Collision-Free Trajectories

Robot manipulators are monitored by constraint-specific indicators whose units and gradient scales are not comparable, so they do not provide a common measure of the configuration-space motion remaining before violation. We define the feasibility distance field (FDF) as the distance, under a fixed positive-definite joint-space metric, to the union of infeasible configuration sets. Classical distance-to-set theory gives 1-Lipschitz continuity, almost-everywhere differentiability, and unit dual-gradient norm wherever the nearest projection is unique. The robotics contribution is an admissibility analysis showing when practical constraints define non-empty closed sets. We derive admissible formulations for external and self-collision, joint limits, dexterity, Cartesian and task-projected compliance, joint torque under payload, and dynamic manipulability. Since every field uses the same metric, heterogeneous constraints compose by a pointwise minimum, conditioned constraints retain a fixed distance space, and multi-robot constraints produce block-sparse gradients that identify which robots must react. We generate projection-based labels and train neural approximations with a distance loss and an Eikonal penalty. Simulations on a UR5e and a dual-arm cell evaluate seven fields using value, projection, sign, gradient, composition, and moving-obstacle diagnostics. Across 8,000 configurations, the largest feasible-side secant ratio is 0.920, mean learned gradient norms range from 0.994 to 0.998, and projection residuals range from 0.011 to 0.034 rad. Across 24 random obstacle paths, the external and composed collision fields achieve 90.4% and 91.6% success within 3 cm, with sign-error rates below 2%. The results support a common configuration-space margin and identify approximation errors near medial axes and sparsely sampled boundaries.

Conventional motion planning treats collision as a binary constraint, although contact with different objects can have drastically different consequences. A robot may safely brush against a cardboard box while even minor contact with a glass, laptop, or unstable object may be undesirable. Moreover, a direct robot--object collision can move the contacted object and trigger secondary object--object collisions, making the risk of a motion depend on the physical evolution of the scene rather than only on the robot's geometric path. We present CaSCo, a cascade-aware soft-collision motion planning framework in which a vision-language or language model assigns semantic risk to objects and a physics simulator predicts the consequences of candidate robot motions. CaSCo searches for a path that minimizes the total semantic risk of the unique objects displaced either directly by the robot or indirectly through cascaded collisions. Because collisions change the environment, we augment roadmap states with the predicted object arrangement and the set of objects whose risk has already been incurred. We develop an optimal graph-search algorithm with an admissible and consistent cascade-relaxed heuristic and caching and pruning mechanisms for efficient search. Experiments in cluttered manipulation environments evaluate semantic risk, cascade reasoning, planning efficiency, and real-robot operation.

Solomonoff induction frames prediction as a mixture over computable hypotheses, typically leading to identification of the true environment. In a finite meta-reinforcement learning setting with nested constraint families, in our previous work, we observe a different regime: a value-mixture (VM) agent achieves near-optimal, zero-collision navigation without identifying the true environment, a phenomenon we call Free Inference. This regime persists up to a sharp density threshold, beyond which performance degrades and posterior-mode selection (PMS) becomes preferable. We formalize this behavior via the Free Inference dimension dFI(S,N), a combinatorial measure of the environmental complexity a VM agent can handle while preserving trajectory coherence. We prove dFI is strictly smaller than the VC-dimension and relates to the Natarajan dimension up to a path-length factor, capturing the cost of non-decomposable loss. A PAC-style relaxation yields generalization bounds driven by dFI^(epsilon,delta). We also define a complementary PMS identification dimension and show that a hybrid strategy---averaging until the first collision, then switching to selection---is optimal, with links to Littlestone-type dimensions supported by grid-world experiments.

Humanoid robots often execute motion commands through whole-body controllers (WBCs) that track targets while maintaining balance and stability. However, most WBCs are blind to scene geometry, which can lead to collisions from imperfect target motions that are geometrically unsafe due to perception, planning, or teleoperation errors. We propose RECAL, a Robot--Environment Cross-Attention Layer that wraps a blind WBC to trade off target tracking against collision avoidance using external scene geometry. RECAL supports collision-aware tracking of floating-base and end-effector commands, including collision avoidance for held objects. It represents the robot, held objects, and environment as point clouds, using cross-attention between robot/object points and the environment to produce geometry-aware control features. In simulation, RECAL improves collision avoidance while preserving target-tracking performance across frozen-arm and adaptive-arm locomotion, object-carrying, and standing-manipulation scenarios relative to alternative geometry-aware WBC architectures. We further demonstrate the controller on a real Digit V3 humanoid robot.

Category-level in-hand manipulation of articulated objects is a formidable yet underexplored challenge for dexterous robotic hands. This difficulty stems from two core bottlenecks: first, controlling an object's internal degrees of freedom is tightly coupled with maintaining grasp stability on a free-floating base; second, acquiring diverse object models and functional grasps at scale is highly labor-intensive, yet vital for generalization given the system's sensitivity to initial configurations. In this work, we present ArtManip, the first category-level articulated in-hand manipulation method that generalizes across object instances and diverse initial grasps. For initial configuration construction, we develop an automated pipeline that procedurally generates diverse articulated objects and synthesizes task-oriented functional grasps. For policy learning, we propose a robust two-stage training strategy that incorporates articulation physics randomization, reward curriculum, and latent representation distillation to handle complex contact and joint dynamics during deployment. Extensive experiments across four object categories demonstrate that our policy generalizes to unseen instances and varied configurations in simulation, and achieves zero-shot transfer to 12 real-world objects featuring diverse shapes and joint mechanics.

