Abstract: Based on the concept of the potential field method, this paper proposes a local collision avoidance simulation method for AUVs based on velocity potential fields. According to the characteristics of AUVs, a spatial collision hazard zone and a three-dimensional velocity potential field composed of horizontal and vertical velocity potential fields are established. This method makes good use of relative velocity information. Simulation experiments demonstrate that this method can achieve good local collision avoidance performance for AUVs in underwater environments with multiple moving obstacles, laying a solid foundation for future sea trials. Keywords: Autonomous underwater vehicle; Local collision avoidance; Velocity potential field; Moving obstacles 1 Introduction Collision avoidance has always been a fundamental problem in the motion planning of AUVs (Autonomous Underwater Vehicles). Due to the complexity of the underwater environment, not only stationary obstacles but also moving obstacles must be considered. Local collision avoidance often uses potential field-based methods. Potential field methods offer advantages such as good real-time performance and practicality in solving local collision avoidance problems involving static obstacles. However, their effectiveness is less than ideal when the obstacle is moving, leading to ineffective AUV movement. A typical example is the moving obstacle pushing the AUV off its trajectory without actually colliding. We believe this ineffective movement occurs because the potential field is generally built on the AUV's configuration space, and its collision avoidance decision only uses the obstacle's distance information, neglecting its velocity information. In reality, AUV collision avoidance planning should include mitigation of future hazards; therefore, the risk of collision must first be predicted before effective movement planning. Consequently, some scholars, in their research on local collision avoidance problems involving moving obstacles, have focused on utilizing obstacle motion information such as velocity and proposed different decision-making methods. Nam uses each observation period as a perception-decision period, employing a stochastic model to predict the movement of the moving obstacle within that period, assigning probability values ​​to its possible spatial points, and establishing a local artificial potential field based on this to achieve local collision avoidance. Ko_4 uses the projection of the relative velocity between the AUV and the obstacle onto the line connecting their positions as a weighting factor to modify the actual distance between them, establishing the concept of virtual distance, and using virtual distance as a variable to build a potential field. Tsubouchi uses the method of virtual impedance, which borrows the concept of damping and uses the relative velocity between the AUV and the obstacle to generate a damping force. This damping force acts in the direction of relative velocity, is proportional to the distance, and is independent of the relative position. Although these methods utilize velocity information in different ways, they are all based on position-based methods, that is, converting velocity information into position information in some way, or using velocity information to weight and correct position information, and then making position-based collision avoidance decisions. In contrast, this paper will directly use relative velocity information, and based on the dynamic environment of the AUV, use the polar coordinates of the relative velocity to establish a three-dimensional velocity potential field composed of a horizontal velocity potential field and a vertical velocity potential field. When the AUV encounters an obstacle, it achieves local collision avoidance by adjusting the velocity vector. 2. Algorithm Description: During the collision avoidance process of moving obstacles, the size of the obstacle is expanded, and the AUV avoids the expanded obstacle. As shown in Figure 1: The AUV (R) is treated as a point, and the moving obstacle O is expanded into a sphere with the center at point O (the radius OA is defined according to the obstacle's orientation and velocity information). A cone-shaped collision hazard zone is formed with the diameter circle O-AB perpendicular to the line connecting RO (the spatial distance between the AUV and the obstacle) as the base and RO as the height. The spatial velocity of the AUV relative to the obstacle is V[sub]RO[/sub]. If V[sub]RO[/sub] falls within the cone R-OAB, i.e., RO n(r-DAB) ≠ 0, then a hazard is constituted. The closer V[sub]RO[/sub] is to RO, the greater the hazard. Changing the size and direction of the AUV will affect the degree of collision hazard. The principle of collision avoidance: By continuously changing the speed and direction of movement, V[sub]RO[/sub] escapes the cone-shaped collision hazard zone and bypasses the obstacle. [align=center] Figure 1 Schematic