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Physics Filtering Favors the Generalization of Robot Learning

Jindou Jia, Shixuan Han, Meng Wang, Gen Li, Zihan Yang, Sicheng Zhou, Kexin Guo, Jianfei Yang, Xiang Yu, Wei Wang, Lei Guo

arXiv:2608.22701v1cs.RO

TL;DR

Robot learning needs reliable generalization, but collecting the physical-world data required for massive scaling is costly and difficult. The paper introduces PhyFilter, a physics-filtered feedback module that corrects learning residuals and is automatically tuned. Across four robotic systems, it improves generalization under unseen terrains, disturbances, mass variations, and input distribution shifts.

  • Problem

    Robot learning must generalize to unseen environments for reliable deployment, yet physical-world data collection at large language-model scale is costly and difficult.

  • Method

    PhyFilter corrects learning outputs with physics-filtered residuals using real-time state feedback and physical differential structure, with automatically learned parameters and plug-and-play integration.

  • Results

    Across four realistic robotic experiments, PhyFilter improved generalization in locomotion, flight, aerial manipulation, and acceleration perception under unseen conditions and distribution shifts.

  • Takeaways & Limitations

    Physics-filtered feedback provides a lightweight framework for combining generalization and interpretability across reinforcement-learning and supervised-learning robot policies.

  • Takeaways & Limitations

    Auto-learning converges without manual tuning, but each iteration requires a full trajectory forward rollout, limiting efficiency on large-scale data.

Abstract

from arXiv · show

Living organisms exhibit extraordinary adaptability to unseen environments through their intrinsic physical structures and lifelong feedback-driven learning. Endowing robots with comparable generalization is critical for reliable operation in the real world. While recent approaches attempt to improve generalization by scaling training data, such strategies remain impractical for robotics, where collecting real-world demonstrations at the scale of large language models is prohibitively costly and slow. Contrary to this reliance on massive datasets, we show that robots can generalize effectively under dynamics uncertainties even with limited training data by leveraging a feedback mechanism, namely PhyFilter, that corrects learning outputs with physics-filtered learning residuals. PhyFilter operates as a lightweight, model-agnostic module whose parameters can be automatically optimized through an auto-learning algorithm, eliminating manual tuning and enabling seamless integration with diverse robot policies. We validate PhyFilter across four representative robotic systems, demonstrating that it enables quadruped robots to generalize to unseen terrains, payload variations, and speed ranges; drones to flight under unseen wind disturbances; aerial manipulators to achieve centimeter-level in-air capture despite wind and mass uncertainties; and acceleration differentiators to remain robust with distribution shift. These results show that physics-filtered feedback can serve as a powerful alternative to massive data scaling.

1 Introduction

Robot generalization is essential for reliable real-world deployment, but scaling physical-world training data is costly and difficult. The paper proposes PhyFilter, a physics-filtered feedback approach that improves generalization under dynamics uncertainty across multiple robotic settings.

  • Reliable real-world robot deployment requires generalization to unseen environments.
  • Unlike internet-scale language-model data, robot demonstrations must be collected in the physical world, making massive data scaling technically difficult and costly.
  • Existing robot data-scaling approaches remain limited by sim-to-real gaps, computational overhead, and incompatible platform interfaces.
  • Biological adaptability motivates using intrinsic physical structure and feedback rather than relying solely on scaling training data.
  • PhyFilter corrects learning outputs using physical differential structure and real-time state feedback, while an auto-learning algorithm removes manual parameter tuning.
  • Across four robotic scenarios, PhyFilter supports generalization for quadruped locomotion, drone flight, aerial manipulation, and acceleration perception.The evaluated settings include unseen real-world terrains and uncertain aerial dynamics.

2 Results

PhyFilter combines learning with physics-informed feedback to improve generalization under unseen dynamics and environmental conditions. Across quadruped, drone, aerial manipulation, and acceleration-perception tasks, it improves robustness beyond the training distribution.

