centroid path planning

Traditional sampling-based motion planning algorithms fail for tasks involving discrete configuration-space symmetries (e.g., manipulation of symmetric objects) due to topological distortions induced by symmetry. Method: This paper establishes the first geometric modeling and sample-complexity theoretical framework for sampling-based planning in symmetric configuration spaces. It introduces group-action-based modeling, quotient-space construction, symmetry-aware distance metrics, and modified RRT/PRM sampling strategies. Contribution/Results: The core innovation is a sampling primitive tailored to finite symmetry groups, with theoretical sample complexity reduced to (O(1/varepsilon^d)), where (d) is the dimension of the quotient space. Experiments demonstrate an average 27% reduction in path length and a 35% decrease in planning time, significantly improving both efficiency and solution quality in symmetric environments.

To address the inefficiency of fixed-size motion primitives in high-degree-of-freedom robotic arm planning within complex environments, this paper proposes adaptive motion primitives—variable-radius *burs* (ball-based motion primitives) in configuration space—integrating sampling-based and search-based paradigms into a unified graph-search planning framework. Leveraging the SMPL library, burs are dynamically generated and collision-checked, with their radii adaptively scaled to local free-space geometry. Experiments demonstrate that the method significantly reduces the number of search nodes and planning time, outperforming fixed-radius primitives in high-dimensional, cluttered scenarios while maintaining robustness and efficiency in simpler environments. The core contribution is the first introduction of variable-scale burs as motion primitives within a cohesive planning framework, effectively balancing exploration efficiency and path quality.

To address the low computational efficiency and poor path quality in kinodynamic motion planning under high-obstacle-density environments, this paper proposes a novel bidirectional kinodynamic planning framework. The method introduces two key innovations: (1) precomputation of forward state transitions coupled with an edge-bundle sorting and concatenation mechanism to enhance transition reuse; and (2) synergistic exploration of the state space via coordinated bidirectional tree expansion and adaptive sampling. Experimental evaluation demonstrates substantial improvements in planning success rate, average path cost, and computation time—particularly in cluttered scenarios. Compared to state-of-the-art kinodynamic planners (e.g., BIT*, SST*), our approach achieves an average speedup of 2.3×, reduces path cost by 18.7%, and significantly improves solution feasibility across complex environments.

This work addresses multi-target motion planning under kinodynamic differential constraints in unstructured obstacle environments. We propose a synergistic framework integrating machine learning, Traveling Salesman Problem (TSP) optimization, and sampling-based search. Specifically, a regression model predicts the time- and distance-weighted cost for single-target planning; this enables construction of a kinodynamically aware TSP cost matrix. During RRT*-style motion tree expansion, low-cost target sequences are prioritized to generate dynamically feasible, collision-free trajectories traversing multiple regions. The method incorporates rigorous kinodynamic feasibility verification and high-fidelity collision checking. Experiments on a car-like vehicle model demonstrate a 3.2× speedup in planning time over baseline approaches, significantly improving computational efficiency and scalability to larger problem instances. Our approach establishes a novel paradigm for multi-target navigation under high-dimensional, nonlinear constraints.

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 work addresses the challenge of deadlock and local infeasibility in robotic task and motion planning under signal temporal logic (STL) specifications within non-convex, complex environments. To overcome these issues, the authors propose a hybrid planning framework that integrates discrete decision variables with continuous dynamics. By constructing control barrier functions in a geometrically transformed, disk-shaped workspace and incorporating local feasibility analysis under input saturation, the approach holistically resolves conflicts among multiple spatiotemporal tasks. The key innovation lies in the co-design of hybrid systems, STL specifications, and geometry-driven barrier functions, which collectively enhance planning feasibility and system robustness. Simulations demonstrate the method’s efficiency and reliability in handling overlapping spatiotemporal tasks.

This study addresses the critical need for real-time path adaptation in robotic navigation within dynamic environments, a challenge inadequately covered by existing surveys. Systematically reviewing 138 studies from 2015 to 2025, this work presents the first unified taxonomy of motion planning approaches, categorizing them into sampling-based, graph-search, model predictive control, learning-based, and classical local planners, while integrating both classical and learning-driven methods. It critically examines how dynamic perception influences planning, with in-depth analysis of core challenges including prediction uncertainty, human-robot interaction, and the “freezing robot” problem. The review encompasses key techniques such as velocity obstacles, potential fields, dynamic window approaches, supervised and reinforcement learning, and perception modalities leveraging cameras, LiDAR, and event-based sensors. By establishing a structured methodological framework, this paper offers researchers a comprehensive understanding of the principles, strengths, and limitations across planning paradigms, thereby advancing the field.

This work addresses the non-convex problem of planning high-order smooth (e.g., minimum-snap), collision-free trajectories for point robots amidst spherical obstacles. The authors formulate the task as a non-convex optimization over polynomial trajectories and present, for the first time, a theoretical analysis of its semidefinite programming (SDP) relaxation. Key contributions include establishing necessary and sufficient conditions for relaxation tightness, revealing the equivalence between relaxed solutions and globally optimal trajectories in an augmented space, and leveraging symmetry to reduce the SDP dimensionality so that it scales linearly with the polynomial degree—irrespective of the ambient environment dimension. Integrated into an RRT framework as a convex steering function, the method achieves 10–100× speedups over SNOPT/IPOPT in quadrotor C⁴-continuous minimum-snap planning, significantly reduces solution time variance, and reliably yields high-quality locally optimal trajectories.

This work addresses the computational inefficiency of motion planning for high-degree-of-freedom robots operating under dynamic constraints in complex environments. The authors propose a high-speed trajectory planning method grounded in differential flatness, which maps the dynamics into a flat output space to enable analytical, time-parameterized trajectory generation. By integrating SIMD-based parallel acceleration with a sampling-based planning framework, the approach achieves, for the first time, a general-purpose, highly accurate, and ultra-fast trajectory planner for differentially flat systems—including robotic arms, ground vehicles, and aerial robots. Experiments demonstrate that the method generates dynamically feasible trajectories in microseconds to milliseconds in both simulated and real-world cluttered dynamic environments, substantially improving planning efficiency while rigorously preserving dynamic feasibility and tracking accuracy.

该研究针对高维空间中的运动规划问题，特别是在狭窄通道和小间隙情况下，通过结合RRT与HAR算法并采用位置-方向解耦的方法有效提高了路径规划效率。