heuristic-guided trajectory search

To address the low efficiency of experience reuse and heavy reliance on manual prior knowledge in heuristic design for robot motion planning, this paper proposes an online heuristic learning framework based on a dynamic path database. Methodologically, it is the first to directly leverage a historical path database for real-time computation of learnable heuristic values at search tree nodes—departing from conventional approaches such as path stitching or sampling bias. It further introduces incremental retrieval and online database updating, enabling adaptive alignment of the database with the implicit configuration space during search. Contributions include: (1) a decoupled design of heuristics and path databases, significantly enhancing composability with diverse search algorithms (e.g., RRT*, A*); and (2) empirical validation across multiple simulation environments, demonstrating 12–35% improvement in planning success rate and 40–62% reduction in average computation time—confirming both effectiveness and generalizability.

Handcrafted heuristic functions in search-based navigation suffer from poor generalization across unseen maps and long-distance paths. Method: This paper proposes a local heuristic learning framework that explicitly defines and end-to-end learns either heuristic bias correction or local cost estimation within a spatial neighborhood—replacing conventional global heuristic modeling. By decomposing complex global prediction into lightweight local regression, the approach significantly reduces learning complexity. Integrated with graph search algorithms (e.g., A*), it operates under supervised learning using local state inputs while preserving bounded suboptimality guarantees. Contribution/Results: Experiments demonstrate 2–20× reduction in node expansions, improved training efficiency, and robust generalization to both unseen maps and long-range trajectories—without compromising solution quality or theoretical guarantees.

To address the stringent real-time, safety, and dynamic feasibility requirements of high-speed autonomous navigation in large-scale, complex environments, this paper proposes a non-optimization-based graph-search and trajectory-stitching framework. The method constructs a state graph from a predefined motion primitive library and integrates heuristic graph search, trajectory stitching, smoothing, and multi-constraint feasibility verification—including state, actuator, and collision constraints—thereby avoiding the computational overhead of numerical optimization. It achieves millisecond-level long-horizon trajectory generation in complex scenes spanning tens of meters, with guaranteed dynamic feasibility, collision-free execution, and full-state constraint satisfaction. Compared to two state-of-the-art optimization-based planners, our approach demonstrates significant improvements in real-time performance, robustness, and computational efficiency. This work establishes a new paradigm for highly reliable, real-time motion planning for agile mobile robots.

To address the slow convergence and redundant exploration inherent in sampling-based motion planning within high-dimensional state spaces, this paper proposes the Greedy Informed Set (GIS) and the Bidirectional Greedy RRT* (G-RRT*) algorithm. Methodologically, we introduce GIS—the first informed sampling set defined solely by the maximum heuristic cost along the current solution path—thereby drastically shrinking the effective sampling region. Building upon GIS, we embed it into a bidirectional RRT* framework that jointly achieves efficient bidirectional guidance and asymptotic optimality guarantees. Extensive evaluations—including simulations, physical experiments on a Barrett WAM robotic arm, and real-world deployment on the Panthera self-reconfigurable robot—demonstrate that G-RRT* consistently generates asymptotically optimal paths. In high-dimensional scenarios, it significantly outperforms state-of-the-art RRT* variants in both convergence speed and path quality.

This work addresses the problem of constructing Safe Flight Corridors (SFCs) for autonomous navigation, aiming to efficiently approximate free space while ensuring trajectory safety. The proposed method introduces an online iterative convex covering optimization framework that alternately optimizes partially distributed variables and incorporates geometric heuristics. It jointly generates overlapping polyhedral segments—subject to waypoint constraints—balancing maximal volume coverage with kinematically feasible initialization. Its key contribution lies in the organic integration of convex optimization, polyhedral geometric modeling, and constraint-satisfaction optimization, enabling real-time SFC reconstruction within a two-stage motion planning pipeline. Extensive evaluation across diverse parametric environments demonstrates significant improvements in trajectory feasibility and computational efficiency. The approach provides a scalable theoretical and practical foundation for online safe navigation in complex, dynamic scenarios.

This work addresses the challenge of continuous trajectory optimization in non-convex environments by proposing a joint discrete–continuous optimization framework based on the Alternating Direction Method of Multipliers (ADMM). The approach parameterizes trajectories as polynomials and introduces a spatiotemporal allocation graph to model coupled spatiotemporal constraints. By integrating mixed-integer programming with shortest-path search, the method enables efficient solution computation. In contrast to conventional decoupled strategies, the proposed framework substantially expands the feasible search space and achieves stable convergence from arbitrary initial conditions without requiring complex warm-start procedures. Experimental results demonstrate significant improvements in both solution quality and robustness.

Traditional heuristic methods in reinforcement learning for shortest-path problems rely on single-step Bellman updates, leading to localized and inconsistent state-value estimates. To address this, we propose a multi-step heuristic learning framework that integrates finite-horizon graph search with deep approximate value iteration. Our method anchors computation at the search frontier and propagates path information backward via bounded-depth search, enabling multi-step, globally consistent value correction. A neural network is trained end-to-end to approximate the heuristic function. Evaluated on diverse pathfinding benchmarks, our approach significantly improves both search efficiency and solution quality: average node expansions decrease by 37%, and optimal solution rates increase by 22% compared to single-step update baselines. These results validate the effectiveness and generalizability of multi-step search-guided heuristic learning.

This work addresses the challenge of motion planning under dynamic constraints while simultaneously achieving rapid acquisition of high-quality initial solutions and efficient convergence to optimality. To this end, the paper proposes the BTIT* algorithm, which integrates anytime bidirectional heuristic search with a novel, strictly verifiable termination criterion—adapted for the first time into MEET-class algorithms—to enable meet-in-the-middle behavior during sampling while preserving asymptotic optimality. BTIT* further supports online early termination within batch sampling, guaranteeing MM-optimality. Experimental results demonstrate that BTIT* significantly reduces time-to-first-solution and accelerates convergence on both a 4D double-integrator system and a 10D linearized quadrotor benchmark, outperforming existing non-lazy informed batch planners.

This work addresses the global path optimization problem for mobile sensors in static two-dimensional continuous environments, aiming to minimize the expected time to localize hidden objects. Due to the intractability of analytically evaluating the objective—stemming from continuous-space modeling and tight perception-motion coupling—existing methods struggle to balance accuracy and efficiency. To overcome this, we propose Milaps: a novel framework featuring (i) model-based formulation integrated with auxiliary objectives; (ii) an adaptive anytime metaheuristic algorithm that guarantees progressively improving solutions upon arbitrary termination; and (iii) synergistic components including TSP-D-inspired heuristics, explicit continuous-environment modeling, static sensing-weighted coverage, and minimum-latency approximation. Evaluated on a large-scale, newly constructed benchmark, Milaps significantly outperforms state-of-the-art approaches—generating high-quality initial solutions within milliseconds and advancing the Pareto frontier of solution quality versus computational efficiency.