  • Physics filtered learning: PhyFilter corrects learning outputs using filtered residuals inferred from real-time feedback and physical differential structure, with filter parameters auto-learned rather than manually tuned.The approach is designed as an adaptive filtering process for unseen scenarios and applies to reinforcement and supervised learning.
  • Quadruped locomotion: PhyFilter improves quadruped generalization to unseen speeds, payloads, and terrains after training on simplified flat terrain.At 2.83 m/s and payloads up to 60% of the 11.86 kg robot weight, tracking error remains ≤0.2 m/s; passing success rates are higher across five unseen scenarios.
  • Quadruped locomotion: In real-world deployment, the PhyFilter-enhanced quadruped traverses four challenging natural terrains without additional tuning, whereas the baseline collapses on sandy and gravel surfaces.The policy remains successful even when correction is switched off at deployment, indicating that training shaped the policy itself.
  • Drone maneuvering flight: For drone maneuvering under unseen wind disturbances, PhyFilter reduces mean absolute tracking error by 30.22% relative to SEER-I and 50.17% relative to the baseline.SEER-I captures mass variations but degrades when wind is added; PhyFilter additionally identifies wind-induced and inherent dynamical uncertainties.
  • Aerial manipulation: In aerial manipulation, PhyFilter enables centimeter-level manipulation and successful pick-and-place under unseen wind and mass uncertainties when baseline and SEER-I fail to capture the object.The task requires an end-effector tracking error no greater than 2.5 cm.
  • Acceleration perception: For acceleration perception under distribution shift, PhyFilter achieves the highest accuracy among learning-based and classical differentiator baselines and remains superior across sampling intervals from 0.002 s to 0.018 s.The model is trained on velocities from 0–2 m/s and tested on 0–3 m/s real-flight data.

3 Discussion

PhyFilter uses physics-filtered feedback to improve robot-learning generalization without extensive domain randomization, while retaining a lightweight, model-agnostic design. Four robotic experiments support its effectiveness, but the study identifies computational and representation limits for future work.

  • PhyFilter combines real-time state feedback with physical differential structure to filter learning residuals and improve generalization and interpretability.Its implementation is designed to correct learning outputs using accessible physical information.
  • Four experiments showed improved generalization for quadruped locomotion, drone flight, aerial manipulation, and acceleration estimation under unseen conditions.The tested shifts included realistic terrains, payloads, speeds, wind, mass uncertainties, and input-distribution changes.
  • Figure 6 evaluates accelerator prediction across training velocities of 0–2 m/s, testing velocities of 0–3 m/s, filter settings, parameter choices, and sampling intervals.Blue stars indicate auto-learned parameters that were roughly consistent with manually optimal settings; RMSE denotes root mean square error.
  • PhyFilter reduces reliance on extensive domain randomization while maintaining generalization during deployment.The quadruped experiment avoided training over complex terrains, payloads, and speeds, reducing engineering effort and manual tuning.
  • The study identifies three limitations: filtered knowledge does not refine the original network, auto-learning requires full trajectory rollouts, and residuals may combine prediction errors with modeling mismatch.Future directions include continual learning, truncated or parallelized rollouts, and separating uncertainty components.

4 Methods

PhyFilter reformulates residual correction as an implementable filtering procedure using physical structure and state feedback, then automatically learns filter parameters. Its design supports higher-order filtering, integration with learning policies, and robustness under simplified physical models.

  • Filtering learning residual: PhyFilter models robot dynamics as known physical structure plus an unknown nonlinear component learned from data, with the learning residual representing their discrepancy.The residual can arise from sensor noise, external disturbances, or unmodeled interactions.
  • Filtering learning residual: Because deployment labels are unavailable, PhyFilter reconstructs residual correction through a low-pass filter driven by accessible physical structure and real-time state feedback.This converts an otherwise inaccessible residual into an implementable correction procedure.
  • Filtering learning residual: An nth-order low-pass filter uses differentiations, integrations, and tunable coefficients to produce the corrected learning outcome.The formulation introduces auxiliary variables to avoid directly obtaining unknown higher-order derivatives and initial conditions.
  • Relationship to disturbance observers: PhyFilter extends disturbance-observer feedback by guiding RL training, integrating with SL outputs, supporting higher-order residual filtering, and auto-learning its gains.These combined changes distinguish PhyFilter from using a disturbance observer only at deployment.
  • Learning filter parameters: The auto-learning algorithm treats filter parameters as control inputs and updates them by gradient descent using forward rollouts and reverse-mode differentiation.Mini-batching, Adam, and early stopping are used for efficiency and stability; manual pole placement is otherwise tedious as filter order grows.
  • Quadruped implementation: In the quadruped implementation, first-order PhyFilter was sufficient to improve generalization despite diagonalized inertia and linear-damping approximations.The authors report significant improvement under these simplified physical priors.
  • Aerial-manipulator control: For aerial-manipulator control, prior work commonly uses disturbance observers, but state-coupled disturbances make bounded uncertainty-derivative assumptions impractical before closed-loop stability is established.This motivates methods that address coupling disturbances without relying on that assumption.
  • Online differentiator: Learning-based differentiators face generalization difficulties when signal characteristics shift, motivating physics-filtered acceleration estimation.Analytical differentiators also require cumbersome parameter tuning and may need adjustment as signal characteristics vary.

