Date of Award

Spring 2026

Abstract

Heuristic search is a core area of artificial intelligence (AI) that explores state spaces using heuristic estimates to support planning and decision-making. In robotics, motion planning is a fundamental problem of computing feasible robot motion under constraints. A central challenge shared by both domains is how to substantially reduce unnecessary computation while preserving strong theoretical guarantees, such as completeness and optimality.

In response to this challenge, each domain has developed its own distinct methodological paradigms. In heuristic search, approaches broadly fall into unidirectional and bidirectional paradigms. Unidirectional heuristic search (Uni-HS) has a mature ecosystem, supported by decades of theory and widely used plug-and-play algorithms. In contrast, bidirectional heuristic search (Bi-HS) has remained comparatively underdeveloped and less standardized, despite important conceptual breakthroughs in ensuring \emph{meet-in-the-middle} property and optimality over the past decade.

In motion planning, planners typically explore the robot's configuration (state) space by either discretizing it into a discrete state space or incrementally approximating it using randomized sampling techniques to find feasible collision-free paths. However, computing high-quality solutions in high-dimensional continuous spaces remains challenging because of the computational cost of collision checks and the ``curse of dimensionality'', even with substantial advances such as anytime performance, informed sampling, heuristic search, and lazy edge evaluation strategy.

To address these challenges, this dissertation advances both bidirectional heuristic search and robotic motion planning. Motivated by the high computational cost and the inefficiency of current state-of-the-art methods, particularly the need to exhaustively explore all potential better solutions to ensure optimality and extensive collision detections for edges, we systematically analyze the factors driving these inefficiencies. This dissertation resolves two long-standing open questions in sampling-based motion planning (SBMP) and bidirectional heuristic search.

For sampling-based motion planning, we introduce Bidirectional Lazy Informed Trees (\blit), which incorporates an \emph{anytime-incremental lazy} bidirectional heuristic search framework for optimal robotic motion planning. \blit\ introduces the first anytime incremental bidirectional heuristic search at the search layer. Additionally, it develops a novel lazy edge evaluation strategy, focusing computational resources on states near obstacles. %\blit\ operates over informed and batch-wise samples in an implicit random geometric graph, performs incremental bidirectional search within each batch, and applies an obstacle-focused lazy edge-evaluation strategy that concentrates the computational resources on candidate solutions and critical connections. \blit\ enables rapid discovery of high-quality initial solutions and efficient convergence in high-dimensional continuous state spaces by significantly reducing the computational cost of collision checks.

For bidirectional heuristic search,we introduce \meet\ (Meet-in-the-middle with Early and Efficient Termination), a new bidirectional heuristic search algorithm that terminates search with a tighter termination condition. \meet\ terminates search without exhaustively exploring all potentially improving solutions. The resulting termination conditions are efficiently checkable, support principled pruning of non-improving states, and enable \emph{on-the-fly} cross-frontier heuristic refinement, all while preserving optimality guarantees on arbitrary graphs.

Empirical results demonstrate that: (i) in sampling-based motion planning, \blit\ outperforms state-of-the-art SBMP planners, including BIT*, AIT*, ABIT*, and EIT*, in both time-to-first-solution and convergence to the optimum across evaluated domains, with particularly strong performance in high-dimensional and complex environments; (ii) in heuristic search, \meet\ achieves runtime improvements of at least two orders of magnitude over \mm\ and is competitive with, or up to an order of magnitude faster than, \astar\ and \bae, particularly as heuristic quality degrades. Ablation and sensitivity studies further quantify the contributions of termination, pruning, heuristic refinement, and lazy evaluation, bridging search theory and scalable optimal motion planning.

Document Type

Dissertation

First Advisor

May-Win Thein

Second Advisor

Elizabeth Varki

Third Advisor

Marek Petrik

Department or Program

Mechanical Engineering

Degree Name

Doctor of Philosophy

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