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

Sangwoo Shin; Ashvin Anilkumar; Ryan Gao; Josiah P. Hanna

cs.ROOct 7, 2026

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

Authors: Sangwoo Shin, Ashvin Anilkumar, Ryan Gao, Josiah P. Hanna

Organizations: University of Wisconsin–Madison

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.

Figures & tables

Fig. 1: Overview of IDTD . (1) A command sequence is rolled out in simulation over $M$ segments. (2) Each segment yields a Fisher information $F^{(s)}$ , from which the per-parameter decoupling factor $d_{i}(F^{(s)};\alpha_{i})$ follows through the Schur complement and the normalization of Sec. IV-B . (3) Each parameter takes the score $c_{i}$ of its best segment, and IDTD optimizes the logarithmic sum of these scores.

Fig. 2: Trajectory matching loss and parameter estimation error over CMA-ES iterations. Shaded regions indicate $95\%$ confidence intervals.

Group	IDTD	SPI-Active	E-Opt	QOED	Passive
Go2 (50D)
$k_{p}$	$\mathbf{5.23}$ $\pm 0.7$	$6.41$ $\pm 0.4$	$9.07$ $\pm 0.8$	$10.38$ $\pm 0.6$	$9.19$ $\pm 0.6$
$k_{d}$	$6.71$ $\pm 0.7$	$\mathbf{6.55}$ $\pm 0.4$	$12.00$ $\pm 1.0$	$113.48$ $\pm 36.9$	$7.79$ $\pm 0.5$
Joint	$\mathbf{10.99}$ $\pm 1.4$	$16.89$ $\pm 1.1$	$26.43$ $\pm 3.1$	$34.67$ $\pm 2.5$	$21.06$ $\pm 0.9$
Foot	$5.90$ $\pm 0.9$	$8.69$ $\pm 0.9$	$7.75$ $\pm 1.3$	$5.18$ $\pm 0.5$	$\mathbf{5.09}$ $\pm 0.3$
Base	$\mathbf{7.71}$ $\pm 1.3$	$12.85$ $\pm 1.4$	$12.44$ $\pm 2.2$	$19.51$ $\pm 1.0$	$12.86$ $\pm 1.1$

TABLE I: Normalized parameter-identification error (%). Mean

\pm

95\%

confidence interval, darker = higher rank.

Fig. 3: (a) Overall identification error on each platform. (b) Error ratio of each baseline to IDTD , where values above the dotted line indicate higher error than IDTD . Shaded bands show $95\%$ confidence intervals.

Fig. 4: Forward-dynamics prediction error versus rollout horizon on the Go2. Shaded bands show $95\%$ confidence intervals.

Method	Lin. (m/s)	Ang. (rad/s)	Fall (%)	Energy (J/m)
IDTD	$\mathbf{0.159}$ $\pm.001$	$\mathbf{0.177}$ $\pm.002$	$\mathbf{0.71}$ $\pm 0.26$	$\mathbf{242.8}$ $\pm 2.7$
SPI-Active	$0.186$ $\pm.002$	$0.187$ $\pm.002$	$1.81$ $\pm 0.41$	$255.4$ $\pm 2.7$
Passive	$0.190$ $\pm.002$	$0.234$ $\pm.003$	$2.59$ $\pm 0.49$	$270.2$ $\pm 3.1$
Zero-shot	$0.364$ $\pm.004$	$0.433$ $\pm.006$	$22.35$ $\pm 1.26$	$547.9$ $\pm 7.4$

TABLE II: Downstream transfer performance on the Go2. Mean

\pm

95% confidence interval, darker = higher rank.

Fig. 5: Left: covariance ellipse for the $(k_{p},k_{d})$ pair of the wrist-pitch joint. Right: $1-|\rho_{ij}|$ for the $(k_{p},k_{d})$ pair of all G1 joints.