Robotic processing of irregular steel scrap requires dense 3-D measurement to replace manual visual assessment in hazardous cutting workcells. The reconstructed map is used to estimate piece dimensions, boundary geometry, feasible preheating and cutting regions, and collision-aware torch paths. The reconstruction errors therefore propagate directly to downstream measurement and planning. Existing multi-view registration methods commonly rely on feature extraction and data association to establish correspondences between views. In workcells with smooth metallic surfaces, repeated structures, occlusions, and partial overlaps, however, wrong correspondences may be established, leading to inaccurate pose estimation and distorted reconstruction. This paper presents an adaptive layered depth-map-guided bundle adjustment framework for correspondence-free multi-view point cloud registration. The scene is represented by a global 2.5-D grid, where each cell can adaptively maintain multiple depth hypotheses. Raw depth observations are directly projected into the global map to form depth constraints without explicit feature correspondences. At grid cells where multiple surfaces produce conflicting depths, a softmax-based layer assignment links each observation to compatible depth hypotheses. The resulting nonlinear least-squares formulation jointly refines sensor poses and the layered depth map, with correspondences implicitly induced by the depth-map representation and projection model. Experiments on self-collected industrial datasets show that the proposed method achieves consistently competitive reconstruction accuracy while maintaining robustness and low computational cost in challenging industrial scenarios. We release the open-source code implementation at: https://github.com/YiranZhou-Robotics/ADM-BA.git

Planners on graphs of convex sets return trajectories that are collision-free by construction, provided the convex regions are collision-free. The region generator only promises that property probabilistically, and no planner in the family verifies it. We report the first measurement of what the gap costs. On a scaled 14-DOF bimanual library, $3.2\%$ of interface samples are in collision, and a search-based GCS planner (\gcsstar) turns that volume error into a $62\%$ answer error: $18$ of $29$ pick-and-place queries return trajectories that drive the arms through the shelves, up to $91$,mm deep, reported as successes. Repairing the library does not work; a ten times stricter acceptance contract, sums-of-squares certified regions, and uniform margins each destroy the connectivity planning needs before they deliver soundness. We instead build a planner that certifies its answers. It samples the overlaps and shared faces of the decomposition, prunes with an admissible informed bound, and verifies the one candidate each search round proposes, continuously, by a chain of clearance certificate balls with no resolution parameter; failures are repaired with local in-region detours, and the convex polish is re-verified. Head-to-head on all $29$ task queries it delivers zero invalid answers against $21$ for the reference, reaches its first certified answer in $0.11$,s against $1.59$,s for the reference's unverified one, and reproduces the reference optimum exactly on every query whose reference answer is physically valid.

Motion planning problems such as collision-free navigation and contact-rich manipulation can be naturally formulated as optimization problems that couple discrete decisions with continuous trajectories. The Graphs of Convex Sets (GCS) framework offers a practical solution to these problems. It represents discrete decisions as nodes of a graph and encodes continuous trajectories in the edges connecting them. However, the resulting optimization subproblems can become computationally prohibitive for online replanning. In this work, we propose a learning-based strategy to mitigate this limitation. Specifically, we replace the costly convex relaxation step required by nominal GCS with a single forward pass through a Graph Attention Network that predicts a set of highly probable candidate paths through the graph. A lightweight ranking network then orders these candidates by their estimated trajectory cost. Evaluating them in this order, we terminate our search early while still recovering a near-optimal motion plan. We validate the resulting pipeline across diverse robotic tasks, including collision-free motion planning for a 3D quadrotor and a 7-DoF manipulator, and planning through contact for planar pushing. Across both convex and non-convex cost and constraint settings, our approach yields up to two orders of magnitude speedup over nominal GCS while maintaining a 100% success rate, at the cost of some suboptimality in the recovered solutions. Code implementations and video demonstrations can be found at https://neural-gcs.github.io/.

Humanoid locomotion in highly confined environments requires navigating dense environmental obstacles and complex self-collision bounds while maintaining multi-contact dynamic feasibility. Traditional trajectory optimizers frequently struggle in these restricted spaces, as navigating the large collision space with splines on particle abstractions is insufficient and leads to poor local minima. To address this, we propose a three-stage whole-body planning framework that formulates kinematic path planning directly over kinematically reachable rigid-body volumes. By integrating differentiable collision avoidance into a reachability-constrained formulation, our framework synthesizes volume-informed guides that reliably guide a full-order trajectory optimizer over long horizons. We show that these optimized plans serve as high-quality references to train a residual reinforcement learning policy for robust online execution. We validate our approach on the Unitree G1 humanoid across three benchmark testbeds exceeding NIST emergency response standards, achieving restricted confinement ratios ($C_r < 1.5$). Our framework generates feasible trajectories across 12-to-18-second tasks with complex foot and hand contacts where standard baselines fail, while the learned policy successfully tracks these plans under extensive domain randomization in physics simulation.

