Stanford Robotics Seminar ENGR319 | Winter 2026 | Robot Motion Learning w/Physics-Based PDE Priors

Optimization methods trap themselves in local minima

While optimization-based planners offer high inference and training efficiency, they fail to adapt to complex terrains and high-DOF constraints because they easily get stuck in local minima.

Classical methods suffer from slow computation

Sampling-based approaches like RRT and search-based methods like A* require no training but have prohibitively slow inference times that prevent real-time application in high-dimensional spaces.

Data-driven approaches demand massive training costs

Imitation and reinforcement learning models adapt well to complexity and infer quickly, but require weeks of expert demonstration data and expensive GPU clusters to train, making transfer to new domains impractical.

Eikonal PDE provides mathematical structure

The method uses the Eikonal PDE—which governs optimal wavefront propagation—as a prior rather than a physics simulator, where the solution represents a value function (travel time) whose gradient indicates optimal motion direction.

Gradient matching eliminates need for expert data

The neural network is trained via gradient matching: the network's gradients are compared against the inverse of obstacle distance constraints, requiring only randomly sampled configurations rather than expert trajectories.

Surpassing numerical solver limitations

Traditional numerical solvers like Fast Marching Method scale only to 3-4 dimensions; the neural approach aims to solve the same PDE for high-DOF robots (12-15 dimensions) where numerical methods fail.

Metric learning handles multimodal solutions

To address the Eikonal PDE's multiple valid solutions (e.g., going left or right around an obstacle), the network uses a specialized structure with latent space encoding and max pooling to enforce geodesic distance properties like symmetry and triangle inequality.

Temporal difference learning controls gradients

To prevent error accumulation between consecutive trajectory points, the model applies Temporal Difference (TD) learning to enforce Bellman's principle of optimality, regulating gradients similarly to Q-learning.

Sub-100-millisecond inference in complex environments

The method achieves approximately 0.07 seconds planning time for 7-DOF robots and scales to 15-DOF systems navigating narrow passages, matching or exceeding the speed of Nvidia's EmpireNet while generalizing across 300 unseen environments.

Training in minutes versus weeks

Compared to baseline methods requiring several weeks of data gathering and one week of training on eight Tesla GPUs, this approach trains in under one hour on a single RTX 3090 after only 50 minutes of data collection.

Zero-shot transfer to new domains

Because the model requires no expert demonstrations and minimal training data, it transfers immediately to new environments without retraining, solving the deployment bottleneck faced by traditional imitation learning systems.