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

Physically consistent motion planning remains a fundamental challenge in embodied AI, as generated trajectories must strictly conform to real-world execution dynamics. While latent world models offer a promising approach by predicting these dynamics, existing methods learn unconstrained future representations where absorbed physics remains implicit. Therefore, they fail to form reusable physical knowledge, which compromises reliability in unpredictable open-world navigation. To address this, we propose a novel Energy-Structured Latent World Model (ELWM). Our key idea is to structure the ELWM latent state to explicitly carry energy and momentum, ensuring strictly causal transitions via dissipation and control ports. Trained on multimodal RGB-D and inertial interaction histories, our model guarantees physically consistent predictions. We further implement this for motion planning by constructing Physics-Conditioned Neural Time Fields (PC-NTF), a key technical cornerstone that integrates ELWM into an arrival time field via the Eikonal equation to yield a physically-informed navigation policy. Across held-out scenes, our evaluation reveals significant improvements. Compared to generic latent models, PC-NTF reduces 0.8-s motion-prediction NRMSE from 0.36 to 0.29. Against Active Neural Time Fields, it improves navigation success from 81.3% to 89.7% and SPL from 0.64 to 0.73, while cutting the physical collision rate from 12.1% to 5.8% and the Eikonal residual from 0.083 to 0.031. Beyond these targeted gains, our results demonstrate that embedding explicit physical structures into latent spaces intrinsically bridges the gap between predictive world models and safe, dynamically feasible motion planning.

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.

We introduce Neural Navigation Functions (Neural-NF), a learned reactive navigation function capable of zero-shot transfer across unseen environment geometries. Neural-NF places data-driven adaptation within a structured elliptic planner, where the navigation objective is learned while planner structure is preserved by construction. Specifically, intrinsic Laplacian-derived features are mapped to local PDE coefficients, and solving the resulting boundary value problem produces a globally consistent value function on each target domain. For every admissible learned model, the resulting policy is collision-free, provides monotonic descent and a global minimum at the goal by construction. This admits a linearly-solvable optimal-control interpretation for any parameter setting. Empirically, Neural-NF achieves strong zero-shot transfer across diverse geometries and outperforms learned planners that directly predict the value function by up to a $5\times$ improvement.