# Multi-Task Agent Hybrid Control in Sparse Maps and Complex Environmental Conditions
## 2 Path Planning Algorithms Under Sparse Map Conditions
### Research Background on Path Planning Under Sparse Map Conditions  
In contemporary path planning research, non-heuristic (i.e., deterministic or exact) path planning algorithms, such as dynamic programming, geometric algorithms, potential field methods, and Mixed Integer Linear Programming (MILP), can provide optimal solutions but typically require substantial computational resources. The core of these methods involves dividing the entire detection area or map into multiple computational domains using tools like matrix decomposition. However, as the problem size increases, their computational demands grow exponentially. In contrast, heuristic path planning algorithms, like the A* algorithm, demonstrate significant advantages in efficiency and versatility by effectively reducing the search range and increasing computation speed, thereby enabling the acquisition of real-time feasible paths.  
The traditional A* algorithm, when used for path planning, only considers two discrete states on the map: \"open space\" and \"obstacles\". This approach often results in planned paths that closely skirt obstacles to minimize travel distance. However, in real-world scenarios, most obstacles do not rise vertically from the ground; their elevation from the ground level typically increases gradually until they reach a point where they are considered \"obstacles\". Existing research on the A* algorithm in three-dimensional spaces is mostly applicable to drones, which have a high degree of mobility freedom [12; 13; 14; 15]. Drones can ascend, descend, and move in any direction in space. This requires their A* algorithm to consider a wider range of movement constraints and flight dynamics, as well as a greater need to adapt to rapidly changing aerial environments and perform real-time obstacle avoidance. In contrast, the movement of ground-based intelligent agents in complex environments is subject to more terrain constraints. Their path planning needs to focus on the passability of the terrain and ground obstacles, requiring more consideration of stability and energy consumption optimization compared to drone path planning algorithms. Figure 1 shows a comparison of the results obtained from path planning using binary maps and elevation maps.  
When planning paths for intelligent agents in complex environments, the objective extends beyond merely finding the shortest route. Additional factors, such as path smoothness, obstacle avoidance, and minimizing turns, must be accounted for, transforming path planning into a multi-constraint optimization problem. In scenarios where only sparse maps are available, the algorithm must address not only path length optimization but also map inaccuracies, striving to maintain a safe distance from obstacles and a smooth trajectory to enhance the adaptability and efficiency of the agent in real-world settings. Despite the effectiveness of the adaptive A* algorithm in improving path robustness, its increased computational time poses a limitation, especially critical in extraterrestrial missions where resources are constrained.  
To mitigate this, future research could explore adaptive tuning strategies that adjust the heuristic based on terrain type, allowing the algorithm to allocate computational resources more efficiently in areas with high gradient variations. Additionally, heuristic optimization techniques, such as hierarchical path refinement or terrain-based heuristic adjustments, could be integrated to dynamically balance computational demands while maintaining high safety standards in complex three-dimensional space path planning for ground-based agents operating with sparse maps. These strategies may help close existing gaps in current research on path planning in such challenging environments.