Long-horizon multi-part object disassembly requires robots to compute feasible sequences of collision-free removal motions, even in the presence of tight, narrow escape corridors. To efficiently solve such disassembly problems, we propose Parallel Extraction for Long-Horizon Disassembly (PEEL), an algorithm which efficiently computes disassembly motions for object assemblies and feeds them to a robot manipulator for execution. PEEL uses sampling-based motion planning to compute single-object motions through the use of a scale-invariant sampling scheme, where the object scale is estimated in a burn-in phase and a subsequent directional sampler exploits the scale. This sampling scheme is integrated into a multi-arm bandit rapidly-exploring random tree (MAB-RRT) planner, which switches between different samplers depending on the reward signal received. Using MAB-RRT, the PEEL algorithm runs a batch of planners in parallel to obtain an ordered graph specifying the sequence in which object parts have to be removed. We show that MAB-RRT can efficiently solve single-part disassemblies with 100 percent success rate on 76 assemblies, and that it is robust to its parameters. By integrating MAB-RRT into PEEL, we solve four long-horizon disassembly problems using the Fetch manipulator robot involving 10 to 17 individual object parts.

We present GASP, a GPU-Accelerated Safe Planner for real-time, collision-aware joint-space motion generation in known environments. GASP combines a clamped B-spline trajectory parameterization with a convolutional residual neural network that predicts the free interior control points, while analytically inserted boundary control points enforce initial and final derivative constraints for collision-aware planning under non-stationary conditions. A conditional variational autoencoder samples multiple trajectory candidates, which are decoded and validated in parallel on the GPU, yielding a batched planner for collision-aware coupled joint-space motion with near-millisecond inference. We validate GASP as an online motion-generation module, where it achieves analytical-level success rates with high collision-aware feasibility and substantially reduces inference time relative to GPU-based trajectory optimization. We further deploy GASP as a reinforcement-learning reset planner in competitive robotic table tennis, matching the baseline return rate while roughly halving training-time collisions.

We present Riemannian Informed Trees (RIT*), a planning framework that replaces Euclidean primitives in batch-informed search with their Riemannian counterparts. RIT* constructs a tighter, cost-consistent informed set, performs a nearest-neighbour search under an anisotropic distance metric, and evaluates edge costs efficiently via a cascading scheme. We further introduce a Collision-Adaptive Metric Refinement (CARM), which learns an obstacle-proximity cost field online from collision feedback, reducing the reliance on prior metric design in practical settings. Experiments across environments from 2-D to 14-D show that RIT* is competitive in low-dimensional and spatially constant-metric settings and produces substantially lower-cost solutions when the metric varies spatially in high-dimensional configuration spaces. Performance gains scale with anisotropy and dimension, reaching up to 13.0% improvement in median initial cost over BIT* in the 3-D anisotropic benchmark, up to 9.0% in median final cost over BIT* in 6-DOF manipulation, and 24.8-63.5% in a 14-DOF bimanual planning problem, where Euclidean-informed baselines degrade. Videos and code can be found here: https://muhayyuddin.github.io/ritstar/

Mainstream plan-then-track approaches to multifingered grasp execution entail selecting a grasp, planning a collision-free trajectory, and tracking the resulting trajectory via a feedback controller. Pose-estimation error during execution or scene motion can invalidate this open-loop commitment and trigger replanning. We thus present Grasp Distance Fields (GDFs), smooth softmin distances to finite sets of arm-hand grasp configurations. Using their negative gradients as feedback, we jointly select and execute grasps without planning a trajectory. A CBF-CLF quadratic program (QP) enforces self-collision, workspace, object, and obstacle-clearance constraints, while its CLF slack quantifies obstruction of task progress. We bound the softmin approximation error by $\log N/ρ$ and prove forward invariance of the filtered safe set. To handle changes in contact topology, we combine a hysteretic contact-mode transition with a wrench-quality CBF that limits degradation of the realized force-closure margin relative to hold onset. Using our method, a fixed-base manipulator and a Unitree G1 equipped with the same underactuated hand grasp and lift 46 of 50 test objects amid clutter and moving obstacles. The realized grasps also retain a median 94% of their synthesized quality margin, and each QP solve requires 0.09 ms within a 20 ms control interval. Project page: www.clintonenwerem.com/gdf.

Satellite constellations require orbital transfers that are both fuel efficient and collision avoidant. Yet, the computational cost of optimization methods traditionally used to plan their trajectories scales poorly with both the number of satellites as well as the number of obstacles to avoid, due to the pairwise safety constraints. In this work, we introduce a permutation-equivariant neural operator for trajectory planning of spacecraft swarms. This neural operator maps distributions of spacecraft initial states, target states, and obstacle initial states to trajectories which avoid collision and conserve fuel. This neural operator output is then paired with a batched Gauss-Newton finish to enforce exact orbital dynamics, and further reduce fuel use. The operator is self-supervised, trained without optimal trajectory labels. When trained on ten spacecraft, the proposed method generalized zero-shot to swarms of 1,000 spacecraft and 11,000 obstacles. The generated trajectories matched a per-agent optimal control solver's accuracy while retaining collision avoidance. Operator learning grounded in physics may offer a fast, scalable alternative to trajectory optimization in the increasingly crowded orbits of the future.

