# Autonomous Mobile Robot Navigation in Sparse LiDAR Feature Environments
## 1 Introduction
### Path Planning and Trajectory-Tracking Algorithms  
In unmanned vehicle navigation, path planning is essential to search for an optimal path from one point to another point in the environment. Researchers have adopted different methods to solve the problem of AGV path planning, two of which are grid search-based methods and intelligent-based methods. Grid Search-based methods include the A\({}^{*}\) algorithm and its variants. [PERSON] et al. [1] proposed an improved A\({}^{*}\) path planning algorithm based on a compressed map to reveal actual narrow areas the robot cannot reach although this approach produces some precision loss, leading the path to be conservative. To reduce the redundant points in A\({}^{*}\) algorithm pathfinding process, [PERSON] et al. [2] used Jump Point Search to obtain jump points in the raster map and speed up the A\({}^{*}\) algorithm based on obtained jump points, though the search time fluctuates in different practical scenarios. For intelligent-based methods, [PERSON] et al. [3] proposed an improved genetic algorithm under a global static environment, which improved the slow convergence and precoity problems. Meanwhile, [PERSON] et al. [4] refined inertia weights and accelerationfactors in Particle Swarm Optimization to prevent local minimum value falling and increase convergence speed.  
Following path planning process, trajectory tracking is required so that the AGV can track the movement according to a set trajectory path. With the development of technology, various trajectory-tracking methods have been proposed. [PERSON] et al. [5] introduced a local linear Model Predictive Control (MPC) to track the nonlinear vehicle model velocity and path simultaneously. In [6], a reference trajectory is predefined using a sigmoid function. Then the trajectory is adjusted dynamically by a nonlinear MPC when an obstacle appears in the predictive horizon. Besides MPC, [PERSON] et al. [7] proposed a Fixed-Time Control method and a Fixed-Time Sliding Mode Controller to trajectory-tracking control while meeting the predetermined performance and disturbance suppression. Furthermore, an adaptive trajectory-following strategy was proposed in [8] that constructs a knowledge database through the Particle Swarm Optimization (PSO) algorithm to optimize the controller parameters set according to various vehicle speed and heading error combinations. Meanwhile, [PERSON] et al. [9] proposed a hybrid visual trajectory strategy in which a 2.5D visual servo framework was used to enhance trajectory-tracking behavior.  
Although non-geometric controllers such as MPC can be applied to linear or nonlinear models with multiple constraints, their limitations are heavy computation and an inability to provide a closed-form solution when the model is sophisticated. On the other hand, the Pure Pursuit (PP) algorithm is a popular trajectory-tracking algorithm because of its simplicity, efficiency, and low computational requirements, even in limited resource conditions. It computes angular velocity to move the robot from its current position to some look-ahead point in front of the robot. However, the tracking performance is poor due to improper selection of the look-ahead distance. [PERSON] et al. [10] combined the PP algorithm with Proportional Integral (PI) Controller to smooth the final output steering angle through a low-pass filter and verify its feasibility through simulation experiments. By analyzing the vehicle speed and the shortest distance between the GPS trajectory and the current vehicle position, [PERSON] et al. [11] proposed an algorithm that can reduce the lateral error when the vehicle tracks the ideal path. Meanwhile, a Pure Pursuit algorithm based on the optimized look-ahead distance (OLDPPA) [12] introduced an adaptive random motion mechanism of particles in the Salp Swarm Algorithm to improve mining and exploration capabilities.