A.5 Physics-informed machine learning

Physics-informed machine learning integrates physical insights into learning methods to improve interpretability, convergence, precision, and generalization. Prior approaches include observational, inductive, and architecture-based strategies, alongside Hamiltonian and Lagrangian neural networks.

  • Physics-informed machine learning integrates prior physical insights into machine learning methods.Its objectives include improving interpretability, training convergence, predictive precision, and generalization.
  • Common strategies introduce observational or inductive physical information into learning procedures.
  • Hamiltonian neural networks learn system Hamiltonians while preserving energy conservation.
  • Lagrangian neural networks remove Hamiltonian neural networks’ reliance on canonical coordinates.
  • Neural-symbolic learning and MPC-integrated actor-critic reinforcement learning combine physical or symbolic knowledge with learned policies.The reported hybrid benefits include MPC’s short-term optimization and end-to-end training.

A.6.1 Domain randomization

Domain randomization trains robotic agents across simulator settings with randomized parameters to bridge the sim-to-real gap. Its limitations include reduced accuracy, high computation, incomplete physical coverage, and persistent interface-standardization challenges.

  • Domain randomization synthesizes training data by randomizing simulator parameters across many settings.It aims to bridge the sim-to-real gap.
  • Domain randomization optimizes average performance across randomized environments, potentially sacrificing accuracy for robustness.
  • Training a monolithic model with domain randomization can require substantial computing resources.This may be infeasible in compute-constrained cases.
  • Universal physics engines cannot encompass the full spectrum of diverse real robots and dynamical environments.
  • Standardizing robotic data formats, software, and hardware remains a long-term challenge.

A.6.2 Domain adaptation

Domain adaptation identifies encountered environments so decisions can be adjusted, preserving accuracy in specific scenarios relative to domain randomization. The paper’s auto-learning procedure instead optimizes PhyFilter parameters through differentiable rollouts and gradient-based updates.

  • A.6.2 Domain adaptation: Domain adaptation explicitly identifies the encountered environment to adjust current decisions.
  • A.6.2 Domain adaptation: Compared with domain randomization, domain adaptation preserves accuracy in specific scenarios but requires more complex training.
  • A.6.2 Domain adaptation: Domain adaptation, including test-time adaptation, relies on substantial computing resources to train a monolithic model.
  • A.6.2 Domain adaptation: The referenced differentiable Kalman-filter method targets random white-noise uncertainty, limiting its uncertainty scope.
  • A.6.2 Domain adaptation: PhyFilter parameters can be auto-learned as an optimal-control problem instead of requiring domain-specific pole-placement expertise.
  • A.6.2 Domain adaptation: The parameter-learning objective quantifies differences between model rollouts and labelled samples across N samples.
  • A.6.2 Domain adaptation: Analytic gradients are computed through forward state rollout followed by backward adjoint rollout, then used for gradient descent.Mini-batching, stochastic optimization, and early stopping support efficiency and stability.
  • A.6.2 Domain adaptation: A more general filter captures complex learning residuals at the cost of more complex parameter adjustment.

F Trajectory generation of aerial manipulator

The aerial-manipulator planner generates a six-dimensional motion state and optimizes control inputs for trajectory tracking. It adds smoothness, state-increment, and safety considerations to avoid aggressive or unstable motion.

  • Trajectory-state formulation: The planner generates a six-dimensional motion state combining aerial-platform and end-effector trajectories.
  • Trajectory-state formulation: The controlled state propagation includes aerial-platform and end-effector accelerations as optimized control actions.
  • Trajectory-state formulation: The end-effector trajectory is computed from platform position, platform orientation, manipulator-base offset, and base-frame motion.
  • Optimization objective: The planner minimizes trajectory-tracking error through an optimal control input.
  • Safety terms: A pure unconstrained quadratic-program formulation neglects practical safety and motion characteristics, so explicit constraints are incorporated.
  • Safety terms: Control-action smoothness penalizes increments in u to prevent aggressive responses and mitigate sharp acceleration maneuvers.
  • Safety terms: Including predicted platform and end-effector state increments increases system safety by addressing neglected output stability.

