# Voxel-Based Navigation: A Systematic Review of Techniques, Applications, and Challenges
## 5 Voxel-Based Navigation
### Outdoor Navigation  
Outdoor and indoor navigation differ significantly. Outdoor navigation involves diverse terrain features, such as city streets, forests, and mountains, and requires handling complex obstacles. We divide outdoor navigation into two scenarios: real-time navigation in unknown environments and path planning in pre-established environments, each with unique challenges and methods. In real-time navigation, sensors like cameras, radar, and LiDAR play a crucial role in generating real-time maps for safe navigation. For example, Ref. [99] developed a navigation system for mobile robots in agricultural environments, using 3D camera data to build a three-dimensional voxel map of the agricultural environment. This voxel map allows the robot to identify open spaces and navigate efficiently within them. The ability to create and update such maps is crucial in dynamic and complex environments. Ref. [103] used scanners mounted on rotating mechanisms to divide scanned spaces into voxels for pedestrian recognition and tracking, minimizing the likelihood of collisions between mobile robots and crowds. Ref. [100] introduced a camera-LiDAR fusion method to address forest occlusion and lighting variation issues. They constructed a three-dimensional voxel map of the forest and introduced adjacency feature assessments based on the voxel map to estimate the navigability of the forest environment, enabling ground autonomous vehicles to traverse complex and dense forest terrains. In the second scenario, path planning in established environments depends on existing maps of the surrounding area. Ref. [104] combined 2D and 3D datasets collected by robot sensors and developed a ground-segmentation method to detect non-ground objects, helping to create detailed and accurate environmental maps. Ref. [105] proposed an integrated path-planning method combining the three-dimensional voxel Jump Point Search (JPS) and the Markov Decision Process (MDP) to address static obstacles and dynamic threats. The 3D voxel JPS is used to generate global reference paths, ensuring collision-free flight paths around known static obstacles, thereby guiding drones safely through urban environments. By dividing complex three-dimensional spaces into regular voxel grids, voxel models can describe obstacles and terrain features in detail, which is crucial for handling complex terrains, such as forests, city streets, or mountainous regions. Additionally, real-time updates to voxel data can address moving obstacles and emergent situations, providing stable and reliable path-planning support for outdoor navigation tasks of varying scales and complexities. Compared to other outdoor scenarios, autonomous driving presents unique challenges, due to the complexity and dynamic nature of the driving environment. Autonomous systems must contend with dynamic obstacles, such as other vehicles, pedestrians, and cyclists, as well as navigate through dense urban structures and narrow roads. These factors place higher demands on environmental perception and path planning, warranting a separate discussion of autonomous driving scenarios. Ref. [52] proposed a voxel-based method to segment static and dynamic obstacles. This system integrates time-dependent data to construct a voxel grid model, and it uses discriminant analysis to detect these obstacles (see Figure 10). Ref. [107] utilized LiDAR sensors on Autonomous Vehicles (AVs) to perceive the surrounding environment by voxelizing the 3D space with a fixed unit size and applying deep-learning techniques to identify voxels that exhibit key dynamic features. This approach enables rapid identification of objects that may impact AV safety and tracks their movement in the 3D observation space around the AV, providing a comprehensive safety assessment of the driving scenario. One critical aspect of vehicle navigation is accurately detecting road features, such as sidewalks, curbs, and lane markings. To this end, ref.