Informationally Decoupled Trajectory Design for Sim-to-Real System Identification

arXiv:2610.10905 · cs.RO · Submitted 2026-10-07 · Read on arXiv

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Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: I'm Rosa, and with me are Dev and Taro, guest researcher.

Dev: Today's paper: "Informationally Decoupled Trajectory Design for Sim-to-Real System Identification".

Rosa: The gist The Informationally Decoupled Trajectory Design framework (IDTD) formulates an objective for exploration policy built on the Schur complement score derived from the Fisher information matrix to ensure every…

Dev: First, who's behind it and why it matters.

Paper summary: Rosa: So we're looking at this paper now called "Informationally Decoupled Trajectory Design for Sim-to-Real System Identification." It’s about how to use simulation to figure out the real physical parameters of a robot system, but it points out that sometimes just collecting more data isn't enough.

Dev: Exactly. The problem they’re tackling is that when you collect trajectories, you might end up with several different combinations of parameters that all look like they could have made those trajectories, which makes the resulting parameter estimates really unreliable.

Rosa: That's the core issue here: if your data doesn't tell you which parameter caused which movement, your identification will be messy. But this paper proposes this framework called IDTD to fix that by changing how you design those training trajectories.

Dev: They’re proposing using a technique based on the Schur complement score from the Fisher information matrix to build an objective for the exploration policy. Basically, they want every single parameter to leave a unique effect on the trajectory so they can be separated cleanly.

Taro: So what does this mean for autonomy when things go wrong in real life? If we can design trajectories that expose every parameter, even if the robot misbehaves, then our AI policy should be much more robust when it encounters those unexpected situations.

Rosa: Right. The paper claims this approach helps reflect parameter separability by normalizing the score against how much information each individual parameter carries. They select the best trajectory segment for each parameter and then aggregate those scores logarithmically to get a final objective function for the exploration policy.

Dev: So, what's the immediate benefit they’re seeing? They tested it across several platforms, including a linear-dynamics system, a Go2 quadruped robot, a G1 humanoid robot, and even a Crazyflie quadrotor in simulation.

Taro: I wonder how much better the identification actually gets on those different robots compared to just running standard active exploration methods. Are we talking about big gains across the board?

Rosa: They found that IDTD reduces the parameter identification error by an average of thirty-nine point six percent when compared to their strongest prior active-exploration baseline across those simulated environments, and they also see improved downstream policy transfer.

Dev: And on the real K1 humanoid robot, things look even better; they demonstrated that these identified parameters more accurately capture the actual system dynamics compared to other methods like SPI-ACTIVE.

Taro: That’s interesting because it moves beyond just getting a number for a parameter and actually makes that number meaningful in the context of real-world motion control.

Rosa: It really does, Taro. The paper shows that by focusing on this decoupling objective, IDTD suppresses the correlation between parameters that causes errors to get absorbed between them. That provides a mechanistic explanation for why their identification accuracy improves so much.

Dev: So, to wrap up on what this whole paper is saying about "Informationally Decoupled Trajectory Design for Sim-to-Real System Identification," it’s really about designing exploration strategies that force the system to show us how each parameter behaves independently.

Rosa: It’s a way to ensure that when we tune a simulator to match the real world, we aren't just getting a good fit on average, but we are actually separating the effects of individual physical properties like joint stiffness or friction.

Dev: The authors show how they build this objective using the Schur complement score and then normalize it by per-parameter information before aggregating them logarithmically across different trajectory segments.

Taro: I guess the implication is that for sim-to-real transfer, we need to be smarter about what we're asking the simulation to generate, not just more data points in general.

Rosa: Precisely. If you can get a trajectory that exposes every parameter somewhere along the motion, then your resulting AI policy will be much better equipped to handle things when it leaves the lab and meets real-world chaos.

Conclusion: Rosa: So we’re wrapping up this look at "Informationally Decoupled Trajectory Design for Sim-to-Real System Identification." Basically, they’ve developed a way to design exploration paths in simulations that makes sure every single physical parameter has a unique moment to show up on the trajectory.

Dev: Right, so instead of just making the robot move around randomly and hoping we get some data, they’re using math from the Fisher information matrix to pick segments where you can actually tell which parameter caused what movement. It’s about forcing separation between those parameters.

