Ergodic Trajectory Design by Learned Pushforward Maps: Provable Coverage via Conditional Flow Matching

• URL: http://arxiv.org/abs/2605.13063v1
• Date: Wed, 13 May 2026 06:34:08 GMT
• Title: Ergodic Trajectory Design by Learned Pushforward Maps: Provable Coverage via Conditional Flow Matching
• Abstract summary: The emphergodic coverage problem is central to UAV-assisted data collection and sensing, robotic exploration, and mobile monitoring.<n>For flying agents, trajectories must balance coverage fidelity against tight energy budgets, no-fly zones, and acceleration limits.<n>We propose a emphepushforward framework that decouples ergodicity from density matching.
• Score: 3.1807155456602274
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Designing continuous trajectories whose time-averaged occupancy provably matches a prescribed spatial density (the \emph{ergodic coverage} problem) is central to UAV-assisted data collection and sensing, robotic exploration, and mobile monitoring. For flying agents in particular, this challenge is acute: trajectories must balance coverage fidelity against tight energy budgets, no-fly zones, and acceleration limits. Existing methods either re-optimize each trajectory online (with cost growing in the horizon and re-running for every target, agent, and realization) or rely on bespoke analytical constructions that must be re-derived for each new constraint. We propose a \emph{epushforward} framework that decouples ergodicity from density matching: an analytic latent trajectory provides exact uniform ergodicity on a simple annular domain, and a single map, learned offline by optimal-transport conditional flow matching, transports this latent occupancy onto the prescribed target density. The composed trajectory is then asymptotically ergodic with respect to the learned pushforward distribution, with deviation from the target controlled by the flow-matching training loss. Once trained for a given target density and constraint set, the map serves an unbounded number of trajectories and a multi-agent fleet without per-agent retraining, and many differentiable operational constraints (no-fly zones, acceleration ceilings, or fairness penalties) enter as additive soft penalties in the training loss without re-deriving the design. We prove three results (an acceleration-energy bound, an $O(1/\sqrt{K})$ ergodic convergence rate in the number of trajectory cycles $K$, and an approximation-error bound) that combine into an end-to-end coverage bound estimable from CFM training diagnostics (certified given an architectural Lipschitz bound on $v_θ$).