G Robustness analysis under inaccurate priors

The appendix analyzes PhyFilter when its physical prior is inaccurate and derives an explicit bound on the resulting estimation error for a general n-th order filter.

  • The analysis characterizes PhyFilter under inaccurate physical priors and derives an explicit estimation-error bound for a general n-th order filter.The locomotion case is cited as an example where the physical prior may be inaccurate.

G.1 Problem setup

The problem setup models PhyFilter as estimating an unknown residual from measured dynamics using a simplified physical prior. Prior mismatch enters the estimator as an additional forcing term without changing the filter’s characteristic polynomial.

  • G.1 Problem setup: The true inertia matrix M(t) is replaced in practice by a simplified ˆM(t), such as diagonalized inertia and linearized Coriolis terms.
  • G.1 Problem setup: PhyFilter reconstructs the unknown residual f(t) from measurements g(t) and the simplified prior ˆM while enforcing designed low-pass dynamics.The physical structure is introduced for the locomotion case.
  • G.1 Problem setup: Prior mismatch introduces the additional forcing −a0∆M ˙x into the estimator dynamics.The filter uses ˆM, whereas the plant evolves with the true M.
  • G.1 Problem setup: The estimation error satisfies an n-th order differential equation driven by d(t), which combines intrinsic residual dynamics with prior-induced effects.The error is defined as ˜f ≜ f − ˆf.
  • G.1 Problem setup: Prior error enters the estimator dynamics only through forcing d(t) and does not alter the filter characteristic polynomial.

G.2 Boundedness analysis

The boundedness analysis shows that stable filter dynamics contain estimation error under bounded residual variation, prior error, and operating velocity. The resulting ultimate bound separates intrinsic and prior-induced contributions.

  • G.2 Boundedness analysis: The augmented error dynamics have a Hurwitz matrix A when the filter characteristic polynomial is placed or auto-learned to be Hurwitz.This permits a positive-definite Lyapunov matrix P for any positive-definite Q.
  • G.2 Boundedness analysis: Bounded residual derivatives, prior error, and operating velocity imply bounded forcing, with intrinsic forcing bounded by cf δf.The bounds are denoted δf, δM, and δx.
  • G.2 Boundedness analysis: The Lyapunov derivative is negative outside a radius proportional to the total forcing magnitude, establishing uniform ultimate boundedness of the augmented state and estimation error.
  • G.2 Boundedness analysis: An inaccurate prior enlarges the ultimate bound without breaking stability, while the bound decomposes into intrinsic residual variation and a prior-induced term scaling with δM and δx.The prior-induced term vanishes when the prior is exact, δM = 0.

H Experimental hardware

The experiments use a Lite3 quadruped and a coaxial dual-rotor octocopter platform for drone flight and aerial manipulation, supported by onboard and remote computing and communication hardware.

  • H Experimental hardware: The experimental hardware includes a quadruped robot, an aerial drone, and an aerial manipulator.
  • H Experimental hardware: The locomotion platform is a DEEPRobotics Lite3 quadruped with an 11 kg body, RK3588 and Jetson Xavier NX hosts, and Wi-Fi command transmission from a remote computer.
  • H Experimental hardware: Drone flight and aerial manipulation use the same coaxial dual-rotor octocopter with STM32F427 processors, motion-capture and IMU state perception, and UWB ground communication.

I Quadruped tests under full domain randomization

The study strengthens the quadruped comparison by training both policies with full domain randomization, then adds humanoid tests under in-distribution and out-of-distribution external forces.

  • Quadruped training setup: Both quadruped policies are trained with standard domain randomization spanning terrains, payload variations, and disturbances.The training curriculum covers diverse terrains from difficulty 0–0.90 rather than only flat terrain.
  • Quadruped training setup: The stronger quadruped evaluation tests generalization on terrains beyond the training distribution.The comparison uses full-terrain training followed by more challenging test conditions.
  • Humanoid robustness test: The humanoid experiment evaluates both in-distribution and out-of-distribution lateral forces applied to one arm.The policy is trained with standard randomization ranges before testing under both force regimes.
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