Taro: I think that makes sense for autonomy because if the data doesn't confuse which parameter is causing a weird wobble, then the AI policy won't learn a good control law for that situation in reality.

Rosa: Exactly, Taro. The authors show this works across different robot types—from simple quadrupeds to humanoids—and they found it cut the identification error by nearly forty percent on average compared to previous methods.

Dev: And for us engineers, the fact that they see improved downstream policy transfer means our control systems will be much more reliable when we move from simulation to the physical robot. That’s a big deal for deployment.

Taro: It shows that just collecting more data isn't the answer; you have to collect *different kinds* of data designed specifically to separate the physics, which is a key insight for autonomous systems operating in messy, real environments.

Rosa: So, they’re moving away from just maximizing excitation and toward designing trajectories that are actually informative about parameter independence. But what happens when we look at the limitations?

Dev: The paper flags that while they do get better identification on things like the K1 humanoid, it still stops short on improving downstream control performance for those real robots, likely because the sensors on a real robot can't even see all the parameters they need.

Taro: So, it’s a powerful tool for figuring out *what* the system is doing physically in simulation, but we still have to worry about how well that information translates when the AI is actually running on hardware with limited sensing.

Rosa: That’s where we head next, because understanding this separation is crucial for designing better learning strategies under real-world uncertainty.

University of Wisconsin–Madison

cs.RO

Submitted: 2026-10-07

Updated: 2026-10-07

Comments: arxiv_r1

Project page: https://newton-physics.github.io/newton

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 83/100

The gist: The gist The Informationally Decoupled Trajectory Design framework (IDTD) formulates an objective for exploration policy built on the Schur complement score derived from the Fisher information matrix

Key concepts

Fisher Information Matrix (FIM)
The FIM is a mathematical tool used to quantify how much information a set of collected data carries about the unknown system parameters. In this context, it helps determine which parameters are most distinguishable from one another, forming the basis for designing informative exploration paths.
Schur Complement Score
This score measures the remaining influence of one specific parameter on the system dynamics after accounting for all other parameters. A high score indicates that a parameter's effect is not easily mimicked by others, meaning it is well-decoupled and its contribution can be clearly identified.
Informationally Decoupled Trajectory Design (IDTD)
IDTD is the proposed method for creating optimal exploration paths. It maximizes a score based on these Schur complement scores, ensuring that different parts of the trajectory excite different parameters uniquely. This prevents parameter effects from being mixed together, leading to more reliable parameter identification.
Normalized Score
To ensure the objective focuses on separability rather than just total excitation, IDTD normalizes each per-parameter score by the information carried by that specific parameter. This prevents parameters with naturally high information content from dominating the optimization process.

Terminology

Summary

The gist The Informationally Decoupled Trajectory Design framework (IDTD) formulates an objective for exploration policy built on the Schur complement score derived from the Fisher information matrix to ensure every parameter leaves a unique effect on the trajectory, thereby improving sim-to-real transfer.

Motivation and Problem Statement

Sampling-based system identification estimates physically meaningful parameters by tuning a simulator to reproduce target system dynamics, but when collected trajectories do not distinguish the effects of different parameters, multiple parameter combinations can reproduce those trajectories, leading to unreliable parameter estimates<ref:2610.10905#pg2>. Prior work addresses this by seeking informative trajectories where informativeness is quantified through the Fisher Information Matrix (FIM), whose inverse lower-bounds the covariance of the parameter estimate<ref:2610.10905#pg3>. However, this criterion does not treat the amount of information and the separability of the parameters as distinct quantities, so increased excitation can improve the aggregate criterion even when some parameter effects become less distinguishable<ref:2610.10905#pg5>.

Informationally Decoupled Trajectory Design (IDTD)

IDTD builds on a per-parameter score derived from the Schur complement of the Fisher information, which measures how much of a parameter’s effect on the motion remains after the effects of all other parameters are accounted for<ref:2610.10905#pg5>. A parameter whose effect can be reproduced by the others scores near zero, while a parameter with a distinct effect scores high, meaning it is cleanly distinguishable or decoupled from the rest<ref:2610.10905#pg5>. To prevent the objective from being improved through excitation alone, IDTD normalizes each score by the information carried by the corresponding parameter<ref:2610.10905#pg5>. It then evaluates these normalized scores across multiple trajectory segments to encourage complementary excitation of different parameters throughout the trajectory<ref:2610.10905#pg5>.

