Designing good heuristic functions for graph search requires adequate domain knowledge. It is often easy to design heuristics that perform well and correlate with the underlying true cost-to-go values in certain parts of the search space but these may not be admissible throughout the domain thereby affecting the optimality guarantees of the search. Bounded suboptimal search using several such partially good but inadmissible heuristics was developed in Multi-Heuristic A* (MHA*). Although MHA* leverages multiple inadmissible heuristics to potentially generate a faster suboptimal solution, the original version does not improve the solution over time. It is a one shot algorithm that requires careful setting of inflation factors to obtain a desired one time solution. In this work, we tackle this issue by extending MHA* to an anytime version that finds a feasible suboptimal solution quickly and continually improves it until time runs out. Our work is inspired from the Anytime Repairing A* (ARA*) algorithm. We prove that our precise adaptation of ARA* concepts in the MHA* framework preserves the original suboptimal and completeness guarantees and enhances MHA* to perform in an anytime fashion. Furthermore, we report the performance of A-MHA* in 3-D path planning domain and sliding tiles puzzle and compare against MHA* and other anytime algorithms.

In unstructured environments like parking lots or construction sites, due to the large search-space and kinodynamic constraints of the vehicle, it is challenging to achieve real-time planning. Several state-of-the-art planners utilize heuristic search-based algorithms. However, they heavily rely on the quality of the single heuristic function, used to guide the search. Therefore, they are not capable to achieve reasonable computational performance, resulting in unnecessary delays in the response of the vehicle. In this work, we are adopting a Multi-Heuristic Search approach, that enables the use of multiple heuristic functions and their individual advantages to capture different complexities of a given search space. Based on our knowledge, this approach was not used previously for this problem. For this purpose, multiple admissible and non-admissible heuristic functions are defined, the original Multi-Heuristic A* Search was extended for bidirectional use and dealing with hybrid continuous-discrete search space, and a mechanism for adapting scale of motion primitives is introduced. To demonstrate the advantage, the Multi-Heuristic A* algorithm is benchmarked against a very popular heuristic search-based algorithm, Hybrid A*. The Multi-Heuristic A* algorithm outperformed baseline in both terms, computation efficiency and motion plan (path) quality.

Recently, several researchers have brought forth the benefits of searching with multiple (and possibly inadmissible) heuristics, arguing how different heuristics could be independently useful in different parts of the state space. However, algorithms that use inadmissible heuristics in the traditional best-first sense, such as the recently developed Multi-Heuristic A* (MHA*), are subject to a crippling calibration problem: they prioritize nodes for expansion by additively combining the cost-to-come and the inadmissible heuristics even if those heuristics have no connection with the cost-to-go (e.g., the heuristics are uncalibrated) . For instance, if the inadmissible heuristic were an order of magnitude greater than the perfect heuristic, an algorithm like MHA* would simply reduce to a weighted A* search with one consistent heuristic. In this work, we introduce a general multi-heuristic search framework that solves the calibration problem and as a result a) facilitates the effective use of multiple uncalibrated inadmissible heuristics, and b) provides significantly better performance than MHA* whenever tighter sub-optimality bounds on solution quality are desired. Experimental evaluations on a complex full-body robotics motion planning problem and large sliding tile puzzles demonstrate the benefits of our framework.

We present a novel heuristic search framework, called Multi-Heuristic A* (MHA*), that simultaneously uses multiple, arbitrarily inadmissible heuristic functions and one consistent heuristic to search for complete and bounded suboptimal solutions. This simplifies the de- sign of heuristics and enables the search to effectively combine the guiding powers of different heuristic func- tions. We support these claims with experimental results on full-body manipulation for PR2 robots.