# High-Efficiency Navigation of Nonholonomic Mobile Robots Based on Improved Hybrid A* Algorithm
## 1 Introduction
The local dynamic path planning is mainly divided into two approaches [14]. The first approach involves the detection  
Figure 1: The collision schematic diagram. (**a**) The collision of Ackermann chassis due to the limitation of transverse angle. (**b**) Avoiding collision via flexible path planning. of new obstacles in the environment and obtaining space information. The robot then conducts replanning at the navigation planning level to obtain a new collision-free path that is sent to the underlying tracking controller for executing movement. The typical methods in this category include the artificial potential field (APF) method, grid planning method, and others. However, these methods require replanning and outputting control commands, resulting in a large amount of computation, and cannot meet the real-time requirements. The other approach to local path planning at the motion control level involves considering the nonholonomic-constraint characteristics of the robot. The primary concept is to establish an optimal control problem in the unit-time step when facing new obstacles and solve the optimization problem while obtaining the optimal trajectory and the corresponding control input. The primary representative methods of this approach include the dynamic window approach (DWA) [15], time-elastic belt (TEB) approach [16], and local planning based on model predictive control (MPC) [17] which is widely used for avoiding collisions [18]. [PERSON] et al. proposed the A1-0 Bg-RRT algorithm to reduce computational time in complex environments [19]. [PERSON] et al. proposed the algorithm for ships with INS-aided shipborne GNSS, which considered the measurement update from one-dimensional speed [20]. [PERSON] et al. introduced the Bezier curve method to smooth the routes [21]. However, when applied to nonholonomic constraints, these algorithms show slow navigation speed and can generate non-optimal paths. Nonholonomic mobile robots such as Ackermann architecture mobile robots, single-wheel inverted pendulum robots and three-wheeled omnidirectional mobile robots have fewer controlled variables than state variables during motion, which can easily lead to motion slipping problems. How to control nonholonomic mobile robots to reach the target location and face the target direction are a challenging task, and extensive research has been conducted in this area. For example, [PERSON] et al. [22] proposed a predictive control scheme based on tailored nonquadratic stage cost to address this issue. [PERSON] et al. [23] proposed a novel evaluation function based on the Theta-star search algorithm. The new function can generate waypoints with an empirically averaged distance to obstacles. In 2020, [PERSON] et al. [24] proposed a graph-based multi-agent path planner. The planner can effectively generate optimal collision-free trajectories for multiple nonholonomic mobile robots in environments with multiple obstacles. [PERSON] et al. [25] proposed the dynamic motion planning networks (Dynamic MPNet) algorithm. They modified the planning network to achieve real-time planning for nonholonomic robot motion planning problems, instead of simply relaxing constraints. By adjusting the steering of the robot through its path planner or driver, [PERSON] et al. [26] developed the method to assist navigation in dense crowds. However, although these path planning algorithms can accommodate nonholonomic constraints in robots, many inherent issues exist, e.g., suboptimal operating speed, failure in producing smoother paths with higher accuracy, and the randomly occurred excessive searches. This is because the heuristic function \(h(x)\) of the conventional A* algorithm is generally the Euclidean distance, which traverses a very large number of unnecessary nodes in planning the path and significantly limits the efficiency of navigation. To optimize the path planning, an improved hybrid A* algorithm was proposed in this paper with the intension to improve the performance of autonomous navigation of mobile robots with nonholonomic chassis.