# Path Planning Based on Artificial Potential Field with an Enhanced Virtual Hill Algorithm
## 1 Introduction  
Unlike complex global path planning [1], which requires a vast amount of prior information, the local method allows for path planning, including obstacle avoidance, in an unknown environment with a small amount of computation. Local path planning using the APF (artificial potential field) technique has been widely used in real-time path planning due to its easy implementation and high computational efficiency [2; 3; 4; 5; 6; 7; 8; 9]. APF is formed by the sum of the attractive potential field to reach the destination and the repulsive potential field to avoid obstacles [10]. Due to the potential at each point, the robot travels to the destination without colliding. In this process, when the sum of potentials approaches '0', local minima may occur, in which the robot stops operating [11; 12]. In order to apply the APF technique, this problem must be solved, and various techniques have been studied so far. There are methods of modifying the potential field function or the repulsive force function [13; 14; 6; 15] or adding vortex fields or local attractors [16; 17; 18]. In [17], vortex fields prevent collisions between obstacles and robots and enable smooth running when the robot moves through narrow corridors. However, it is difficult to determine when to apply vortex potential for optimal performance, and it may not be effective in complex environments. References [7; 19] propose a short and optimal path planning method using bacterial foraging optimization. In [7], virtual particles are initially moved randomly, the cost is calculated at each location, the best particle is found, and the robot's driving path is created. The optimal path can be found even in complex environments. Reference [19] shows that when a robot is trapped in a local minimum, a virtual obstacle suitable for the location condition is created, and the robot is guided to move to a new path. However, both of these techniques require an iterative learning process to optimize the path and virtualobstacles. In the bacterial potential field method [20], the problems of the APF are solved by applying the bacterial evolutionary algorithm (BEA) in addition. There are also methods to plan the optimal path while solving the local minimum using simulated annealing (SA), a genetic algorithm (GA), or reinforcement learning [21; 22; 23; 24]. Reference [24] introduces an algorithm that converges to the optimal path using reward and value functions. The optimal path can be found through automatic learning without prior information. However, since it starts randomly, it can be unstable and requires a lot of calculations to optimize the path. References [25; 26] propose new algorithms to be combined with APF. In [26], the improved A* algorithm is fused with APF, and search accuracy and efficiency are improved using a heuristic method. To escape the local minimum, a virtual target point is set in [27; 28], and a grid-based obstacle cell is used in [29; 30]. In [30], efficient computation is possible using a discrete grid, and local minima can be avoided by creating a new repulsive potential between adjacent obstacles. However, if the resolution of the grid is low, precise path planning is difficult, and if the resolution is high, the amount of calculation increases. A perpendicular approach based on APF has been proposed as a local path plan for unknown obstacles along with a global path plan performed before the departure of the robot [31]. This method can solve the local minima problem with a relatively short calculation time, but it is difficult to apply in an unknown environment because it requires prior information about obstacles. Recently, research on learning-based optimization techniques has been introduced to overcome the shortcomings of APF. These methods can find the optimal path for robots even in complex environments and efficiently avoid and escape local minima.