This work proposes Function-Space Diffusion for Motion Planning (FSD-MP), a diffusion-based motion planner that models trajectories as continuous functions and performs diffusion directly in function space, achieving discretization-invariant trajectory generation.
Abstract
Diffusion-based motion planners have demonstrated strong performance in generating diverse and high-quality robot trajectories in cluttered environments with multiple feasible solutions. However, existing approaches typically operate on fixed-length waypoint sequences, making the learned model resolution-dependent, thereby preventing zero-shot generalization across resolutions. In this work, we propose Function-Space Diffusion for Motion Planning (FSD-MP), a diffusion-based motion planner that models trajectories as continuous functions and performs diffusion directly in function space, achieving discretization-invariant trajectory generation. We define a mode-wise forward process in the spectral domain, driven by Gaussian noise with a Mat\'ern-type covariance, and parameterize the reverse process with a boundary-compatible Discrete Sine Transform-based Fourier Neural Operator (DST-FNO) that preserves start-goal constraints across resolutions. We evaluate FSD-MP on 2D point robot and 7-DoF Franka manipulator planning benchmarks. Our method achieves competitive planning performance at the training resolution and generalizes zero-shot across resolutions up to 16$\times$ higher, preserving consistent planning behavior without retraining. These results demonstrate that function-space diffusion provides an effective framework for discretization-invariant motion planning.
This work introduces Model-Based Diffusion Optimal Control (MDOC), a model-based diffusion planner that efficiently produces dynamically feasible trajectories without relying on data, and shows that MDOC's safety mechanism naturally scales to multi-robot planning settings through Conflict-Based Search.
Guided diffusion planners for robot manipulators often fail in bottleneck scenes. The reason is that local collision corrections must be coordinated through a limited latent parameterization. This study examines the issue at the level of trajectory representation. Spectral-linear representation is introduced as a compact joint-space representation that combines an endpoint-conditioned linear reference path with a small set of globally supported eigenmodes derived from a conditioned temporal kernel. Using a shared training corpus, conditioning scheme, guidance rule, and dense-evaluation protocol, spectral-linear representation is compared with five representative alternatives across six representation families and dimensionality sweeps from 14 to 448 dimensions. With 14 latent dimensions, spectral-linear representation attains the highest structured-scene success rates among the tested families, reaching 74.2% on narrow-passage scenes and 84.5% on rack-like scenes. Expert-only controls, per-family guidance tuning, and a Transformer-backbone rerun are consistent with the same broad ranking pattern. These results indicate that, under limited guidance budgets and within the tested protocol, the representation structure is more predictive of bottleneck success than latent width alone.
Zongjian Chen, Zichao Zou, Rongqian Yang et al.· Machines· 0 citations
This work introduces Model-Based Diffusion via Constraint Optimization and Adaptive Scheduling (MD-COAS) for SRMP that unifies the inexact Augmented Lagrangian Method (iALM) soft diffusion prior with a Convex Feasible Set (CFS)-based hard projection operator, and adaptively schedules and co-optimizes safety enforcement, along with diffusion scheduling.
Zhilin He, Bowei Li, Jianlin Dou et al.· 1 citation
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/.
Ananya Trivedi, Sarvesh Prajapati, M. K. M. Jaffar et al.· 0 citations
This research proposes a constrained motion planning framework for robot manipulators in human-robot interaction (HRI). For a non-redundant manipulator with a fully specified end-effector pose, additional requirements such as collision avoidance and self-collision avoidance are difficult to handle as simple null-space secondary tasks. This limitation makes it challenging to generate feasible joint-space trajectories in HRI environments where safety and kinematic constraints must be considered simultaneously. To address this limitation, collision- and self-collision-aware trajectories are generated using Rapidly-exploring Random Tree (RRT) and RRT* algorithms, and the resulting dataset is used to train a diffusion model that generates constraint-satisfying trajectories through guided sampling. To reduce the inference time required for iterative diffusion sampling, consistency distillation is applied, and a joint-weighted jerk regularization term is incorporated into the loss function to promote smoother trajectories by penalizing abrupt changes in joint acceleration. Simulation results show that the consistency model generates 150 trajectory candidates in less than 100 ms, maintains a high episode success rate, and substantially reduces joint and end-effector jerk when jerk regularization is applied.
Byeong-Il Ham, Hyunbin Kim, Kyung-Soo Kim· 0 citations
The deployment of Artificial Intelligence (AI)-based autonomous mobile robots in high-stakes environments, such as defense swarms and large-scale warehouse logistics, demands path planners that are not only theoretically optimal but scalable. While traditional search-based methods like A* guarantee resolution optimality, they suffer from exponential complexity in high-resolution maps. Conversely, sampling-based algorithms like Rapidly-exploring Random Tree* (RRT*) efficiently explore large spaces but lack path smoothness. State-of-the-art diffusion planners predominantly rely on computationally intensive backbones, rendering them unsuitable for real-time deployment where bandwidth and compute are constrained. To bridge this gap, we introduce NeuralPathLite, a lightweight neural-network-based, image-conditioned diffusion planner specifically optimized for embedded and centralized swarm architectures. Unlike prior works that struggle with visual ambiguity, we introduce a Semantic Visual Anchoring mechanism that explicitly disentangles start-goal semantics from obstacle features, preventing mode collapse in multi-colored, cluttered environments. Furthermore, we demonstrate a novel Secure Copy Protocol (SCP)-based deployment framework, exploiting our model’s low latency to enable centralized path generation for distributed robot swarms. Evaluated on the Mobile Robot Local Planning Benchmark (MRPB) and deployed on a Husky A200, NeuralPathLite achieves an inference latency of 0.16 seconds, a $7.4\times $ speedup over competing state-of-the-art methods with a 96.12% success rate in out-of-distribution scenarios. This combination of algorithmic efficiency and robust visual conditioning establishes NeuralPathLite as a viable backbone for AI-based robotic automation. The source code and dataset will be publicly available. Note to Practitioners—This paper addresses the critical challenge of deploying high-performance path planning in real-time robotic systems where computational resources are limited or environment complexity is high. While modern learning-based planners offer sophisticated results, their high inference time often makes them impractical for real-world hardware. We introduce NeuralPathLite, a fast and robust planning method designed to bridge this gap by providing high-quality, smooth paths with minimal computational overhead. Beyond the algorithm, we present a scalable Server-Client Protocol (SCP) framework specifically engineered for high-risk or large-scale deployments, such as search and rescue in hazardous zones, warehouse automation, and monitoring of life-critical environments where human access is restricted. This architecture allows for the centralized management of multiple robots using SCP to offload heavy generative compute, effectively reducing the hardware cost per unit by enabling the use of low-power AI agents without dedicated high-end Graphics Processing Units (GPUs). The system has been validated using the Husky A200 differential drive robot, demonstrating its readiness for field applications. For practitioners, this work offers a ready-to-implement strategy for managing fleets of autonomous robots economically.