collision checking

In semi-static environments, motion planning must satisfy strict fixed-time response constraints while providing formal safety guarantees—a longstanding challenge. To address this, we propose the Coverage-Verified Roadmap (CVRM) framework: it incrementally constructs a roadmap, partitions the obstacle configuration space into disjoint subregions, and systematically verifies path feasibility within each subregion—thereby enabling theoretically guaranteed fixed-time query resolution. CVRM is the first approach to introduce coverage-based verification into continuous configuration spaces, eliminating reliance on configuration-space discretization inherent in conventional methods. Evaluated on 7-DOF Panda robot tabletop manipulation simulations, CVRM achieves a 23% higher query success rate and expands feasible configuration coverage by 31% compared to baseline methods, significantly improving both practical utility and formal assurance.

Functional safety verification of autonomous driving motion planners faces challenges posed by complex and learning-based planners. This paper proposes a real-time runtime protection framework for trajectory safety validation, introducing— for the first time—a temporal protection module that jointly enforces geometric feasibility, dynamic feasibility, and cost rationality checks. The framework adopts a modular architecture and implements online validation of trajectory candidates on a real-time operating system, with successful deployment on embedded hardware. Experiments demonstrate that the system reliably detects unsafe trajectories under millisecond-level latency constraints. The source code is publicly available, and comprehensive fallback strategies are under integration. This work significantly enhances runtime safety assurance for black-box or learning-based planners, bridging a critical gap between planning flexibility and functional safety compliance.

Real-time multi-step planning and obstacle avoidance for autonomous robots in dynamic environments remain challenging, particularly under resource constraints and without prior map knowledge. Method: We propose a lightweight, closed-loop reactive planning framework that requires no pre-mapping or offline computation. Our approach integrates biologically inspired attention mechanisms with local LiDAR perception to construct transient control-chain plans. It introduces forward depth-first model checking—novel in real-time multi-step planning—combined with environment-aware 2D LiDAR discretization and closed-loop feedback control. Contribution/Results: The framework provides theoretical guarantees on safety and interpretability. Empirically, it generates safe, multi-step local trajectories within 100 ms on low-power embedded hardware. In complex scenarios—including dead ends and playgrounds—it significantly outperforms single-step reactive systems in obstacle avoidance success rate and response robustness.

This work addresses the challenge of efficiently updating roadmap-based motion planners in non-static environments. To this end, the authors propose a “red–green–gray” three-state labeling mechanism that classifies nodes and edges according to their validity through inexpensive heuristic checks, enabling rapid semi-lazy updates. The approach leverages simplified geometric computations to approximate the robot’s swept volume, performs lazy collision checking, and integrates an enhanced SPITE strategy to improve the accuracy of edge validity assessment. Experimental results demonstrate that, while achieving update times comparable to the classical method by Leven and Hutchinson, the proposed technique significantly improves the precision of identifying invalid edges.

To address the challenge of rapidly detecting path infeasibility in robot motion planning, this paper proposes the first lightweight discriminative framework based on incremental sampling and image segmentation. Methodologically, it discretizes the configuration space, performs obstacle-guided incremental sampling to construct a binary occupancy map, and then applies connected-component analysis—inspired by image segmentation—to determine whether the start and goal configurations reside in the same free-connected component. Crucially, the framework avoids full configuration-space modeling and eliminates dependence on path-search algorithms. Evaluated across five representative scenarios with up to 5 degrees of freedom, it achieves high-accuracy infeasibility identification while reducing average detection time by approximately two orders of magnitude compared to conventional feasibility verification methods such as RRT and PRM, thereby significantly lowering computational overhead.

Sample-based motion planners (SBMPs) suffer from low efficiency and slow convergence in complex environments due to uniform sampling, which wastes computational resources on low-value regions. Method: This paper proposes a theoretically grounded non-uniform sampling strategy that integrates conformal prediction—introduced to motion planning for the first time—to provide distribution-free, confidence-level–controlled guarantees that the optimal solution lies within certified high-probability sampling regions. Leveraging heuristic path predictors (e.g., A* or vision-language models), the method generates an initial trajectory and quantifies its epistemic uncertainty to identify high-value sampling zones. Contribution/Results: The approach significantly accelerates feasible path discovery while ensuring theoretical validity of sampling coverage. Extensive experiments demonstrate superior generalization and robustness over state-of-the-art baselines, particularly in previously unseen environments, validating both computational efficiency and reliability under uncertainty.

This work addresses the challenge of generating constrained, interpretable, and domain-compliant trajectory patterns for moving objects in real-world dynamic environments. It proposes a hybrid qualitative-quantitative approach based on Answer Set Programming (ASP), which traverses the environmental graph structure and integrates geometric constraint reasoning with stable model semantics to enumerate geometrically feasible motion behaviors. To the best of our knowledge, this is the first application of ASP to generate diverse trajectory patterns that are verifiable, traceable, and seamlessly incorporate domain knowledge with environmental topology. Experiments on the large-scale Argoverse 2 autonomous driving benchmark demonstrate that the generated trajectories exhibit high interpretability and practical applicability, effectively overcoming the limited explainability inherent in purely data-driven methods.

This work proposes an online trajectory generation method based on piecewise quintic/quartic splines to address the challenge of converting arbitrary geometric paths into kinematically feasible and collision-free trajectories in dynamic environments. The approach explicitly enforces jerk constraints and supports real-time replanning under high-frequency goal updates. By integrating dynamic environment perception and a responsive adaptation mechanism, it guarantees collision avoidance within finite time while permitting bounded deviations from the original path. Both simulation and real-world experiments demonstrate that the method outperforms existing approaches in trajectory smoothness, computational efficiency, and real-time performance, achieving stable operation in human-in-the-loop dynamic scenarios with target update rates up to 1 kHz.

This work addresses the problem of safe motion planning for robots operating in complex, cluttered environments under stochastic disturbances with unknown distributions. The authors propose a sampling-based, provably safe planning algorithm that constructs Wasserstein ambiguity tubes from trajectory data to tightly envelop the evolution of state distributions with high confidence. Building upon these tubes, the method incrementally grows a planning tree that satisfies chance constraints. A key innovation lies in replacing a single high-dimensional ambiguity tube with multiple lower-dimensional ones, substantially reducing conservatism and improving scalability. Additionally, an efficient, probabilistically complete bandit-style validity checker is introduced. Experimental results demonstrate that the approach reliably generates feasible trajectories meeting stringent safety thresholds in highly cluttered scenarios, significantly outperforming state-of-the-art methods.

This work addresses the limitations of traditional signal temporal logic (STL)-based sampling-based planning, which relies on min-max robustness metrics that consider only critical time points and subformulas, resulting in non-smooth optimization landscapes and inefficient search. To overcome this, the authors propose the RRT$^\eta$ framework, which introduces arithmetic-geometric mean (AGM) robustness semantics to evaluate satisfaction across all time points and subformulas, enabling continuous and globally aware trajectory reasoning. The approach integrates efficient incremental monitoring with a fulfillment-priority-logic-derived gradient-like vector that guides the search toward higher satisfaction. Experiments on a double integrator, unicycle, and a 7-DOF manipulator demonstrate that the method significantly improves planning performance and robustness under multi-constraint and weakly guided scenarios, while preserving probabilistic completeness and asymptotic optimality.