asymptotically optimal planning

Real-time robot replanning in dynamic environments incurs high computational overhead and relies heavily on explicit change detection and graph updates. Method: This paper proposes a novel incremental planning paradigm that eliminates the need for explicit reuse or update of historical paths. It decouples dynamic replanning into a sequence of independent, asymptotically optimal sampling-based planning problems—thereby avoiding dependence on obstacle change perception and dense graph reconstruction. The approach leverages almost-surely asymptotically optimal algorithms, including Effort-Informed Trees* (EIT*) and Asymptotically Optimal RRT-Connect (AORRTC), to balance rapid initial solution generation with continuous path refinement. Contribution/Results: Simulation results show that EIT*-generated paths achieve significantly shorter median lengths than those produced by mainstream reactive planners. Physical experiments on a robotic manipulator demonstrate AORRTC’s effectiveness and robustness in complex, dynamic task scenarios.

Multi-robot motion planning faces the challenge of simultaneously achieving fast initial solution generation, efficient optimization of solution quality, and scalability. This work proposes AO-ARC, the first approach to integrate the anytime-optimal AO-x meta-algorithm with an adaptive (de)coupled ARC solver. AO-ARC rapidly produces feasible solutions while guaranteeing asymptotic optimality with respect to makespan and maintaining consistent cost bounds across varying robot decompositions. Experimental results demonstrate that AO-ARC matches state-of-the-art feasibility solvers in initial solution speed and significantly outperforms existing anytime methods in both convergence rate of solution quality and reliability, across 2D coordination scenarios and 3D robotic arm tasks.

To address the challenge of balancing real-time performance and asymptotic optimality in high-degree-of-freedom robot motion planning, this paper proposes AORRTC: the first connection-based sampling planner that integrates the Anytime Optimal (AO)-x-ary optimization framework into the RRT-Connect architecture. AORRTC achieves millisecond-scale initial solution generation while guaranteeing almost-sure asymptotic optimality (a.s.a.o.). We formally prove its probabilistic completeness and a.s.a.o. property. To accelerate convergence, we introduce SIMD-based parallelization and a heuristic fast-connect strategy. Experiments on the 7-DOF Panda and 8-DOF Fetch robots demonstrate that AORRTC matches RRT-Connect’s initial solution speed, yet converges to optimal solutions significantly faster than existing a.s.a.o. planners. Moreover, it achieves high success rates in complex environments with average computation times of only a few milliseconds.

To address the inefficiency of replanning in dynamic environments where edge evaluation is computationally expensive, this paper proposes an asymptotically optimal lifelong sampling-based motion planning algorithm. The method integrates lifelong planning, lazy edge evaluation, sampling-based search, and graph rewiring. Its key contributions are: (1) a novel lazy subpath evaluation mechanism that defers costly edge validation until necessary; and (2) a heuristic rewiring cascade strategy enabling incremental, efficient repair of the search tree. Together, these innovations preserve asymptotic optimality while substantially accelerating replanning. Extensive simulations demonstrate that the proposed approach outperforms state-of-the-art sampling-based planners in both static and dynamic environments, reducing total planning time by 37%–62% and computational overhead by 41%–58%.

To address the challenge of generating kinematically feasible paths for non-circular mobile and ground robots—such as Ackermann-steering and legged platforms—in complex environments, this paper introduces Smac Planner: an open-source, search-based motion planning framework. Its core innovation is the “Cost-Aware” variant, which unifies and enhances A*, Hybrid-A*, and state lattice planners by explicitly incorporating kinematic constraints and trajectory cost models directly into the graph-search process. This significantly improves the trade-off between path feasibility and computational efficiency. The framework is deeply integrated with ROS 2 Nav2 and has become its default global planner. Deployed on thousands of academic, commercial, and field-deployed robots, Smac Planner demonstrates a 30–50% reduction in planning latency and over a 20% increase in task success rate in real-world experiments.

This work addresses the challenges of planning for high-dimensional dynamical systems in unstructured environments, where the curse of dimensionality and the infeasibility of precomputed motion primitives hinder effective control. To overcome these issues, the paper proposes the Bidirectional Incremental Generalized Hybrid A* (Bi-IGHA*) algorithm, which introduces bidirectional search into the IGHAs* framework for the first time. By integrating multi-resolution state space discretization, bidirectional tree expansion, and a node freezing mechanism, Bi-IGHA* enables efficient trajectory planning under arbitrary time horizons. The approach substantially reduces search depth, mitigates the obscuring of feasible solutions caused by frozen nodes in unidirectional search, and guarantees monotonic cost improvement and termination. Experimental results demonstrate that Bi-IGHA* significantly decreases the number of expanded nodes in R³, R⁴, and R⁶ planning tasks and achieves closed-loop control performance comparable to existing methods in high-speed off-road autonomous driving with lower computational overhead.

This study addresses the challenge of evaluating real-time motion planning in dynamic hazard fields by establishing a unified benchmark within rotating hazardous environments to systematically compare classical planning and learning-based paradigms. Through experiments employing classical planners, Proximal Policy Optimization (PPO) reinforcement learning, and dynamic obstacle simulation, this work reveals that environmental uncertainty is the predominant factor determining the effectiveness of a given planning paradigm. The results demonstrate that in stochastic dynamic environments, the PPO approach significantly outperforms classical methods in terms of computational latency, planning success rate, and path quality. These findings provide critical theoretical justification and empirical evidence for selecting appropriate motion planning paradigms for autonomous agents operating in complex scenarios.

This work addresses the limitations of traditional sampling-based motion planning algorithms in real-time performance and integration with modern AI research workflows by presenting a systematic upgrade to the open-source OMPL library. For the first time, hardware acceleration support—encompassing GPUs and FPGAs—is introduced into OMPL, alongside enhanced compatibility with mainstream AI toolchains. The extension supports diverse planning paradigms, including asymptotically optimal planning, lazy sampling, constraint handling, and task specifications expressed in linear temporal logic. These advancements substantially improve computational efficiency and scalability, reinforcing OMPL’s foundational role in motion planning while significantly broadening its applicability to complex intelligent systems and autonomous robotic platforms.

本文针对基于采样的运动规划算法中δ-相似轨迹假设不成立导致的问题，提出了一种在考虑‘拥挤排除’情况下仍能实现渐近近似最优性的方法。

This work addresses multi-objective motion planning for systems subject to dynamic constraints by proposing a unified framework based on Stable Sparse-RRT (SST), encompassing lexicographic optimization, constrained optimization, and Pareto front approximation. The approach introduces three algorithmic variants—lexSST, coSST, and poSST—by replacing the single sample within each witness neighborhood with a locally Pareto-optimal set of nodes. This method is the first to simultaneously guarantee both completeness and asymptotic Pareto optimality in continuous dynamical systems, thereby overcoming the limitations of conventional scalarization strategies. Theoretical analysis establishes the correctness and convergence properties of the proposed algorithms, while empirical evaluations demonstrate their effectiveness in efficiently approximating multi-objective optimal solutions in complex dynamical environments.