Fig. 6: Left: the excitation of each kinematic channel relative to SPI-Active on a

\log_{2}

scale. Right: the per-group mean of the decoupling factor

d_{i}

Group	IDTD	Mean agg.	Unidelta	$\boldsymbol{\alpha=0}$
$k_{p}$	$\mathbf{5.23}$ $\pm 0.7$	$8.18$ $\pm 1.0$	$7.39$ $\pm 0.4$	$16.30$ $\pm 0.9$
$k_{d}$	$\mathbf{6.71}$ $\pm 0.7$	$11.72$ $\pm 1.5$	$9.05$ $\pm 0.7$	$14.85$ $\pm 1.8$
Joint	$\mathbf{10.99}$ $\pm 1.4$	$19.63$ $\pm 1.5$	$11.03$ $\pm 0.7$	$51.41$ $\pm 2.7$
Foot	$5.90$ $\pm 0.9$	$7.31$ $\pm 1.0$	$\mathbf{4.29}$ $\pm 0.5$	$15.09$ $\pm 0.8$
Base	$7.71$ $\pm 1.3$	$\mathbf{5.51}$ $\pm 2.3$	$9.81$ $\pm 1.2$	$15.77$ $\pm 1.9$
All	$\mathbf{7.31}$ $\pm 0.6$	$10.47$ $\pm 0.9$	$8.31$ $\pm 0.4$	$22.68$ $\pm 0.9$

TABLE III: Ablation of IDTD design choices on the Go2 (50D). Mean

\pm

95% confidence interval, darker = higher rank.

Method	Cost	$q$ (deg)	$\dot{q}$ (rad/s)	$\omega$ (rad/s)	Orient. (deg)
Nominal	$2.291$	$1.146$	$0.519$	$0.322$	$1.247$
Passive	$2.018$ $\pm.003$	$1.095$ $\pm.001$	$0.482$ $\pm.001$	$0.314$ $\pm.001$	$1.242$ $\pm.004$
SPI-Active	$2.061$ $\pm.005$	$1.108$ $\pm.004$	$0.489$ $\pm.001$	$\mathbf{0.312}$ $\pm.001$	${1.252}$ $\pm.003$
IDTD	$\mathbf{1.961}$ $\pm.005$	$\mathbf{1.074}$ $\pm.002$	$\mathbf{0.473}$ $\pm.001$	$0.314$ $\pm.001$	$\mathbf{1.233}$ $\pm.005$

TABLE IV: Open-loop prediction on real-world K1 trajectories. Mean

\pm

95% confidence interval; darker = higher rank.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Setting	Go2	G1	Crazyflie
SysID dimension $P$	50	68	17
Command dimension $C$	9	3	2
CMA-ES population	20	12	20
Maximum generations	3000	3000	3000
Initial $\sigma_{0}$	0.25	0.25	0.25
Segments $M$	5	5	5

Appendix

TABLE V: Trajectory-optimization settings used in the simulation experiments.

Platform	Parameter group	$\alpha_{i}$
Go2	Base mass/inertial	1.00
	Actuator PD	0.90
	Foot friction	0.70
	Contact	0.75
G1	Base inertial	0.80
	$k_{p}$	1.00

Appendix

TABLE VI: Decoupling exponents

\alpha_{i}

used for each parameter group.

Platform	Parameter	Dim.	Range	$\delta\theta_{i}$
Go2	Base inertial	10	Nominal $\pm$ margin	0.10
	$k_{p}$ (N m/rad)	12	$[5.0,100.0]$	2.00
	$k_{d}$ (N m s/rad)	12	$[0.1,10.0]$	0.10
	Joint friction (N m)	12	$[0.0,5.0]$	0.05
	Foot friction	4	$[0.1,2.0]$	0.05
G1	Base inertial	10	Nominal $\pm$ margin	0.10

Appendix

TABLE VII: Parameter ranges and finite-difference perturbations used in simulation.

Parameter	Dim.	Range	$\delta\theta_{i}$	$\alpha_{i}$
Torque lag ( $10$ ms)	8	$[0,15]$	0.50	0.80
Dynamic gain	8	$[0.1,1.0]$	0.02	0.70
Joint friction	22	$[0,0.8]$	0.02	0.70
Armature ( $10^{-2}$ )	22	$[0.05,15]$	0.10	1.00

Appendix

TABLE VIII: Parameterization and optimization settings for the real Booster K1.

