Embedding Physics Priors in Robot Learning: A Survey
Mattia Piccinini, Lucas Schulze, Alice Plebe, Matteo Saveriano, Thomas Beckers, Yuan Gao, Oleg Arenz, Baha Zarrouki, Dingrui Wang, Finn Rasmus Schäfer, Jan Peters, Johannes Betz, Gastone Pietro Rosati Papini
cs.RO
2026-09-16
A TUM survey sorts physics-embedded robot learning into guided inputs, encoded architectures, and informed losses. Architectures are 71%; arms and vehicles 62%, legged 7%.
Robot learning sits between two incomplete toolkits. Analytical models miss friction, contact, and compliance. Purely data-driven models starve for samples. Arms, quadrupeds, and soft robots are expensive to instrument, high-dimensional, and expected to run safely in real time. The scale-data-and-compute recipe that worked in vision and language does not transfer cleanly.
Physics priors are the obvious robotics-specific inductive bias: Newton-Euler and Euler-Lagrange equations, energy conservation, SE(3) symmetry, inertia positive-definiteness. Papers call this physics-informed, physics-guided, or physics-encoded, often interchangeably. Earlier surveys stay in PDE scientific computing or only graze robotics. Piccinini and colleagues at TUM Autonomous Vehicle Systems, with TU Darmstadt, University of Trento, and Ulm University, recut the literature through August 2026 by where the prior is injected. Of 329 cited works, 232 actually embed physics into a robot-learning method.
The taxonomy extends Faroughi et al. 2024. The three routes are complementary, not exclusive.
Lifecycles differ. Guided modules sit on the data path. Encoded structure is active at train and test time. Informed losses vanish after training; only the fitted weights remain. Priors themselves fall into five families: governing equations, conservation and symmetry, geometry and kinematics, constitutive and contact laws, and physical admissibility (positive-definite inertia, passivity). Applications span dynamics identification, planning and prediction, control, and estimation. RL is included only when physics enters through one of these three routes; RL that injects physics solely via state-space design or simulator tricks is left to Banerjee et al. 2025.
This is a survey, not a new bake-off. The distribution, counted by primary route when a paper uses two, is the result.
| Slice | Number | Contrast |
| Physics-encoded architectures | 71% | Guided 16%, informed 13% |
| Manipulators + vehicles | 62% | Legged robots 7% (16 papers) |
| Pendulum / cart-pole only | 17 papers | High-DoF systems barely appear |
| Two routes combined | 4% | Combinations remain ad hoc |
| Informed share in aerial robotics | 43% | Field-wide informed share is 13% |
| Published 2023-2025 | more than half | Acceleration after 2020 |
Prior surveys under-cover robotics: Geist and Trimpe 2021 have 16/108 robot-learning physics papers, Watson 2025 have 21/359, Sivtsov 2025 have 16/112 in a PINN survey. This is the first review that covers all three injection routes and stretches from perceptrons to VLAs, diffusion policies, and video world models. A software map compares NeuroMANCER, nnodely, torchdiffeq, PySINDy, DeepXDE, PhysicsNeMo, Brax, and Warp by encoded-architecture versus informed-loss support. A public repository keeps the classification and search flow current.
The usable artifact is a decision map. Known rigid-body energetics and a need for interpretable inertia point to DeLaN. Energy exchange and dissipation point to HNNs or port-Hamiltonian models. Partial known dependencies point to MSNNs or an analytical backbone plus a learned residual. Unknown but sparse governing laws point to SINDy. Generative policies and world models mostly take the guided route: kinematic constraints or differentiable simulation steer sampling, while the base network stays untouched.
Physics complements data; it does not replace it. Stronger priors buy interpretability and sample efficiency, and they also lock the model to the assumed physics. On contact, compliance, and high DoF, a structural bias often becomes a structural error. For anyone shipping to hardware, this paper is a map, not a new algorithm.
The authors list the hard gaps. There is no principled rule for which prior to embed, or how tightly. Reusable building blocks barely exist; a new embodiment usually means a redesign. A wrong prior becomes a structural bias that extra real data cannot fully undo in sim-to-real. Interpretability is mostly qualitative, with almost no attribution studies or user tests. Physical-consistency metrics are fragmented; video world models in particular lack a dynamics-aware protocol. Closed-loop stability or passivity proofs are rare.
Evaluation is skewed. 62% of the work stops at arms and vehicles with fewer than ten degrees of freedom. Contact, impact, and hybrid modes remain one-off case studies. The 4% of papers that mix two routes do so ad hoc, such as a DeLaN plus a power-consistency loss. A living repository is useful, and it also means the printed taxonomy will age.