diagram of relative velocity and collision area[/align] 3 Establishment of velocity potential field Due to the special nature of the AUV's working environment, it is necessary to establish a corresponding underwater three-dimensional velocity potential field. This paper divides the above-mentioned collision hazard area into horizontal and vertical planes, and decomposes the spatial velocities V[sub]R[/sub], V[sub]O[/sub], and V[sub]RO[/sub] between the AUV and the obstacle into V[sub]Rxy[/sub], V[sub]Oxy[/sub], V[sub]ROxy[/sub] (horizontal plane) and V[sub]Rxz[/sub], V[sub]Oxz[/sub], V[sub]ROxz[/sub] (vertical plane), and represents all velocity vectors in polar coordinates (V, ), where V is the magnitude of V and is the angle between V and P. Thus, the three-dimensional spatial collision hazard area is transformed into horizontal and vertical collision areas, as shown in Figure 2. The horizontal danger zone is R-KI-O-K2. If the relative velocity V[sub]ROxy[/sub] falls within this zone, a collision hazard is considered to exist. Similarly, the vertical danger zone is R-KI-O-K2. If V[sub]ROxz[/sub] falls within this zone, a collision hazard exists. [align=center]Figure 2 Planar division of collision hazard zone[/align] Establish a horizontal velocity potential field Us and a vertical velocity potential field Uc on (V, ): Us represents the velocity potential field of the AUV on the horizontal plane, representing the collision hazard degree of the AUV on the horizontal plane. Where: is the horizontal distance from the AUV to the moving target 0, d[sub]ms[/sub] is the shortest allowable distance between the AUV and the moving target; xy is the angle between V[sub]ROxy[/sub] and R0. Where, U[sub]ds[/sub] is used to measure the shortest distance between the AUV and the target, and U[sub]ts[/sub] is a measure of the time of collision. When U[sub]s[/sub]>0, it indicates that the horizontal relative velocity vector is within the collision region; the larger U[sub]s[/sub] is, the higher the collision risk. According to the magnitude of U[sub]s[/sub]>, the AUV should make a corresponding decision to reduce U[sub]s[/sub]>. Similarly, we can obtain the expression for the vertical surface velocity potential field U[sub]c[/sub]>: If both U[sub]ds[/sub] and U[sub]ts[/sub] are greater than 0, the final synthesized velocity potential field U is obtained from equation (9): Where: "" is the synthesis operator, and the influence of the horizontal surface velocity potential field is considered first in this paper. In the collision avoidance process, we adopt the common method in the potential field algorithm to make U[sub]ds[/sub] and U[sub]ts[/sub] change along their negative gradient direction, because the negative gradient direction is the direction in which U decreases the fastest. Therefore, we calculate the gradients of U[sub]ds[/sub] and U[sub]ts[/sub] respectively: We take the negative gradient direction of the potential field as the expected increment direction of the relative velocity vector of the moving obstacle in the horizontal plane XY and the vertical plane XZ. By setting the increment length, we obtain the expected relative velocity increment vectors △V[sub]ROxy[/sub] and △V[sub]ROxz[/sub]. Since the obstacle is uncontrolled, △V[sub]ROxy[/sub] and △V[sub]ROxz[/sub] can only be achieved by the velocity change of the AUV. When there are multiple moving obstacles, the multiple increment vectors can be added together to synthesize the velocity vector. 4 Simulation example To illustrate the effectiveness of the three-dimensional velocity potential field established in this paper, a simulation example of the AUV encountering moving obstacles A and B is given below. In the simulation, the AUV is a circular omnidirectional mobile robot. The velocity of the AUV is decomposed into the y (horizontal) direction and the -z (vertical) direction, and the XY and XZ planes are established. As shown in Figures 3 and 4: Figure 3 shows the horizontal trajectory curves of the AUV and obstacles at t=2 s, t=16 s, and t=24 s after the start of the simulation, where the dashed line represents the horizontal trajectory of the AUV without obstacles; Figure 4 shows the vertical trajectory curves of the AUV and obstacles A and B at t=2 s, t=16 s, and 24 s after the start of the simulation, where the dashed line represents the vertical trajectory of the AUV without obstacles. It can be clearly seen that by changing the relative velocity vector of the AUV, a good collision avoidance effect can be achieved. [align=center] [/align] 5 Conclusion This paper proposes a local collision avoidance method for AUVs based on three-dimensional velocity potential field theory. It makes full use of the information of relative velocity in the form of velocity potential field, thus achieving good local collision avoidance of moving obstacles. At the same time, since the algorithm is derived using relative velocity, it is applicable to both moving and stationary obstacles.