Explore similar work

Jun 20, 2026cs.RO

How Should a Simulation-to-Reality Transfer Budget Be Spent?

Simulation-to-reality transfer, often called sim-to-real transfer, is a central challenge in robot learning. Yet, the tradeoff between measuring a system more accurately and training over a broader range of simulated dynamics is still poorly understood. In this work, we focused on the allocation of real-robot measurement time between system identification and domain randomization. We studied this tradeoff in a controlled sim-to-sim pendulum setting, where a hidden-parameter model stands in for the physical robot, and the experiment sweeps identification rollouts against the width of the randomization distribution. Across the reality gaps and noise levels we tested, the measurement budget did most of the work. A small number of identification rollouts closed most of the transfer gap, and once any real data was available, policies performed best when trained at the estimated parameters rather than over a widened randomization band. Broad randomization that contained the true system still did not substitute for measurement. These results hold in a benign regime where the dynamics are identifiable and only two parameters are unknown, so structural model mismatch remains the setting where randomization breadth may become more valuable. Overall, our results suggest that sim-to-real pipelines should first measure the parameters they can and reserve randomization for the uncertainty that remains.

Syed Hamzah Rizvi, Yash Vardhan Tomar

Purdue University West Lafayette, USA

Robot Dynamics Identification Domain Randomization Sim-to-Real Transfer System Identification Robot Learning

Ask PDF

Oct 1, 2026cs.RO

EIDA: Execution-Interface Dynamics Adaptation for Real-to-Sim-to-Real Robot Navigation

Simulation-to-robot transfer can fail when velocity commands produce motion and feedback that differ from those modeled during policy training. We present execution-interface dynamics adaptation (EIDA), which fits these responses from target-platform execution data without reconstructing actuator dynamics. A model of body-frame pose increments updates simulator geometry, while a separate model predicts the velocity feedback observed by the policy; a short history of velocity feedback is included in the policy input. The fitted models are used within a lightweight GPU-parallel simulator. On the full Jackal and Go2 validation sets, the fitted models reduced position and yaw prediction errors relative to the simulator's predefined motion model. Across 100 benchmark navigation environments evaluated in a separate physics-based simulator, EIDA achieved the highest success rate and navigation score among the compared learned policies, both with and without global guidance. Feedback ablations further supported the need to match policy-facing velocity estimates. On a physical Unitree Go2, EIDA reached the goal without collision in all 20 static-scene trials, compared with 4 of 20 for the baseline. These results show that execution-interface adaptation can improve navigation transfer without detailed actuator simulation.

Yiwei Qian, Shanze Wang, Qingyuan Hu +2

Eastern Institute of Technology, Ningbo, China · National University of Singapore, Singapore · Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Hong Kong +1

Robot Dynamics Identification Robotics Simulation Robot Navigation Sim-to-Real Transfer Robot Dynamics Learning

Ask PDF

Aug 8, 2026cs.LG

Adaptive Symmetry Discovery for Dynamical System Identification

Dynamical systems model trajectory data generated by fixed underlying dynamics, with applications ranging from biology to physics. Especially in scientific settings, dynamical systems are not generic but often exhibit symmetries imposed by physical laws, formalized through equivariance with respect to group actions. The identification problem concerns recovering the parameters of a system from observed trajectories. In this work, we study adaptive symmetry discovery for dynamical system identification and address how a system can be identified from a single trajectory when it is equivariant with respect to an unknown symmetry group. To this end, we first show that for known symmetries, the system can be identified from a significantly shorter single trajectory than in the generic setting, and we precisely characterize this improvement. We then consider the automatic symmetry discovery setting, proposing a method to learn the symmetry group directly from a single trajectory and incorporate it into the identification procedure, achieving the same optimal trajectory length as in the known-symmetry case. Our analysis relies on tools from group representation theory and the expander properties of Cayley graphs, and may be of independent interest for the study of symmetries in dynamical systems.

Behrooz Tahmasebi, Melanie Weber

Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.

Dynamical Systems Nonlinear System Identification System Identification

Ask PDF