graph sparse sampling

This work addresses the exponential growth in computational complexity with planning horizon that plagues online planning in continuous Markov decision processes due to tree-based structures. To overcome this limitation, the authors propose the Graph-based Sparse Sampling (GSS) algorithm, which introduces a branching-free graph structure into online planning for continuous MDPs for the first time. GSS enables efficient allocation of computational resources by sharing sampled future trajectories across multiple candidate actions and integrating smooth backtracking with heuristic policies, while also supporting GPU-accelerated batch processing. Under conditions of trajectory overlap, regularity, and action coverage, theoretical analysis shows that GSS incurs only polynomial growth in performance error with respect to the planning horizon, thereby circumventing the exponential bottleneck inherent in traditional tree search. Empirical results demonstrate that GSS significantly outperforms existing tree-based planners in continuous control tasks, achieving near-optimal performance especially in long-horizon scenarios.

This work addresses the challenge of generating temporally and spatially collision-free trajectories for multi-robot motion planning (MRMP) in dynamic, narrow, and cluttered environments. We propose ST-GCS, the first framework to extend Graph-based Convex Sets (GCS) to the spatiotemporal domain. It employs Exact Convex Decomposition (ECD) for tight modeling of spatiotemporal obstacles and explicitly reserves trajectory corridors within a priority-based planning scheme. The method integrates convex optimization, spatiotemporal graph construction, and kinematic constraints—including velocity bounds and flexible arrival times—thereby eliminating the randomness and low reliability inherent in sampling-based approaches. Experiments demonstrate that ST-GCS achieves significantly higher success rates and solution quality than state-of-the-art sampling-based planners across complex scenarios, with runtime improvements of up to an order of magnitude. ST-GCS establishes a new paradigm for deterministic, efficient MRMP in highly dynamic, shared environments.

To address inefficient exploration in sampling-based motion planning caused by non-uniform sampling distributions in high-dimensional configuration spaces, this paper proposes an adaptive sampling optimization framework based on Message-Passing Monte Carlo (MPMC). It is the first to jointly integrate Graph Neural Networks (GNNs) with the $L_p$-discrepancy metric to enable learnable, low-discrepancy dynamic sampling distribution modeling—significantly improving spatial coverage uniformity and sample quality. Embedded within mainstream planners such as RRT*, the method reduces required sample counts and computational overhead by 30–50% across diverse high-dimensional tasks, while simultaneously enhancing planning success rates and convergence speed. The core contribution lies in establishing an end-to-end differentiable closed loop comprising sampling, evaluation, and optimization—yielding a novel paradigm for high-dimensional motion planning that offers both theoretical guarantees and practical deployability.

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.

Coverage motion planning for complex robotic tasks suffers from low computational efficiency, poor parallelizability, and inability to globally model the distribution of trajectory spaces. This paper introduces a flow-matching-based statistical inference framework that, for the first time, formulates coverage planning as a probabilistic trajectory distribution matching problem. It unifies statistical divergences—including KL and Sinkhorn divergences—with LQR control structure, enabling decoupled trajectory generation and nonlinear control synthesis. We design a lightweight, scalable GPU-parallel architecture supporting real-time trajectory optimization in large-scale scenarios. Experiments demonstrate significant improvements over conventional waypoint-following and sampling-based planners in coverage completeness, computational speed, and scalability. The method establishes a novel paradigm for efficient coverage control in high-dimensional, dynamic environments.

Motion planning for high-dimensional robotic systems—such as manipulator arms and mobile manipulation platforms—often suffers from high computational cost and solution instability. This work proposes the Multi-Graph Search (MGS) algorithm, which introduces, for the first time, a multi-implicit-graph structure into search-based motion planning. By concurrently maintaining and incrementally expanding multiple state subgraphs, MGS dynamically focuses computational effort on high-potential regions and merges subgraphs during search to efficiently discover feasible paths. The method is theoretically guaranteed to be complete and bounded-suboptimal. Experimental results demonstrate that MGS significantly outperforms existing approaches across a variety of high-dimensional tasks, achieving notable advances in computational efficiency, solution consistency, and scalability.

To address state-set storage explosion and excessive memory overhead in large-scale explicit-state-space search, this paper proposes the Dynamic Trie Database (DTDB)—the first trie-based structure extended from static to fully dynamic, supporting incremental insertions and deletions without pre-allocated memory. DTDB guarantees theoretically provable compression ratios while maintaining high query efficiency. It uniformly compresses states encoded with both propositional and numeric variables, and is applicable to both grounded and lifted settings in classical and numeric planning. Experimental evaluation across multiple benchmark domains demonstrates memory compression ratios of 10×–1000× over baseline methods, with runtime overhead under 2%. This substantially improves scalability in representing and processing states for large-scale planning problems.

This paper introduces GCS-TSP, a novel variant of the Traveling Salesman Problem on Graphs of Convex Sets (GCS), where edge costs are trajectory-dependent—i.e., determined by the actual geometric path traversing each convex region—rendering classical TSP algorithms inapplicable. To address this, we propose GHOST, a hierarchical framework: its upper layer generates candidate visit sequences via abstract path expansion and combinatorial search; its lower layer jointly optimizes both continuous trajectories and switching points using mixed-integer convex programming, subject to continuity constraints. GHOST yields verifiable lower bounds, enabling efficient branch-and-bound pruning and formal optimality guarantees. Experiments demonstrate that GHOST achieves speedups of several orders of magnitude over baseline methods and is the first scalable approach capable of solving GCS-TSP instances with high-order continuity constraints, incomplete GCS graphs, and bounded-suboptimal trajectory planning.

This work addresses the challenge of collision-free motion planning for multiple robots operating in spatiotemporally continuous environments with transient, geometrically constrained regions. The authors propose the Space-Time Geometric Convex Set (ST-GCS) framework, which integrates Exact Convex Decomposition (ECD) to jointly model dynamic obstacles and inter-robot interactions, augmented by an occupancy reservation mechanism. The approach combines heuristic best-first graph search with continuous trajectory optimization and employs a windowed coordination strategy to enable efficient large-scale computation. Experimental results demonstrate that the method significantly outperforms existing planners in narrow, transient scenarios, achieving high-quality solutions for problems involving up to one hundred robots within several minutes.