# Improved JPS Path Optimization for Mobile Robots Based on Angle-Propagation Theta* Algorithm
## 1 Introduction
### Related Work  
Path planning for mobile robots is actually the selection of a shortest obstacle avoidance path in the task area that can be connected from the starting point to the end point. The essence of this is the problem of optimal solution of the path [20]. The path planning should fully take into account the feasibility constraints that arise during the practical application of the robot [21]. More precisely, the path generated by the path planning algorithm of the mobile robot should satisfy the shortest and most efficient path with continuous and smooth transition of the path node states (position, velocity, acceleration and other information). Various path optimization methods have been developed in previous studies. Among the most intuitive methods for path smoothness optimization are Bessel curves [22] and B spline curve optimization [23]. This approach allows curve fitting using trajectory control points in the path generation phase to achieve path smoothing. Usually, the initial number of control points obtained by the global path planning algorithm is low fitting, and the fitted paths are prone to re-collide with obstacles. To increase the curve fit, the path control points are usually added. However, a single increase in the number of control points can lead to a significant decrease in the efficiency of the algorithm [24]. In the paper [13], a polynomial interpolation-based method is proposed to improve the continuity problem in the automatic parking process. Polynomial interpolation is a simple functional approach [25]. This method is solved by finding a polynomial containing all path nodes and adding continuity constraints for node positions, velocities, accelerations, etc. In  
Figure 1: Non-smooth path for mobile robots. addition, the polynomial interpolation method can be used to construct a Safe Flight Corridor (SFC) by generating collision avoidance linear constraints using the convex packet property of Bernstein polynomials as a further solution to the safety of mobile robots during operation [26]. The JPS method using heuristic search methods has been proposed in recent years driven by the efficiency of path planning for mobile robots. The classical JPS algorithm is built on the basis of the evaluation function of the A* algorithm, which improves the search efficiency of the A* algorithm by ignoring useless nodes and retaining only key nodes, thus greatly reducing the time consumption in the search process [27]. However, on the other hand, the JPS algorithm still cannot escape the limitation of the search direction imposed by the discretized grid map [28]. When planning a grid map, JPS usually plans from the center of each grid cell and only allows transitions to the center of adjacent grid cells. This will cause the JPS algorithm path direction variation to be limited to a multiple of \(\Pi/4\), resulting in a suboptimal path, as shown in Figure 2.  
The article [29] proposes an improved version of Field D* based on the D* algorithm. The algorithm generates smoother paths by linearly interpolating the grid so that the path points are not limited to endpoints and the planning direction is no longer limited to integer multiples of \(\Pi/4\). However, from the experimental results of the Field D* algorithm, the paths are not optimal, and there are still optimizable sections in the overall path. The Theta* family of algorithms is a good choice, where the Basic Theta* and AP-Theta* algorithms avoid the limitation of the angular direction of the search by passing information along the edges of the grid during the pathfinding process [30]. Among them, the AP-Theta* algorithm further solves the problem of insufficient operational efficiency of the Basic Theta* algorithm through the propagation of angular information. However, since the Theta* family of algorithms is designed based on the A* algorithm framework [31], it still suffers from the A* algorithm in terms of operational efficiency.