TUM team surveys 329 works on physics-embedded robot learning: 71% encode physics in architectures, only 4% combine multiple embedding routes

The survey proposes and applies a unified taxonomy that sorts fragmented literature into three categories by where physics priors are embedded: physics-guided inputs, data, and representations; physics-encoded model architectures; and physics-informed training loss functions, accompanied by a reusable classification decision flow. Earlier related surveys either focus on other domains such as fluid and solid mechanics or scientific computing, or touch robotics only with a limited set of models and applications, leaving no structured overview of physics-embedded robot learning as a whole. The taxonomy adapts and extends the classification of Faroughi et al., spans machine learning models from single-layer perceptrons to generative foundation models, and covers five families of physics priors from Newton-Euler and Lagrangian dynamics to conservation laws, symmetries, and invariances; the authors also maintain a public repository collecting all reviewed papers and their classification.

The survey quantifies the distribution across the three embedding routes: physics-encoded architectures are the largest body of work at 71% of surveyed methods, physics-guided at 16%, and physics-informed at 13%, with more than half of the reviewed methods published between 2023 and 2025. These proportions give a quantitative picture of the field's internal structure, showing that the current center of gravity lies in architectural physics encoding, while the physics-guided and physics-informed routes started later but have grown rapidly since 2022. The statistics come from the authors' classification of journal and conference papers published up to August 2026 plus a few arXiv preprints, and the paper states that when a paper belongs to two routes the percentages use the primary embedding route.

The survey groups work by application into dynamics learning, trajectory planning and prediction, control, and estimation, and notes that validation concentrates on low-dimensional systems: manipulators and vehicles together account for 62% of reviewed methods, legged robots only 7%, and 17 papers report results exclusively on canonical mechanical systems such as pendulums and cart-poles. This distribution turns the question of which platforms physics-embedded methods have actually been validated on from anecdotal impressions into comparable statistics, and shows that high-degree-of-freedom systems and contact-rich tasks remain thinly covered. The statistics come from the authors' classification of all reviewed papers by application category and robot type, including manipulators, mobile robots, vehicles, legged robots, soft robots, collaborative robots, and underwater and aerial robots.

The survey reviews the open-source software ecosystem supporting physics-embedded robot learning, comparing frameworks across model-structured and hybrid physics learning, neural ordinary differential equations, equation discovery and system identification, physics-informed machine learning, and differentiable simulation, in terms of support for physics encoding and physics-informed losses, language, optimization approach, license, and hardware support. Earlier surveys of scientific machine learning libraries and differentiable simulators focused on differential-equation solving or simulation design choices respectively; this survey instead organizes the comparison around how each tool supports embedding physics priors in robot learning. The comparison is based on specific frameworks and their public repository links, and the authors note that no framework currently supports physics-guided, physics-encoded, and physics-informed learning within a unified workflow spanning model definition, training, evaluation, deployment, and embedded execution.

The survey targets researchers and practitioners who want to bring physics priors into robot learning, and applies to four robot task categories: dynamics learning, trajectory planning and prediction, control, and estimation, covering manipulators, mobile robots, vehicles, legged robots, soft robots, collaborative robots, and underwater and aerial robots. Its taxonomy can be applied to an entire learning pipeline, an individual model, or a specific submodule within a larger architecture, and it is paired with a public repository and decision flow so the community can keep classifying new papers. The software comparison targets practitioners choosing tools, distinguishing them by support for physics encoding and physics-informed losses. The authors stress that physics priors should serve as robotics-specific inductive biases complementing rather than replacing data-driven learning, and note that stronger priors improve interpretability and generalization while potentially constraining model expressiveness, so applicability depends on prior fidelity, available data, and the required closed-loop properties.

The survey flags several open questions: which physics priors to embed and how strongly to constrain learning still lacks principled guidelines; most methods are tailored to a specific robot, and transfer across embodiments, contact conditions, sensing modalities, and actuation mechanisms still requires considerable redesign; when the assumed model omits dominant error sources such as friction, contacts, compliance, or actuator dynamics, embedded priors can introduce structural bias that data alone cannot eliminate; interpretability results are often qualitative and standardized quantitative metrics are lacking, while explicit explainability and formal safety guarantees such as Lyapunov analysis, control barrier functions, and reachability analysis remain rare; metrics for physical consistency are fragmented across prediction horizons, perturbation scenarios, and tasks with no unified benchmark, and in video world models visual realism remains distinct from physical validity; moreover, as a survey this work provides no new experimental data, and its statistics depend on the authors' search and classification criteria.