Robots in cluttered indoor spaces often fail not because they cannot generate collision-free paths, but because a fixed safety margin is mis-calibrated: conservative margins cause detours and timeouts, while permissive margins lead to near-boundary shortcuts under perception bias. Diffusion-based planners propose diverse trajectory candidates from egocentric RGB-D, yet reliable selection remains the bottleneck. We propose a context-conditioned safety critic that learns an adaptive clearance preference for ranking diffusion proposals, decomposed into three complementary terms: (i) a safety term with a clearance-budget penalty and a control-barrier-function residual for waypoint- and transition-wise safety, (ii) an efficiency term combining a smoothness penalty with a safety-gated detour-ratio penalty that avoids detours without incentivizing risky shortcuts, and (iii) a distance-constraint matching term that anchors the learned budget to realized ESDF clearances to prevent margin collapse. We train the critic with privileged ESDF geometry in simulation and distill it into a perception-only selector via a two-stage teacher-student procedure. On PointGoal navigation in HM3D and MP3D, including cross-dataset transfer, our method achieves the highest success rate (SR) and success weighted by path length (SPL) among strong diffusion, optimization, and RL baselines. Trained purely in simulation, it transfers to a Unitree G1 humanoid and navigates cluttered indoor scenes without task-specific tuning.

Active 3D reconstruction requires selecting informative viewpoints under limited sensing budgets. In multi-agent settings, coordination inefficiencies such as redundant observations and spatial clustering can significantly reduce reconstruction quality. We present COLMAR, a cooperative view policy learning framework for multi-agent active 3D reconstruction. COLMAR formulates viewpoint allocation as a shared policy optimization over map-centric observations and introduces a reconstruction-aware objective that promotes overlap-aware coverage, team-level discovery, and collision-safe exploration. Dense feedback derived from incremental reconstruction updates aligns exploration behavior with downstream geometric quality. The policy is trained using parameter-sharing Proximal Policy Optimization (PPO) with independent per-agent action selection at deployment, conditioned on a fused team map and without inter-agent message passing for decision making. Selected viewpoints are then reconstructed with 3D Gaussian Splatting (3DGS) for high-fidelity photometric evaluation. Experiments on GLEAM and Replica demonstrate consistent improvements over heuristic and non-cooperative baselines, achieving up to 54% higher reconstruction accuracy and 49% greater coverage under matched sensing budgets.

Multi-Robot Motion Planning in continuous environments, where robots must generate dynamically feasible, collision-free trajectories, is challenging due to the combinatorial growth of the joint trajectory space and the difficulty of enforcing dynamic feasibility and hard safety constraints. Recent approaches recast trajectory planning as probabilistic inference, sampling from a posterior over trajectories using diffusion models whose score functions are learned from demonstration data. While showing promising performance, these approaches are limited: they often rely on sizable demonstration datasets and struggle to rigorously enforce dynamics and hard safety constraints during sampling. To this end, we introduce Model-Based Diffusion Optimal Control (MDOC), a model-based diffusion planner that efficiently produces dynamically feasible trajectories without relying on data. Crucially, we show that MDOC's safety mechanism -- combining known dynamics models with Control Barrier Function-constrained projections -- naturally scales to multi-robot planning settings through Conflict-Based Search. Across simulation experiments, this integrated method consistently outperforms representative baseline planners in sample efficiency, geometric smoothness, and success rate, while reducing computation time and producing collision-free trajectories.

Physics-based Human-Scene Interaction (HSI) imitation learning is crucial for embodied intelligence as it bridges the gap between kinematic 3D motions and real-world dynamics. However, most existing methods focus on simplified scene settings, leaving complex environments largely unexplored, which limits their applicability in real-world scenarios. In this paper, we focus on HSI mimicry in complex environments. Under this complex setting, we observe an inherent trade-off between successfully performing interaction and maintaining natural, physically plausible motions. To address this challenge, we propose ComplexMimic, a framework that reconstructs diverse HSI by interpreting imperfect MoCap data. First, we introduce a Dual Flow Strategy, which learns two complementary experts: an imitation expert for accurate motion tracking and an interaction expert for collision-aware adaptation in complex scenes. Second, naive multi-expert distillation, which treats all experts equally, often under-samples challenging behaviors, limiting effective learning. To mitigate this issue, we propose a difficulty-aware distillation strategy that adaptively weights supervision and prioritizes hard-yet-learnable trajectories guided by failure statistics and learning progress signals. Extensive experiments on three benchmark datasets demonstrate that our approach outperforms current state-of-the-art methods.

