Shape-Aware Neural Time Fields for Rigid-Body Motion and Manipulation Planning

Yanming Zhou; Yuchen Liu; Ahmed H. Qureshi

cs.ROOct 16, 2026

Shape-Aware Neural Time Fields for Rigid-Body Motion and Manipulation Planning

Authors: Yanming Zhou, Yuchen Liu, Ahmed H. Qureshi

Organizations: Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA

Abstract

Rigid-body motion planning is fundamental to robotic transport and manipulation, where both object position and orientation determine whether a body can move through cluttered environments. This coupling makes planning chal- lenging because translation and rotation can be constrained very differently by surrounding geometry. We propose Shape- Aware Neural Time Fields, a physics-informed neural motion planning framework that learns a reusable travel-time, or cost- to-go, representation for rigid-body motion while explicitly accounting for these distinct geometric restrictions. The learned field captures local motion difficulty in translation and rotation and is paired with a sampling-based planner that balances progress toward the goal with the cost of reaching nearby poses. We evaluate the framework across 2D and 3D rigid- body planning tasks and non-prehensile manipulation through object pushing in diverse environments. Results show substantial improvements in planning success and inference efficiency over physics-informed neural planning baselines, while remaining competitive with classical sampling-based planners at significantly lower planning times. Ablation studies further validate the contributions of both the learned representation and the proposed planning strategy. Finally, closed-loop pushing experiments under execution deviations and external disturbances demonstrate that fast replanning enables reactive and adaptive task execution.

Figures & tables

Fig. 1: Shape-NTFields enables closed-loop UR5e pushing with fast trajectory inference (0.048 s on average in the 2D benchmark). (a) Planned T-block path around fixed obstacle regions. (b) to (e) Intermediate execution with updated paths. (f) Final observed pose. The system measures the block pose and replans after each short push.

Fig. 2: Method overview. (1) Start and goal poses share an encoder with separate translation and rotation branches followed by fusion. Comparing their embeddings gives the approximate travel time

T(q_{s},q_{g})

. (2) Geometry supplies speed targets

S_{c}^{\star}

and normals

n_{c}

for translation and rotation (

c

). Gradients of

T

give network-implied speeds

S_{c}

. Blockwise Eikonal regularization aligns them with the targets using inverse-speed weighting; Relative Normal Loss encourages speed decrease along

n_{c}

with the goal fixed. Both losses train the same field. (3) The trained field scores candidates using remaining time

T(q_{i,h},\bar{q})

and local slowness

T(q,q_{i,h})/\ell_{i,h}

, the predicted time per displacement from the current pose. Scores weight first steps, while inverse slowness supplies speeds for fitting a steering direction. The planner corrects the weighted step and repeats, extending both endpoints until their paths connect.

Table 3

Fig. 3: Qualitative path comparison across six planners. Rows show A-shaped planar navigation and T-shaped spatial navigation. Columns show Ours, TDM, PC-Planner, LazyPRM, RRTConnect, and STOMP. Overlaid object poses show translation and rotation along each path; red poses indicate collisions. TDM fails to converge in the A-shaped tasks and collides in the T-shaped task. PC-Planner and STOMP produce collisions in both tasks.

Table 5

Environment	SR (%) $\uparrow$	Collision (%) $\downarrow$
1	78.0	22.0
3	93.3	6.7
4	89.3	10.7
Overall	86.9	13.1

TABLE V: Closed-loop planning and pushing control in simulation. Each environment includes 100 trials per shape (rectangle, L, A). Success requires goal attainment without collision.

Fig. 4: Real-world Push-T with an external perturbation. (a) Initial planned path. (b) Perturbation during execution. (c) Updated path from the measured block pose. (d) Final observed pose. The planner reuses the learned travel-time field within the repeated loop of perception, planning, and pushing.

Motion Planning

Motion planning finds safe, feasible paths and trajectories for robots and vehicles amid geometric, dynamic, and task constraints.

See all 405 papers

Weakly-supervised Learning for Physics-informed Neural Motion Planning via Sparse Roadmap
Apr 14, 2026Ruiqi Ni, Yuchen Liu, Ahmed H. QureshiPhysics-Informed ML Weakly Supervised Learning
Department of Computer Science, Purdue University, West Lafayette, IN, USA, 47907.
Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities
Mar 25, 2026Davood Soleymanzadeh, Ivan Lopez-Sanchez, Hao Su +3Motion Planning Robot Motion Planning
J. Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, TX, USA · Lab of Biomechatronics and Intelligent Robotics, Department of Biomedical Engineering, Tandon School of Engineering, New York University, NY, USA · Department of Computer Science, Columbia University, NY, USA +1
NeurRAFT: Robot Motion Planning via Anchor-Level Flow Matching with Clearance-Aware Preference Tuning
Aug 25, 2026Sibo Tian, Chang Liu, Minghui Zheng +1Robot Motion Planning Safe Motion Planning
J. Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA

Apr 14, 2026J/K move · Enter open · S save

Weakly-supervised Learning for Physics-informed Neural Motion Planning via Sparse Roadmap

Ruiqi Ni, Yuchen Liu, Ahmed H. Qureshi

Department of Computer Science, Purdue University, West Lafayette, IN, USA, 47907.

Physics-Informed ML Weakly Supervised Learning Roadmap-Based Motion Planning

Open paper AskPDF arXiv

The motion planning problem requires finding a collision-free path between start and goal configurations in high-dimensional, cluttered spaces. Recent learning-based methods offer promising solutions, with self-supervised physics-informed approaches such as Neural Time Fields (NTFields) solving the Eikonal equation to learn value functions without expert demonstrations. However, existing physics-informed methods struggle to scale in complex, multi-room environments, where simply increasing the number of samples cannot resolve local minima or guarantee global consistency. We propose Hierarchical Neural Time Fields (H-NTFields), a weakly-supervised framework that combines weak supervision from sparse roadmaps with physics-informed PDE regularization. The roadmap provides global topological anchors through upper and lower bounds on travel times, while PDE losses enforce local geometric fidelity and obstacle-aware propagation. Experiments on 18 Gibson environments and real robotic platforms show that H-NTFields substantially improves robustness over prior physics-informed methods, while enabling fast amortized inference through a continuous value representation.

Abstract

Motion Planning

Explore similar work

Weakly-supervised Learning for Physics-informed Neural Motion Planning via Sparse Roadmap

Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities

NeurRAFT: Robot Motion Planning via Anchor-Level Flow Matching with Clearance-Aware Preference Tuning