the path can be increased with the help of splines [12], but their use makes the planning process more complicated due to the need to meet the geometrical constraints of obstacles. Another common approach for satisfying kinematic constraints consists in building a path of minimum curvature via solving a nonlinear programming problem [20]. The path planning problem can be considered in three different contexts, depending on the global goal pursued by the AUV. The variety of possible goals includes achieving a target point, navigating through a sequence of waypoints, and following a predefined reference path, in particular a path that connects waypoints by line and arc segments. Most of the studies mentioned above focus on path-planning within the first setting. Despite the great applied value, the path planning problem in which the AUV has to pass through a bunch of waypoints in a given order is practically not investigated. In this context, we can only refer to paper [21]. The main difficulties in handling multiple waypoints arise when some of them are located on obstacles. In this case, an additional mechanism for managing the activity of waypoints are required. The need for the AUV to follow the desired path makes the problem more complicated, since it is necessary to provide the return of the AUV to the reference path after completing obstacle avoidance manoeuvres. Once a path is generated, one needs to make the AUV follow the path accurately, when considering its dynamic model, control constraints, and kinematics.