As technology advances, many path-planning algorithms have been proposed for Air Traffic Management, yet their operational adoption in tactical control remains limited, revealing a misalignment between algorithmic design priorities and air traffic controllers' needs. This underscores the need for decision-support solutions that are inherently interpretable, computationally efficient, and explicitly designed for human use. Focusing on this design challenge, this study develops a conflict-free path-planning algorithm for en-route Air Traffic Control (ATC) designed to be compatible with two guiding considerations: (1) the interpretability and flexibility offered by solution-space displays, which motivate constructing an algorithm that exposes all feasible safe actions and accommodates shifting optimization goals; and (2) the decision logic controllers naturally apply when enforcing operational constraints, such as separation standards, maneuverability limits, waypoint minimization, and routing practicality. Centered on these principles, the algorithm integrates three intent-based conflict detection methods -- distance-based, time-interval-based, and zone-based -- within a solution-space framework to identify conflict-free paths in computationally efficient ways. Additionally, vertex-based and edge-based search nodes are proposed for solution space path planning (SSPP), resulting in two variants -- SSPPV and SSPPE, respectively, which are evaluated in terms of computational speed and solution quality. Empirical results show that SSPPV paired with zone-based conflict detection achieves the best performance, computing paths in 3.69 ms on average in operational-relevant scenarios based on the Delta sector of the Maastricht Upper Area Control Centre (MUAC) using a 5 nmi grid.

Redundant robotic multi-axis additive manufacturing (MAAM) enables support-free and conformal fabrication, but trajectory optimization for long-horizon paths remains challenging under strict deposition-position constraints and time-varying collision constraints. This work proposes a computational framework for collision-aware trajectory optimization in redundant robotic MAAM. We first formulate nozzle-workpiece relative kinematics using a relative Jacobian, and develop a differentiable SDF-based collision model that captures fabrication-induced geometry evolution and provides optimization gradients. The deposition position is then enforced as a hard waypoint-wise equality constraint through iterative projection onto the self-motion manifold, with the loss gradient restricted to the corresponding tangent space. Experiments on an 8-DOF robotic MAAM platform with diverse long-horizon support-free and conformal toolpaths show that our method maintains a mean nozzle-position error below 10μm, reduces maximum joint jerk by up to $77.6\%$, and eliminates all sampled collision and orientation violations. Compared with the SQP-based baseline, it achieves up to a 10.2x speedup and improved convergence. Physical fabrication experiments further verify that the resulting smooth, collision-free trajectories enable successful printing of complex geometries with fewer visible deposition artifacts.

Massive robot swarms can explore unknown environments quickly, but adding robots eventually stops helping. Doorways and dense traffic create congestion, increasing inter-robot contacts and reducing the value of each additional robot. We study this safety-efficiency tradeoff for ground swarms of tens to hundreds of robots. We present SPACE, Swarm Pheromone Fields for Adaptive Collision-Aware Exploration. Inspired by ant foraging, SPACE maintains a shared environmental field with an attractive frontier pheromone, a repellent explore pheromone, and a fast robot-density field. Coordination is decentralized and mediated through this field. We evaluate SPACE on real building floorplans, namely sixteen home layouts from the HouseExpo dataset and eight campus floors from the KTH dataset, with swarms of up to two hundred and fifty-six robots. SPACE lies on the empirical Pareto frontier. It attains the lowest inter-robot contact rate at every congested swarm size, four to seventeen times fewer than a greedy nearest-frontier planner, while keeping coverage time within about two percent of that near time-optimal planner. The results indicate that, at this scale, coordination mainly improves safety rather than coverage time.

Multi-Agent Path Finding (MAPF) is a problem that requires computing collision-free paths for a set of agents from their start locations to designated goal locations. The problem has broad applications in domains where teams of robots must operate in a coordinated manner. ORCA* is a real time MAPF solver that assigns for each timestep a velocity for each agent. Due to its real time nature, it is myopic to future deadlocks that result from current decisions. ORCA*-MAPF attempts to remedy this limitation by introducing fallback mechanisms when deadlocks are detected. However, post hoc interventions often introduce significant flowtime overhead. In this paper, we introduce C-ORCA* and C-ORCA*-MAPF, continuous space MAPF algorithms that incorporate agents' entire spatial trajectory and their spatial dependencies to proactively prevent deadlocks from occurring, thus avoiding the high flowtime overhead associated with post hoc corrections in ORCA*-MAPF. The C-ORCA* family of algorithms significantly outperform previous state-of-the-art in terms of solve rate, runtime, and flowtime.

Quadruped robots are increasingly expected to navigate through narrow passages, cluttered indoor scenes, and large-scale 3D unstructured environments. Existing local planners commonly approximate the robot using isotropic geometric inflation or rely on planar and elevation-map representations, leading to conservative motion in tight spaces and limited reasoning about overhanging structures. This letter presents SCAN-Planner, a spatial collision-aware local planning framework for long-range quadruped navigation. A yaw-aware twin-cylinder footprint is used to model the elongated robot body, enabling whole-body collision evaluation through sparse queries in an inflated 3D occupancy map. We further introduce a projected A* search that generates collision-free guidance on an interpolated ground-following surface, with z-gradient suppression to avoid obstacles horizontally while maintaining vertical stability. For large-scale deployment, a robot-centric sliding map with boundary fallback provides high-resolution local collision checking and recovery from local dead ends. Simulation and real-world experiments demonstrate that SCAN-Planner generates safe, smooth, and efficient trajectories in dense clutter, 3D unstructured scenes, stair traversal, and long-range navigation tasks.