IDTD Objective and Implementation

The IDTD objective is to maximize the logarithmic sum of the per-parameter coverage scores defined in Eq. (14)<ref:2610.10905#pg6>. This formulation emphasizes poorly covered parameters while still rewarding improvements across all parameters, encouraging different trajectory segments to provide complementary information<ref:2610.10905#pg6>. The complete trajectory design pipeline of IDTD is summarized in Fig. 1, and the corresponding optimization procedure is given in Algorithm 1<ref:2610.10905#pg6>.

Experimental Validation and Results

IDTD was evaluated on a linear-dynamics system, Unitree Go2, Unitree G1, and Crazyflie in simulation, demonstrating improved parameter identification, target-system prediction, and downstream policy transfer<ref:2610.10905#pg6>. On the real K1 humanoid Booster K1 robot, the identified parameters more accurately capture the target-system dynamics<ref:2610.10905#pg6>. Across Go2 and G1, IDTD achieves the lowest overall identification error, reducing the error from 10.28% to 7.31% on the Go2 and from 3.72% to 1.28% on the G1 compared to SPI-ACTIVE<ref:2610.10905#pg7>. Furthermore, IDTD achieves the lowest linear and angular velocity tracking errors, fall rate, and energy consumption among all methods on the Go2<ref:2610.10905#pg8>. The parameter coupling analysis on G1 shows that IDTD produces a substantially more isotropic ellipse, indicating weaker parameter coupling compared to SPI-ACTIVE and E-OPTIMAL<ref:2610.10905#pg8>.

Conclusion

IDTD combines a normalized Schur-complement score with segment-wise coverage and logarithmic aggregation to balance parameter separability and information quantity<ref:2610.10905#pg6>. Across simulated Go2, G1, and Crazyflie platforms, IDTD improved identification accuracy, dynamics prediction, and parameter decoupling<ref:2610.10905#pg8>. On the real K1 humanoid the identified parameters predicted unseen real trajectories more accurately<ref:2610.10905#pg8>. The lower energy consumption is consistent with improved PD-gain identification reducing unnecessary corrective actuation<ref:2610.10905#pg8>. Together, these results demonstrate that the decoupling objective of IDTD suppresses the parameter correlation responsible for error absorption between parameters, providing a mechanistic explanation for the improved identification accuracy<ref:2610.10905#pg8>.

How it works

  1. The framework formulates an objective for the exploration policy built on the Schur complement score derived from the Fisher information matrix<ref:2610.10905#pg5>.

  2. IDTD normalizes each score by the information carried by the corresponding parameter to prevent excitation alone from improving the objective<ref:2610.10905#pg5>.

  3. The trajectory is partitioned into M equal-length segments, and for each segment, a decoupling factor di(F(s); αi) is computed using Eq. (13)<ref:2610.10905#pg6>.

  4. IDTD maximizes the logarithmic sum of the per-parameter coverage scores defined in Eq. (15), which encourages different trajectory segments to provide complementary information<ref:2610.10905#pg6>.

  5. The parameter-specific exponent αi controls how much of the diagonal magnitude is removed, with larger values more strongly removing the contribution of absolute information magnitude<ref:2610.10905#pg5>.

Key Contributions

(i) We address the challenging yet practical problem of designing exploration trajectories that distinguish the effects of physical parameters, enabling reliable sampling-based system identification<ref:2610.10905#pg3>.

(ii) We propose IDTD, a trajectory design framework that explicitly balances information quantity with parameter distinguishability through a normalized Schur-complement score and parameter-wise trajectory coverage<ref:2610.10905#pg5>.

(iii) We demonstrate that IDTD improves parameter identification accuracy and downstream policy transfer across simulated Unitree Go2, Unitree G1, and Crazyflie platforms, and better captures realworld dynamics on a Booster K1 humanoid<ref:2610.10905#pg6>.

Limitations and Future Work

While IDTD improves forward-dynamics prediction on the real K1, downstream control improvements remain limited, possibly due to the restricted parameter space identifiable from onboard sensing<ref:2610.10905#pg8>. Future work could use more accurate state estimation, such as external motion capture, to identify a broader parameter set and improve downstream transfer<ref:2610.10905#pg8>.