Related papers

• Some Modifications to Our End-to-End UAV Planner [2.3190673374277524]
  The one-stage planner maps a single depth image and the robot state directly to a set of candidate trajectories.<n>We show that YOPO's multi-modal prediction span to distinct homotopy classes, treating each motion as a trajectory that confines the trajectory to a feasible - without explicit safe-building or construction penalties.
  arXiv  Detail & Related papers  (2026-08-16T13:39:46Z)
• Model Predictive Planner for UAV Navigation in Non-Convex Air Corridors [1.2617078020344616]
  This work presents a motion motion framework for UAV air corridors.<n>The planner is based on a mixed-integer tracking model that enforces external feasibility.
  arXiv  Detail & Related papers  (2026-07-27T12:42:38Z)
• G2DP: Diffusion Planning with Spatio-Temporal Grid Guidance [44.0166619948181]
  In autonomous driving, diffusion-based planners have emerged as a promising paradigm for robust motion planning in dense and interactive traffic.<n>Existing guidance typically relies on sparse, entity-centric geometric queries or post-hoc refinement, yielding limited awareness and fragile performance in interactive scenes.<n>G2DP (GuidedGrid-Guided Planning) constructs a differentiable-temporal cost volume by fusing probabilistic future occupancy guidance with a route-time map.<n>It achieves state-of-the-art performance on nuPlan, outperforming the strongest imitation-learning baseline by +7.2 points in reactive transfers.
  arXiv  Detail & Related papers  (2026-06-24T16:38:55Z)
• Wind-Aware Optimal Trajectory Planning for Efficient Gliding of Fixed-Wing Aerial Systems [7.0414059106180025]
  Gliding offers small fixed-wing UAVs extended endurance and silent operation.<n>Traditional Total Energy Control Systems based controllers regulate the trade between potential and kinetic energy reactively.<n>We present a nonlinear, multi-cost trajectory planner for small UAV gliders.
  arXiv  Detail & Related papers  (2026-05-15T05:01:09Z)
• Self-Distilled Trajectory-Aware Boltzmann Modeling: Bridging the Training-Inference Discrepancy in Diffusion Language Models [65.89572755202245]
  Diffusion Language Models (DLMs) offer stronger global awareness and highly parallel generation.<n>Post-training DLMs with standard Negative Evidence Lower Bound (NELBO)-based supervised fine-tuning remains inefficient.<n>We propose a self-distilled trajectory-based post-training framework that aligns training with the easy-to-hard structure of inference.
  arXiv  Detail & Related papers  (2026-05-12T09:39:06Z)
• RAD-2: Scaling Reinforcement Learning in a Generator-Discriminator Framework [49.531001563853984]
  RAD-2 is a unified generator-discriminator framework for closed-loop planning.<n>It produces diverse trajectory candidates, while an RL-optimized discriminator reranks these candidates according to their long-term driving quality.<n>It reduces the collision rate by 56% compared with strong diffusion-based planners.
  arXiv  Detail & Related papers  (2026-04-16T17:59:44Z)
• Collision-Free Velocity Scheduling for Multi-Agent Systems on Predefined Routes via Inexact-Projection ADMM [0.0]
  In structured multi-agent projects, agents often must follow predefined routes, making rerouting or impossible.<n>This paper addresses route-constrained multi-agent coordination by optimizing waypoint times while preserving each agent's assigned waypoint order and nominal route assignment.
  arXiv  Detail & Related papers  (2026-03-23T12:34:18Z)
• Amortizing Trajectory Diffusion with Keyed Drift Fields [2.5352713493505785]
  Keyed Drifting Policies is a one-step trajectory generator trained with a drift-field objective.<n>It repels generated trajectories toward condition-matched dataset windows.<n>It achieves strong performance with one-step inference and substantially lower planning latency than diffusion sampling.
  arXiv  Detail & Related papers  (2026-03-14T17:56:15Z)
• Consistent and Efficient MSCKF-based LiDAR-Inertial Odometry with Inferred Cluster-to-Plane Constraints for UAVs [46.21996481591401]
  This paper proposes a consistent and efficient LiDAR-Inertial Odometry framework tailored for UAVs.<n>By applying null-space projection to sliding-window coplanar constraints, we eliminate the direct dependency on feature parameters in the state vector.<n>It exhibits improved robustness in degenerate scenarios, achieves the lowest memory usage via its map-free nature, and runs in real-time on resource-constrained embedded platforms.
  arXiv  Detail & Related papers  (2026-03-13T11:09:50Z)
• Vision-Guided MPPI for Agile Drone Racing: Navigating Arbitrary Gate Poses via Neural Signed Distance Fields [8.66703842496129]
  Drone racing requires tight coupling of perception, planning, and control under extreme agility.<n>Recent approaches rely on precomputed spatial reference trajectories or explicit 6-DoF gate pose estimation.<n>We propose a vision guided optimal control framework that enables reference-free agile flight through arbitrarily placed and oriented gates.
  arXiv  Detail & Related papers  (2026-03-07T13:18:07Z)
• DRIFT: Diffusion-based Rule-Inferred For Trajectories [15.78457153766977]
  Trajectory generation for mobile robots in unstructured environments faces a critical dilemma: balancing smoothness for safe execution with terminal precision for fine-grained tasks.<n>This article proposes DRIFT, a conditional framework designed to generate high-fidelity reference trajectories by integrating two complementary inductive biases.<n>Results demonstrate that DRIFT reconciles these conflicting objectives, achieving centimeter-level imitation fidelity (0.041m FDE) and competitive smoothness (27.19 Jerk)
  arXiv  Detail & Related papers  (2026-03-01T05:54:38Z)
• Spatially-Aware Adaptive Trajectory Optimization with Controller-Guided Feedback for Autonomous Racing [74.83272587893508]
  We present a framework for autonomous raceline optimization that combines NURBS-based trajectory representation, CMA-ES global trajectory optimization, and controller-guided spatial feedback.<n>In simulation, our approach achieves a 17.38% lap time reduction compared to a controller parametrized with maximum static acceleration.<n>On real hardware, tested with different tire compounds ranging from high to low friction, we obtain a 7.60% lap time improvement without explicitly parametrizing friction.
  arXiv  Detail & Related papers  (2026-02-17T15:10:44Z)
• Mastering Diverse, Unknown, and Cluttered Tracks for Robust Vision-Based Drone Racing [22.63301233637327]
  Most reinforcement learning methods for drone racing target fixed, obstacle-free tracks, leaving the generalization to unknown, cluttered environments largely unaddressed.<n>This challenge stems from the need to balance racing speed and collision avoidance, limited feasible space causing policy exploration trapped in local optima during training.<n>We propose a two-phase learning framework: an initial soft-collision training phase that preserves policy exploration for high-speed flight, followed by a hard-collision refinement phase that enforces robust obstacle avoidance.
  arXiv  Detail & Related papers  (2025-12-10T12:02:48Z)
• NOVA: Navigation via Object-Centric Visual Autonomy for High-Speed Target Tracking in Unstructured GPS-Denied Environments [56.35569661650558]
  We introduce NOVA, a fully onboard, object-centric framework that enables robust target tracking and collision-aware navigation.<n>Rather than constructing a global map, NOVA formulates perception, estimation, and control entirely in the target's reference frame.<n>We validate NOVA across challenging real-world scenarios, including urban mazes, forest trails, and repeated transitions through buildings with intermittent GPS loss.
  arXiv  Detail & Related papers  (2025-06-23T14:28:30Z)
• Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach [76.45949280328838]
  We propose a Laplacian enhanced low-rank tensor (LETC) framework featuring both lowrankness and multi-temporal correlations for large-scale traffic speed kriging. We then design an efficient solution algorithm via several effective numeric techniques to scale up the proposed model to network-wide kriging.
  arXiv  Detail & Related papers  (2022-10-21T07:25:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.