Graph-Based Planning

Efficient path following for mobile manipulators is often hindered by high-dimensional configuration spaces and kinematic constraints. This paper presents a robust two-stage configuration planning framework that decouples the 8-DoF planning problem into a tractable 2-DoF base optimization under a yaw-fixed base planning assumption. In the first stage, the proposed approach utilizes IRM to discretize the task-space path into a multi-layer graph, where an initial feasible path is extracted via a Dijkstra-based dynamic programming approach to ensure computational efficiency and global optimality within the discretized graph. In the second stage, to overcome discrete search quantization, feasible base regions are transformed into convex hulls, enabling subsequent continuous refinement via the L-BFGS algorithm to maximize trajectory smoothness while strictly enforcing reachability constraints. Simulation results demonstrate the theoretical precision of the proposed method by achieving sub-millimeter kinematic accuracy in simulation, and physical experiments on an omnidirectional mobile manipulator further validate the framework's robustness and practical applicability.

Procedural planning aims to predict a sequence of actions that transforms an initial visual state into a desired goal, a fundamental ability for intelligent agents operating in complex environments. Existing approaches typically rely on large-scale models that learn procedural structures implicitly, resulting in limited sample-efficiency and high computational cost. In this work we introduce ViterbiPlanNet, a principled framework that explicitly integrates procedural knowledge into the learning process through a Differentiable Viterbi Layer (DVL). The DVL embeds a Procedural Knowledge Graph (PKG) directly with the Viterbi decoding algorithm, replacing non-differentiable operations with smooth relaxations that enable end-to-end optimization. This design allows the model to learn through graph-based decoding. Experiments on CrossTask, COIN, and NIV demonstrate that ViterbiPlanNet achieves state-of-the-art performance with an order of magnitude fewer parameters than diffusion- and LLM-based planners. Extensive ablations show that performance gains arise from our differentiable structure-aware training rather than post-hoc refinement, resulting in improved sample efficiency and robustness to shorter unseen horizons. We also address testing inconsistencies establishing a unified testing protocol with consistent splits and evaluation metrics. With this new protocol, we run experiments multiple times and report results using bootstrapping to assess statistical significance.

Footstep planning involves a challenging combinatorial search. Traditional A* approaches require discretising reachability constraints, while Mixed-Integer Programming (MIP) supports continuous formulations but quickly becomes intractable, especially when rotations are included. We present CASSR, a novel framework that recursively propagates convex, continuous formulations of a robot's kinematic constraints within an A* search. Combined with a new cost-to-go heuristic based on the EPA algorithm, CASSR efficiently plans contact sequences of up to 30 footsteps in under 125 ms. Experiments on biped locomotion tasks demonstrate that CASSR outperforms traditional discretised A* by up to a factor of 100, while also surpassing a commercial MIP solver. These results show that CASSR enables fast, reliable, and real-time footstep planning for biped robots.

In this paper, we present a novel learning framework for finding shortest paths in graphs utilizing Generative Flow Networks (GFlowNets). First, we examine theoretical properties of GFlowNets in non-acyclic environments in relation to shortest paths. We prove that, if the total flow is minimized, forward and backward policies traverse the environment graph exclusively along shortest paths between the initial and terminal states. Building on this result, we reduce shortest-path finding in an arbitrary unweighted graph to finding a non-acyclic GFlowNet with minimal total flow, and approximate it in practice by training with flow regularization. We experimentally demonstrate the performance of our method in pathfinding in permutation environments and in solving Rubik's Cubes of various sizes. For the latter problems, our approach shows competitive results with state-of-the-art machine learning approaches designed specifically for this task in terms of the solution length, while requiring smaller search budget at test-time.

The performance of search algorithms for grid-based pathfinding, e.g. A*, critically depends on the heuristic function that is used to focus the search. Recent studies have shown that informed heuristics that take the positions/shapes of the obstacles into account can be approximated with the deep neural networks. Unfortunately, the existing learning-based approaches mostly rely on the assumption that training and test grid maps are drawn from the same distribution (e.g., city maps, indoor maps, etc.) and perform poorly on out-of-distribution tasks. This naturally limits their application in practice when often a universal solver is needed that is capable of efficiently handling any problem instance. In this work, we close this gap by designing an universal heuristic predictor: a model trained once, but capable of generalizing across a full spectrum of unseen tasks. Our extensive empirical evaluation shows that the suggested approach halves the computational effort of A* by up to a factor of 2.2, while still providing solutions within 3% of the optimal cost on average altogether on the tasks that are completely different from the ones used for training $\unicode{x2013}$ a milestone reached for the first time by a learnable solver.

