How Should Robots Learn from Physical Laws? Finding the Best Way to Embed Physics in Robot Learning

Institut

Professur für autonome Fahrzeugsysteme (TUM-ED)

Typ

Masterarbeit /

Inhalt

 

Beschreibung

WHY THIS THESIS?

Foundation models have been used to learn language from internet-scale data. Robots don't have that luxury: real-world data are expensive, scarce, and safety-critical. However, robots do have one advantage: they obey physics. Newton's laws, symmetries, energy conservation, and kinematic constraints are a free source of knowledge that a learning algorithm can exploit.

This idea is behind physics-informed robot learning, a fast-growing field. Our recent survey paper on embedding physics priors in robot learning (https://arxiv.org/abs/2609.22319) reviews more than 300 papers and classifies them into three routes for injecting physics into machine learning:

- Physics-guided learning: physics shapes the inputs and data of machine learning models (physics-based features, symmetry-based data augmentation).
- Physics-encoded learning: physics is built into the architecture of machine learning models.
- Physics-informed learning: physics enters the loss function (e.g., PINN-style residuals of the equations of motion).

The open question is surprisingly fundamental: given the same physical knowledge, which of the three routes should you use, and is it worth combining them? Less than 4% of existing works combine routes, and no study has compared them fairly. Your thesis will provide some of the first answers.

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THE CORE IDEA

You will take pieces of physical knowledge and inject them into a learning model through all three routes, then compare the routes and their combinations. Take left/right steering symmetry of a vehicle as an example: steering left mirrors steering right. This physical prior can be embedded in three ways:

- Physics-guided: mirror the training data, for free data augmentation.
- Physics-encoded: build the architecture of the neural network or learning model so that its output is odd in the steering input, by construction.
- Physics-informed: add a loss term that penalizes asymmetric predictions, even on unlabeled states.

By keeping the physics fixed and changing only where it enters the learning pipeline, you can answer:

- Which route is most data-efficient when only minutes (or seconds) of data are available?
- Which route generalizes best to unseen conditions (new speeds, tires, payloads)?
- What happens when the physics prior is slightly wrong? Which route breaks, and which degrades gracefully?
- When do routes reinforce each other, and when are they redundant or even conflicting?

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WHAT YOU WILL WORK ON

The thesis is flexible and can be shaped around your interests. A possible path:

1. Get started (month 1). Learn the three routes and set up the software: nnodely, our open-source library for embedding physics priors into neural networks.
2. Build the comparison (months 2-3). Implement specific physical priors through each route, with black-box baselines (MLP, GRU, Transformer).
3. Run the experiments (months 3-5). Vary the amount of training data, the correctness of the prior, and the test conditions. Measure accuracy, long-horizon prediction, and physical consistency.
4. Distill the insights (months 5-6). Turn the results into practical guidelines: "if you have this much data and this good a model, use this route."

Application domains (more than one choice is possible):

- Simple mechanical systems: pendulums, double pendulums, and similar. Good to start with, because the physics is simple and the data are cheap to generate.
- Vehicle dynamics: real driving data from our 1:10-scale autonomous RoboRacer, and from a full-scale autonomous race car. The task is learning how a car accelerates, brakes, and turns near its handling limits.
- Robot dynamics: manipulators, legged robots.

Types of machine learning models:

- Neural networks (MLPs, recurrent networks, ...)
- Custom-designed neural architectures that encode physics priors (model-structured neural networks)
- Vision-Language-Action models (optional track): extend the study to large multimodal models that generate driving trajectories from images and language instructions. 

 

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WHAT YOU WILL GAIN

- Hands-on experience at the intersection of machine learning, robotics, and dynamics, one of the most active research directions in robot learning.
- Real data from real robots, from small-scale vehicles to a full-scale autonomous race car.
- A research contribution that addresses an open question highlighted in the literature. Strong results are intended to become a scientific publication, co-authored with the team.
- Close supervision in an international group working on autonomous vehicles, physics-informed learning, and differentiable control, with collaborators in other universities in Germany and Italy.
- Open-source impact: your implementation can become part of the nnodely library.

Voraussetzungen

Required:
- Good Python skills and basic experience with PyTorch / Keras / Tensorflow / learning frameworks.
- Curiosity about how machine learning can benefit from physics, and a structured, experimental mindset.

Nice to have:
- Background in vehicle dynamics, robot dynamics, or control.

Tags

AVS Piccinini

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Kontakt

Mattia Piccinini
mattia.piccininitum.de