AIT* and EIT*: Asymmetric bidirectional sampling-based path planning (2111.01877v2)

Abstract: Optimal path planning is the problem of finding a valid sequence of states between a start and goal that optimizes an objective. Informed path planning algorithms order their search with problem-specific knowledge expressed as heuristics and can be orders of magnitude more efficient than uninformed algorithms. Heuristics are most effective when they are both accurate and computationally inexpensive to evaluate, but these are often conflicting characteristics. This makes the selection of appropriate heuristics difficult for many problems. This paper presents two almost-surely asymptotically optimal sampling-based path planning algorithms to address this challenge, Adaptively Informed Trees (AIT*) and Effort Informed Trees (EIT*). These algorithms use an asymmetric bidirectional search in which both searches continuously inform each other. This allows AIT* and EIT* to improve planning performance by simultaneously calculating and exploiting increasingly accurate, problem-specific heuristics. The benefits of AIT* and EIT* relative to other sampling-based algorithms are demonstrated on twelve problems in abstract, robotic, and biomedical domains optimizing path length and obstacle clearance. The experiments show that AIT* and EIT* outperform other algorithms on problems optimizing obstacle clearance, where a priori cost heuristics are often ineffective, and still perform well on problems minimizing path length, where such heuristics are often effective.

• The paper introduces novel AIT* and EIT* algorithms employing asymmetric bidirectional search to adaptively refine heuristics.
• The methodology combines forward search for path discovery with reverse search to efficiently compute and update heuristics without full collision detection.
• Experimental results show that AIT* and EIT* outperform traditional methods like RRT* and BIT* across various domains, particularly in challenging environments.

Asymmetric Bidirectional Sampling-Based Path Planning: AIT* and EIT*

The paper under discussion presents two novel sampling-based path planning algorithms—Adaptively Informed Trees (AIT*) and Effort Informed Trees (EIT*)—designed to efficiently navigate complex environments using adaptive heuristics. These algorithms address the challenge of selecting appropriate heuristics in path planning, where the goal is to determine an optimal sequence of states between a start point and a goal. AIT* and EIT* represent a significant advancement over traditional approaches by utilizing an asymmetric bidirectional search that employs both forward and backward search strategies to continuously inform each other. This technique allows the algorithms to adaptively enhance the accuracy of heuristics over time.

Overview and Methodology

1. Adaptive Heuristics:

AIT* improves planning performance by calculating and exploiting accurate, problem-specific heuristics during the search process. It leverages an asymmetric bidirectional approach where the forward and reverse searches enhance heuristic accuracy. This is particularly advantageous in scenarios where a priori heuristics are either not available or not sufficiently informative. EIT* further extends AIT* by integrating both cost and effort heuristics, thereby yielding even superior performance under diverse optimization objectives.

2. Reverse Search for Heuristic Calculation:

The reverse search component of AIT* and EIT* focuses on calculating heuristics by examining the sampled states and their interconnections, without performing full collision detection. By synthesizing estimates of edge heuristics, the reverse search achieves computational efficiency and contributes to more informed forward searches. This results in an increasingly accurate heuristic landscape that guides the forward search more effectively.

3. Forward Search for Pathfinding:

The forward search is responsible for finding valid paths through the approximated state space graph. It exploits the calculated heuristics from the reverse search to prioritize paths likely to reach a solution swiftly. This informed search order reduces unnecessary evaluations, as exemplified by the comparison of evaluated edges in traditional and informed approaches (see accompanying illustrations).

Experimental Evaluation

The paper demonstrates the efficacy of AIT* and EIT* through evaluations on twelve diverse path planning problems, encompassing abstract, robotic, and biomedical domains, and optimizing for objectives like path length and obstacle clearance. AIT* and EIT* consistently outperform other algorithms, such as RRT* and BIT*, particularly in scenarios with no readily available admissible cost heuristics. EIT* shows notable superiority in problems optimizing obstacle clearance, where prior heuristic methods fall short.

Implications and Future Directions

The introduction of AIT* and EIT* holds promising implications both theoretically and practically. The enhanced ability to handle varied and dynamic environments with adaptive heuristics opens avenues for further research into heuristic adaptation across more complex objectives, potentially merging with machine learning techniques for online heuristic adaptation. The integration of both cost and effort metrics in a dynamic search environment suggests potential expansions into other domains requiring real-time decision-making under uncertainty.

In summary, the AIT* and EIT* algorithms represent a significant evolution in sampling-based path planning, offering a robust framework for incorporating adaptive, problem-specific heuristics in search processes. Such innovations hold substantial promise for advancing the field of autonomous planning and robotics.