The performance of heuristic search-based planners depends heavily on the quality of the heuristic function used to focus the search. These algorithms work fast and generate high-quality solutions, even for high-dimensional problems, as long as they are given a well-designed heuristic function. On the other hand, their performance can degrade considerably if there are large heuristic depression regions, i.e. regions in the search space where heuristic values do not correlate well with the actual cost-to-goal values. Consequently, the research in developing an efficient planner for a specific domain becomes the design of a good heuristic function. However, for many domains, it is hard to design a single heuristic function that captures all of the complexities of the problem. Furthermore, it is hard to ensure that heuristics are admissible (provide lower bounds on the cost-to-goal) and consistent, which is necessary for A* like searches to provide guarantees on completeness and bounds on sub-optimality. In this paper, we develop a novel heuristic search, called Multi-Heuristic A* (MHA*), that takes in multiple, arbitrarily inadmissible heuristic functions in addition to a single consistent heuristic, and uses all of them simultaneously to search in a way that preserves guarantees on completeness and bounds on sub-optimality. This enables the search to combine very effectively the guiding powers of different heuristic functions and simplifies dramatically the process of designing heuristic functions by a user because these functions no longer need to be admissible or consistent. We support these claims with experimental analysis on several domains ranging from inherently continuous domains such as full-body manipulation and navigation to inherently discrete domains such as the sliding tile puzzle.

Incremental heuristic search algorithms reuse their previous search efforts whenever these are available. As a result, they can often solve a sequence of similar planning problems faster than planning from scratch. State-of-the-art incremental heuristic searches (such as LPA*, D* and D* Lite) work by propagating cost changes to all the states in the search tree whose g values (the costs of computed paths from the start state) are no longer optimal. This work is based on the observation that while a complete propagation of cost changes is essential to ensure optimality, the propagations can be stopped earlier if we are looking close-to-optimal solutions instead of the optimal one. We develop a framework called Truncated Incremental Search that builds on this observation and uses a target suboptimality bound to efficiently restrict cost propagations. We present two truncation based algorithms, Truncated LPA* (TLPA*) and Truncated D* Lite (TD* Lite), for bounded suboptimal planning and navigation in dynamic graphs. We also develop an anytime replanning algorithm, Anytime Truncated D* (ATD*), that combines the inflated heuristic search with truncation, in an anytime manner. We discuss the theoretical properties of these algorithms proving their correctness and efficiency, and present experimental results on 2D and 3D (x, y, heading) path planning domains evaluating their performance. The empirical results show that the truncated incremental searches can provide significant improvement in runtime over existing incremental search algorithms, especially when searching for close-to-optimal solutions in large, dynamic graphs.

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