perform collision-aware planning

Time-optimal, collision-free trajectory planning in complex dynamic environments suffers from sensitivity to initialization and difficulty handling spatiotemporal coupling constraints. Method: This paper proposes a global optimization framework based on Spatio-Temporal Graph-of-Convex-Sets (ST-GCS). It systematically models diverse spatiotemporal constraints—e.g., obstacle avoidance, dynamic obstacles, timing bounds—as convex set constraints, eliminating dependence on initial guesses. By integrating graph neural network–guided structural modeling with efficient convex optimization, the framework enables consistent time-optimal trajectory generation across both static and dynamic scenarios. Results: Experiments demonstrate that the method reliably produces time-optimal, collision-free trajectories without requiring an initial guess. Its planning performance matches standard GCS while offering greater generality. Crucially, it significantly enhances ST-GCS’s capability to model intricate spatiotemporal constraints and improves solver robustness in dynamic environments.

To address the limitations of conventional local planners—namely, their reliance on empirical robustness and lack of formal modeling of dynamic obstacles—this paper proposes Dynamic Gap Planning (DGP). DGP explicitly models how dynamic obstacles affect the structure of traversable gaps in real time. It integrates polar-coordinate-based gap tracking, future gap propagation, and pursuit-guidance theory to construct a locally reactive trajectory generation framework with formal collision-free guarantees. Key innovations include a novel gap propagation algorithm and a center-of-obstacle-based gap-closure handling mechanism, significantly enhancing safety and robustness in complex dynamic environments. Extensive evaluations across diverse dynamic scenarios demonstrate that DGP outperforms both classical and learning-based planners. Furthermore, DGP has been successfully deployed on a TurtleBot2 platform, validating its effectiveness in real-world obstacle avoidance.

Existing robot self-collision matrix tools suffer from static visualization, lack of proximity query support, reliance on a single geometric primitive assumption, and cumbersome optimization workflows—limiting flexibility and reusability. This paper proposes an interactive, dynamic matrix generation framework implemented in Rust using the Bevy engine, featuring multi-level collision geometry abstraction, real-time rendering, and interactive fine-tuning. It introduces the first dynamic matrix construction and visualization method supporting proximity queries. Departing from conventional single-primitive constraints, the framework natively supports diverse geometric representations—including spheres, capsules, and convex hulls. The generated matrices are exported in reusable JSON/YAML formats. Evaluation across multiple robotic platforms demonstrates significant improvements: average speedup of 2.3× in both self-collision and self-proximity queries, and a 41% reduction in false-positive rates.

Existing robot collision-avoidance methods predominantly rely on spherical robot models and raw point clouds, struggling to simultaneously achieve accuracy, computational efficiency, and principled uncertainty modeling. This paper addresses the interaction between ellipsoidal robots and environments represented by Gaussian surface models, proposing the first continuous-space algorithm that jointly estimates collision probability, Euclidean distance, and analytically differentiable gradients. Key contributions include: (1) the first extension of ellipsoid–ellipsoid distance and collision-probability estimation to Gaussian mixture and splat-based surface representations; (2) a geometric fusion strategy that improves probabilistic estimation accuracy; and (3) support for hybrid Gaussian modeling accommodating both free space and obstacles. By bypassing dense point-cloud computations, the algorithm achieves microsecond-scale per-ellipsoid-pair inference—enabling deployment on embedded, low-power platforms. Extensive 2D/3D experiments on real point-cloud data demonstrate significant performance gains over direct point-cloud processing methods.

To address the slow generation and low reliability of convex sets in configuration space for real-time robotic motion planning under dynamic environments, this paper proposes the first GPU-accelerated online probabilistic collision-free convex decomposition method—Safe Convex Sets (SCS). Our approach enables efficient iterative refinement of SCS sequences via parallelized configuration-space inflation, joint SCS optimization, trajectory-guided collision-feedback pruning, and Dynamic Random Map (DRM) search. Furthermore, we integrate piecewise-linear path inflation with nonlinear trajectory optimization subject to convex-set constraints to support perception-closed-loop online planning. Evaluated on standard simulation benchmarks, our method achieves a 17.1× speedup over CPU-based baselines and improves collision-free success rate by 27.9%. Real-world experiments on a KUKA iiwa 7 robot demonstrate millisecond-level response times and high robustness in dynamic settings.

This work addresses the challenge of robotic navigation in highly discontinuous and fragmented 3D environments, where disconnected pathways prevent the robot from reaching its goal. To overcome this, we extend Navigation Among Movable Objects (NAMO) to 3D settings by proposing a novel approach that strategically rearranges movable objects—such as boxes—to construct traversable bridges rather than merely removing obstacles. We introduce BRiDGE, a probabilistically complete incremental sampling-based planner that jointly explores the configuration spaces of both the robot and movable objects. BRiDGE incorporates a non-uniform sampling strategy to enhance computational efficiency and supports constraints on the number of objects to be moved. Experimental results demonstrate that our method effectively enables goal-reaching in complex, disconnected 3D environments across multiple simulated and real-world robotic platforms, with formal guarantees of probabilistic completeness.

This work addresses the conservatism of conventional motion planning approaches that model robots as points or circles, which often hinder efficient navigation in narrow environments. To overcome this limitation, the authors propose a safe local motion planning method based on discrete-time control barrier functions, unifying the representation of polyhedral robots and dynamically updated convex free space as polyhedra. This formulation ensures that the number of safety constraints scales only with local geometric complexity, substantially improving scalability. Notably, the approach eliminates the need for explicit obstacle detection by directly integrating occupancy grids and LiDAR measurements into a model predictive controller for real-time collision avoidance. Extensive simulations and hardware experiments demonstrate up to a 91-fold reduction in computation time, enabling real-time 10 Hz control on embedded platforms.

This work addresses the non-smoothness in contact kinematics—manifested in distance, position, and normal mappings—arising from degenerate geometric configurations such as zero or undefined curvature, which impedes gradient-based robotic methods. To resolve this, the authors propose the iDCOL framework, which regularizes degenerate geometries into strictly convex implicit surfaces and solves a fixed-size nonlinear system via a geometrically scaled convex optimization formulation, thereby restoring uniqueness and smoothness to contact mappings. For the first time, analytical derivatives of contact kinematic quantities are derived using the implicit function theorem and integrated into a Newton-based solver to enable efficient differentiable computation. Experiments demonstrate robust performance across extensive collision simulations and successful application in differentiable motion planning, multi-body rigid collisions, and soft robot interaction scenarios.

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.

This work addresses the collision risks posed by occluded traffic participants in urban autonomous driving. The authors propose a formal occlusion-aware trajectory planning framework that, for the first time, unifies reachability reasoning under both future observability and complete non-observability within a single model. Integrated with a tree-based motion planner, the approach reduces the excessive conservatism of traditional methods while preserving formal safety guarantees. By explicitly modeling occlusion states and the evolution of observability, the framework enables proactive and efficient trajectory planning. Experimental results demonstrate that the method effectively avoids collisions and significantly improves traffic throughput in challenging simulated occlusion scenarios.