In this paper, we present a method of multi-robot motion planning by biasing centralized, sampling-based tree search with decentralized, data-driven steer and distance heuristics. Over a range of robot and obstacle densities, we evaluate the plain Rapidly-expanding Random Trees (RRT), and variants of our method for double integrator dynamics. We show that whereas plain RRT fails in every instance to plan for $4$ robots, our method can plan for up to 16 robots, corresponding to searching through a very large 65-dimensional space, which validates the effectiveness of data-driven heuristics at combating exponential search space growth. We also find that the heuristic information is complementary; using both heuristics produces search trees with lower failure rates, nodes, and path costs when compared to using each in isolation. These results illustrate the effective decomposition of high-dimensional joint-space motion planning problems into local problems.

Large environments are challenging for path planning algorithms as the size of the configuration space increases. Furthermore, if the environment is mainly unexplored, large amounts of the path are planned through unknown areas. Hence, a complete replanning of the entire path occurs whenever the path collides with newly discovered obstacles. We propose a novel method that stops the path planning algorithm after a certain distance. It is used to navigate the algorithm in large environments and is not prone to problems of existing navigation approaches. Furthermore, we developed a method to detect significant environment changes to allow a more efficient replanning. At last, we extend the path planner to be used in the U-Shift concept vehicle. It can switch to another system model and rotate around the center of its rear axis. The results show that the proposed methods generate nearly identical paths compared to the standard Hybrid A* while drastically reducing the execution time. Furthermore, we show that the extended path planning algorithm enables the efficient use of the maneuvering capabilities of the concept vehicle to plan concise paths in narrow environments.

Recent work aimed at developing a deeper understanding of suboptimal heuristic search has demonstrated that the use of a cost-based heuristic function in the presence of large operator cost ratio and the decision to allow re-opening of visited nodes can have a significant effect on search effort. In parallel research, phase transitions in problem solubility have proved useful in the study of problem difficulty for many computational problems and have recently been shown to exist in heuristic search problems. In this paper, we show that the impact on search effort associated with a larger operator cost ratio and the number of node re-expansions is concentrated almost entirely in the phase transition region. Combined with previous work connecting local minima in the search space with such behavior, these observations lead us to hypothesize a relationship between the phase transition and the existence of local minima.

In various domains, such as computer games, robotics, and transportation networks, shortest paths may need to be found quickly. Search time can be significantly reduced if it is known which parts of the graph include "swamps" - areas that cannot lie on the only available shortest path, and can thus safely be pruned during search. We introduce an algorithm for detecting hierarchies of swamps, and exploiting them. Experiments support our claims of improved efficiency, showing significant reduction in search time.