References

[1] J. Lee, A. Dosovitskiy, D. Bellicoso, V. Tsounis, V. Koltun, and M. Hutter, “Learning agile and dynamic motor skills for legged robots,” Sci. Robotics, vol. 4, no. 26, 2019<ref:2610.10905#pg10>.

[2] W. Zhao, J. P. Queralta, and T. Westerlund, “Sim-to-real transfer in deep reinforcement learning for robotics: a survey,” in 2020 IEEE Symposium Series on Computational Intelligence, SSCI 2020<ref:2610.10905#pg10>.

[3] J. Tobin, R. Fong, A. Ray, J. Schneider, W. Zaremba, and P. Abbeel, “Domain randomization for transferring deep neural networks from simulation to the real world,” in 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2017<ref:2610.10905#pg10>.

[4] X. B. Peng, M. Andrychowicz, W. Zaremba, and P. Abbeel, “Sim-to-real transfer of robotic control with dynamics randomization,” in 2018 IEEE International Conference on Robotics and Automation, ICRA 2018<ref:2610.10905#pg10>.

[5] N. Sobanbabu, G. He, T. He, Y. Yang, and G. Shi, “Sampling-based system identification with active exploration for legged robot sim2real learning,” CoRR, vol. abs/2505.14266, 2025<ref:2610.10905#pg10>.

[6] M. Memmel, A. Wagenmaker, C. Zhu, D. Fox, and A. Gupta, “ASID: active exploration for system identification in robotic manipulation,” in The Twelfth International Conference on Learning Representations, ICLR 2024<ref:2610.

Improvements for AI systems

  1. Bold header: Explicit Parameter Separability in Trajectory Design

The improved AI system can achieve reliable sampling-based system identification by formulating an objective that explicitly accounts for parameter separability through the Schur complement score, which measures how much of a parameter’s effect on the motion remains after the effects of all other parameters are accounted for.

  1. Bold header: Dynamic Trajectory Segmentation and Specialization

The system can design trajectories that expose every parameter somewhere along the motion rather than accumulating information for only a small subset by partitioning exploration into M equal-length segments and assigning each parameter to the segment in which it is most cleanly separated, as indicated by the score ci = max s∈[1,M] di(F(s); αi).

  1. Bold header: Adaptive Decoupling Normalization

The AI can dynamically balance excitation strength with parameter distinguishability by employing a normalization factor, defined as di(F; αi) = Si(F) / (Fii z) information quantity, resulting in weaker parameter separation in practice, controlled by the exponent αi.

  1. Bold header: Enhanced Downstream Policy Transfer

The improved system will produce policies that translate into better downstream policy transfer to the target dynamics, as demonstrated by achieving the lowest linear and angular velocity tracking errors, fall rate, and energy consumption on real-world hardware like the K1 humanoid.

Abstract

Sampling-based system identification estimates physically meaningful parameters by tuning a simulator to reproduce the target system dynamics, providing an interpretable approach to improving sim-to-real transfer. Yet when the collected trajectories do not distinguish the effects of different parameters, multiple parameter combinations can reproduce those trajectories, leading to unreliable parameter estimates. To address this challenge, we introduce an Informationally Decoupled Trajectory Design framework (IDTD), which formulates the objective for the exploration policy built on the Schur complement score derived from the Fisher information matrix. To faithfully reflect parameter separability in the exploration objective, IDTD normalizes the score against the per-parameter information, selects the most favorable trajectory segment for each parameter, and aggregates the resulting scores logarithmically. The optimized trajectory is therefore composed of complementary intervals, each exposing a distinct subset of parameters whose contribution to the motion over that interval can be attributed unambiguously. Across diverse simulation environments, ranging from a linear-dynamics system to the Go2 quadruped, G1 humanoid, and Crazyflie quadrotor, IDTD reduces the parameter identification error by 39.6% on average relative to the strongest prior active-exploration baseline and attains improved downstream policy transfer. Furthermore, we validate the proposed trajectory design on a real K1 humanoid, demonstrating that the resulting identified parameters accurately capture the real-system dynamics.

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