Autonomous exploration in unknown environments is key for mobile robots, helping them perceive, map, and make decisions in complex areas. However, current methods often rely on frequent global optimization, suffering from high computational latency and trajectory oscillation, especially on resource-constrained edge devices. To address these limitations, we propose SCOPE, a novel framework that incrementally constructs a real-time skeletal graph and introduces Implicit Unknown Region Analysis for efficient spatial reasoning. The planning layer adopts a hierarchical on-demand strategy: the Proximal Planner generates smooth, high-frequency local trajectories, while the Region-Sequence Planner is activated only when necessary to optimize global visitation order. Comparative evaluations in simulation demonstrate that SCOPE achieves competitive exploration performance comparable to state-of-the-art global planners, while reducing computational cost by an average of 86.9%. Real-world experiments further validate the system's robustness and low latency in practical scenarios.

While passive agents merely follow instructions, proactive agents align with higher-level objectives, such as assistance and safety by continuously monitoring the environment to determine when and how to act. However, developing proactive agents is hindered by the lack of specialized resources. To address this, we introduce ProAct-75, a benchmark designed to train and evaluate proactive agents across diverse domains, including assistance, maintenance, and safety monitoring. Spanning 75 tasks, our dataset features 91,581 step-level annotations enriched with explicit task graphs. These graphs encode step dependencies and parallel execution possibilities, providing the structural grounding necessary for complex decision-making. Building on this benchmark, we propose ProAct-Helper, a reference baseline powered by a Multimodal Large Language Model (MLLM) that grounds decision-making in state detection, and leveraging task graphs to enable entropy-driven heuristic search for action selection, allowing agents to execute parallel threads independently rather than mirroring the human's next step. Extensive experiments demonstrate that ProAct-Helper outperforms strong closed-source models, improving trigger detection mF1 by 6.21%, saving 0.25 more steps in online one-step decision, and increasing the rate of parallel actions by 15.58%.

Autonomous high-speed navigation through large, complex environments requires real-time generation of agile trajectories that are dynamically feasible, collision-free, and satisfy state or actuator constraints. Modern trajectory planning techniques primarily use numerical optimization, as they enable the systematic computation of high-quality, expressive trajectories that satisfy various constraints. However, stringent requirements on computation time and the risk of numerical instability can limit the use of optimization-based planners in safety-critical scenarios. This work presents an optimization-free planning framework called STITCHER that stitches short trajectory segments together with graph search to compute long-range, expressive, and near-optimal trajectories in real-time. STITCHER outperforms modern optimization-based planners through our innovative planning architecture and several algorithmic developments that make real-time planning possible. Extensive simulation testing is performed to analyze the algorithmic components that make up STITCHER, along with a thorough comparison with three state-of-the-art optimization planners. Simulation tests show that safe trajectories can be created within a few milliseconds for paths that span the entirety of two 50 m x 50 m environments. Hardware tests with a custom quadrotor verify that STITCHER can produce trackable paths in real-time while respecting nonconvex constraints, such as limits on tilt angle and motor forces, with flight speeds up to 63 km/h.

This article proposes a new path planning method for addressing multi-level terrain situations. The proposed method includes innovations in three aspects: 1) the pre-processing of point cloud maps with a multi-level skip-list structure and data-slimming algorithm for well-organized and simplified map formalization and management, 2) the direct acquisition of local traversability indexes through vehicle and point cloud interaction analysis, which saves work in surface fitting, and 3) the assignment of traversability indexes on a multi-level connectivity graph to generate a weighted traversability graph for generally search-based path planning. The A* algorithm is modified to utilize the traversability graph to generate a short and safe path. The effectiveness and reliability of the proposed method are verified through indoor and outdoor experiments conducted in various environments, including multi-floor buildings, woodland, and rugged mountainous regions. The results demonstrate that the proposed method can properly address 3D path planning problems for ground vehicles in a wide range of situations.