Diffusion-based visuomotor policies deployed with asynchronous inference often exhibit inter-chunk discontinuities and lack explicit mechanisms for obstacle-aware execution, leading to jerky motions and collisions that hinder reliable manipulation in real-world scenes. To address these issues, we propose LAGO Policy, a unified asynchronous action-generation framework that integrates trajectory optimization with diffusion policy for smooth and safe execution. LAGO Policy improves inter-chunk consistency via latency-aware classifier-free guidance conditioning on future actions. It further enables goal-directed collision-free trajectory planning by predicting a task-relevant interaction goal from demonstrations. Finally, spatial-temporal trajectory optimization refines the actions to be executed for low-jerk and feasible motion. Extensive real-world experiments demonstrate that LAGO Policy achieves smooth collision-free execution with high task success across challenging manipulation tasks. Project Website: https://lago-policy.github.io/

We study semidefinite relaxations for collision-free motion planning. We focus on a point robot moving from start to goal through spherical obstacles in $\mathbb{R}^n$, subject to path continuity constraints and squared derivative costs; a setting that is conceptually simple yet captures the hardness of collision-free motion planning. We formulate this problem exactly as a nonconvex problem over polynomial curves, and present a natural semidefinite relaxation. We contribute two key theoretical insights; to our knowledge this is the first theoretical analysis of semidefinite relaxations for collision-free motion planning. First, we show that solving the convex relaxation is equivalent to solving, to global optimality, a related motion planning problem in a potentially higher-dimensional space. This geometric interpretation yields necessary and sufficient conditions for tightness, and a clear intuition for when the relaxation is loose. Second, we show that the relaxation admits a symmetry reduction that makes it significantly smaller than one might expect, with positive semidefinite cone sizes that scale linearly with the polynomial degree and are independent of the ambient dimension. The resulting relaxation is 10 to 100 times faster than direct nonlinear programming transcriptions solved with SNOPT and IPOPT, exhibits significantly lower variance in solve times, and reliably finds a locally optimal path for the original problem. We demonstrate its effectiveness as a convex steering function in an RRT planner for minimum-snap quadrotor planning with $C^4$ continuous trajectories.

Reactive motion generation in unstructured environments remains an open challenge in robotics. Due to the computational complexity of collision-free motion generation, existing methods either generate global trajectories for static scenarios, or employ models that make conservative assumptions about the environment. This paper identifies the primary bottleneck as the runtime performance demand of planning on high-fidelity environments, and the temporal integration between the perception and planning modules. Therefore, we propose a framework that does not compromise on runtime performance and world representations for perception and planning by accelerating world modeling and vector-field based planning using the GPU. This allows us to achieve faster parallel state exploration for quasi-global trajectory planning, and tighter coupling of the perception-action loop in real-time for dynamic cluttered environments with off-the-shelf depth sensors. We quantitatively evaluate the computation-time and success rate differences for the CPU and GPU versions of our planner, and perform qualitative evaluations of our coupled framework using real-world experiments on a 7-DoF Franka Emika robot. Experimental results demonstrate that our GPU-based framework achieves up to a 5x speedup over the CPU version and successfully avoids collisions across both trivial and challenging physical world scenarios.

Collision-free path planning in cluttered, real-world environments relies on a representation of the collision-free space, and existing representations broadly fall into two categories. Explicit representations, such as unions of convex sets, can be plugged into optimization-based planners as hard collision-free constraints, but their parameters scale poorly with configuration-space dimension. Implicit representations, by contrast, are flexible and scale well to complex geometries, yet typically lack such guarantees. We bridge this gap with ILD (Invertible Latent Decomposition), a framework that jointly learns an invertible mapping and a union of explicit convex polytopes in the resulting latent space. Planning is carried out over these latent convex sets, and the invertible mapping decodes the resulting paths back to the original configuration space while preserving feasibility with respect to the refined explicit safe regions. We further propose Visibility-Guided Sampling (VGS) to keep the convex sets connected for path planning. Across 2D navigation, 6-DoF, and 14-DoF manipulation environments, ILD achieves broader coverage, better inter-set connectivity, and higher path-planning success rates than prior baselines, with zero observed false positives after test-time refinement. On a 14-DoF bimanual manipulator, we further demonstrate real-time collision-free planning, with test-time refinement adapting to scene-geometry changes during real-world deployment on a single 6-DoF arm.

In teleoperation, the human operator typically controls only the end-effector pose, which often leads to self-collisions of the manipulator and collisions with environmental obstacles, since joints and links are not controlled individually. A common strategy to mitigate this issue is to enhance the operator's input using optimal-control-based trajectory planning. As derivative-based solvers require differentiable constraints, existing approaches either approximate robots and obstacles with spheres, reducing geometric accuracy, or approximate derivatives, degrading convergence and increasing computation times. We address these limitations by adapting a recent formulation of differentiable collision-avoidance constraints, based on duality in convex optimization, to the teleoperation setting. The robot is approximated with capsules and the environment with polytopes. We compare the resulting trajectory planning method against state-of-the-art techniques in simulation with varying numbers of obstacles and evaluate it on a UR5e manipulator in a real-world teleoperation test. Results show that our approach achieves lower computation times while enabling more accurate obstacle modeling, leading to smoother and collision-free end-effector teleoperation.

Despite a great deal of prior research into Procedural Content Generation (PCG), relatively little prior work has explored generating enemies for video games. In particular, there is almost no work on generating enemy morphologies, the basic body plan or collision information for in-game enemies, despite the existence of related morphology generation work in robotics. In this paper, we explore three different novel approaches to generate enemy morphologies based on player collision information. We found that each approach provides different strengths and weaknesses, but all had equivalent or better performance than an evolutionary baseline adapted from prior robotics morphology work.

Robot teleoperation enables safe, non-contact task execution in hazardous environments where direct human access is difficult, and its application has expanded with recent VR technologies. Many VR teleoperation studies, however, have primarily served as data-collection tools for robot imitation learning, so they often do not explicitly address dynamic obstacles, workspace changes, or collision risks during operation. For real deployment aimed at operator safety, teleoperation must react to dynamic situations with low latency and remain robust to mistakes made by inexperienced operators. This paper presents a VR teleoperation framework that supports real-time manipulation while handling collisions with both static and moving obstacles. The framework integrates GPU-accelerated inverse kinematics and trajectory optimization within a VR interface to generate feasible joint commands at each control cycle under robot constraints. Experiments with a 7-DoF manipulator demonstrate stable online behavior and collision-aware motion generation across three scenarios: obstacle-free, static-obstacle, and moving-obstacle environments. The results indicate that the proposed approach generates motion consistent with the operator's command while producing safe detours when obstacles interfere with the commanded path.

Decentralized multi-robot motion planning requires each robot to generate collision-free trajectories from local observations, without global sensing or reliable communication. However, most existing planners, whether classical or learning-based, generate trajectories from a static snapshot of the local observation, which limits their ability to anticipate the future behavior of neighboring robots. This limitation is critical as the number of robots increases and the environment becomes more cluttered. To overcome this challenge, this paper introduces Simulation-Informed Diffusion (SID), a decentralized framework built on constraint-aware diffusion models (CADM). SID first uses CADM to simulate the future trajectories of neighboring robots from their currently observed states, and then uses the same CADM to plan each robot's own trajectory under safety constraints informed by these simulations. Crucially, the accurate simulation of neighbors enables a minimal communication scheme that triggers coordination only when necessary in highly congested scenarios. Experiments across diverse environments show that SID consistently outperforms baseline methods in terms of planning effectiveness and constraint satisfaction, and scales to scenarios with 108 robots and 160 obstacles.

The motion planning problem for robotic manipulation can be addressed through classical or deep learning approaches. Existing methods face significant challenges in generalizing to diverse settings. In this study, we present a method with high generalization capability that generates collision-free trajectories using diffusion models where the denoising process is guided by the gradient of the total collision cost. We are also presenting a dynamic approach for choosing start step of the gradient guidance. Experimental results demonstrate that guiding the diffusion model dynamically with the sum of collision costs offers more robust performance by overcoming the generalization issues faced by competing methods. The proposed model demonstrates its effectiveness by achieving the highest performance on diverse test settings in M$π$nets\ dataset among the compared methods.

We study a graph pathfinding problem Distance-$r$ Independent Unlabeled Multi-Agent Pathfinding, finding a set of collision-free paths between two sets where agents must stay at pairwise distance at least $r+1$ at all times. This additional constraint, generalizing collision modeling for classical MAPF, targets aspects of real-world multi-agent coordination. This additional distance constraint makes feasibility (i.e., whether a solution exists) PSPACE-complete, in contrast to standard (unlabeled) MAPF, where it can be decided in polynomial time. We address the challenge via two complementary approaches: (i) reduction-based optimal algorithms with a feasibility-preserving compression procedure, and (ii) a configuration generator-based search. Despite the hardness, empirical results show that our algorithm can handle hundreds of agents in a practical timeframe.

Stochastic Human Trajectory Prediction (HTP) using generative modeling has emerged as a significant area of research. Although state-of-the-art models excel in optimizing the accuracy of individual agents, they often struggle to generate predictions that are collectively compliant, leading to output trajectories marred by social collisions and environmental violations, thus rendering them impractical for real-world applications. To bridge this gap, we present JACoP: Joint Alignment for Compliant Multi-Agent Prediction, an innovative multi-stage framework that ensures scene-level plausibility. JACoP incorporates an Anchor-Based Agent-Centric Profiler for effective initial compliance filtering and employs a Markov Random Field (MRF) based aligner to formalize the joint selection for scene predictions. By representing inter-agent spatial and social costs as MRF energy potentials, we successfully infer and sample from the joint trajectory distribution, achieving prediction with optimal scene compliance. Comprehensive experiments show that JACoP not only achieves competitive accuracy, but also sets a new standard in reducing both environmental violations and social collisions, thereby confirming its ability to produce collectively feasible and practically applicable trajectory predictions.

Approximating collision-free space is fundamental to robot planning in complex environments. Convex geometric representations, such as polytopes and ellipsoids, are widely employed due to their structural properties, which can be easily integrated with convex optimization. Iterative optimization-based inflation methods can generate large volume polytopes in cluttered environments, but their efficiency degrades as the obstacle set becomes more complex or when sensor data are noisy. These methods are also sensitive to initialization and often rely on accurate geometric models. In this paper, we propose the STAR-Filter, a lightweight framework that employs starshaped set construction as a fast filter for convex region generation in collision-free space. By identifying obstacle points as active supporting constraints, the proposed method significantly reduces redundant computation while preserving feasibility and robustness to sensor noise. We provide theoretical and numerical analyses that characterize the structural properties of the starshaped set and proposed pipeline in environments of varying complexity. Simulation results show that the proposed framework achieves the lowest computation time and reduces conservativeness in polytope generation for real-world noisy and large-scale data. We demonstrate the effectiveness of the framework for Safe Flight Corridor (SFC) generation and agile quadrotor planning in noisy environments.

Convex free regions provide a structured and optimization-friendly representation of collision-free space for robot navigation in unknown and cluttered environments. However, existing methods typically enlarge local collision-free regions mainly according to surrounding obstacle geometry. In cluttered environments, such strategies may fail to generate regions that both accommodate robot geometry and preserve traversable extension along candidate motion directions, thereby limiting downstream traversal, especially in narrow passages. Even when such a region is available, safe motion generation remains challenging, because safety checking at discretized trajectory samples does not guarantee continuously collision-free motion when robot geometry is modeled explicitly. To address these issues, we propose a navigation framework that jointly incorporates candidate motion directions and robot geometry into convex free-region generation, and achieves continuously collision-free motion through continuous-safe trajectory generation. Within each region, the framework performs geometry-aware target pose selection and trajectory generation, together with Lipschitz-based continuous safety certification and local refinement. The resulting free regions and candidate motions are maintained in a region-based graph to support incremental planning. Quantitative results in cluttered 2D navigation scenarios show that the proposed method generates free regions better aligned with downstream traversal and enables reliable collision-free navigation, while additional 3D and real-world experiments on a quadrupedal robot and a UAV demonstrate the extensibility and practical applicability of the framework. The open-source project can be found at https://github.com/ZhichengSong6/FRGraph.

Coordinating the motions of multiple autonomous vehicles (AVs) requires planning frameworks that ensure safety while making efficient use of space and time. This paper presents a new approach, termed variable-time-step spatio-temporal corridor (V-STC), that enhances the temporal efficiency of multi-vehicle coordination. An optimization model is formulated to construct a V-STC for each AV, in which both the spatial configuration of the corridor cubes and their time durations are treated as decision variables. By allowing the corridor's spatial position and time step to vary, the constructed V-STC reduces the overall temporal occupancy of each AV while maintaining collision-free separation in the spatio-temporal domain. Based on the generated V-STC, a dynamically feasible trajectory is then planned independently for each AV. Simulation studies demonstrate that the proposed method achieves safe multi-vehicle coordination and yields more time-efficient motion compared with existing STC approaches.

In this paper, we present an online method for converting an arbitrary geometric path, represented by a sequence of states, and generated by any planner (e.g., sampling-based planners such as RRT or PRM, search-based planners such as ARA*, etc.), into a kinematically feasible, jerk-limited trajectory. The method generates a sequence of quintic/quartic splines that can be discretized at a user-specified control rate and streamed to a low-level robot controller. Our approach enables real-time adaptation to environmental changes and can be re-invoked at any instant to generate a new trajectory from the robot's current state to a desired target state or sequence of states. Under a bounded-obstacle-velocity assumption, the method provides conditional stopping-safety guarantees over a finite time interval in dynamic environments, while allowing bounded geometric deviation from the original path. Kinematic constraints, including jerk limits, are explicitly considered. We validate the approach in a comparative simulation study against a competing method, demonstrating favorable behavior w.r.t. smoothness, computational time, and real-time performance, particularly with frequent target-state changes (up to 1 [kHz]). Real-robot experiments demonstrate applicability in real-world scenarios, including scenarios with a human as an obstacle.

This paper investigates a problem called Multi-Agent Path Finding with Elevators (MAPF-E), which seeks conflict-free paths for multiple agents from their start to goal locations that may locate on different floors, and the agents can use elevators to travel between floors. The existence of elevators complicates the interaction among the agents and introduces new challenges to the planning. On the one hand, elevators can cause many conflicts among the agents due to its relatively long traversal time across floors, especially when many agents need to reach a different floor. On the other hand, the planner has to reason in a larger state space including the states of the elevators, besides the locations of the agents.