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

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

arXiv:2610.10905v1cs.RO

TL;DR

When parameter effects are coupled, different parameter combinations can reproduce the same trajectories, making reliable identification difficult. IDTD designs exploration using normalized Schur-complement scores and complementary trajectory segments. It improves identification and policy transfer across the evaluated simulations and better captures unseen real K1 dynamics, though downstream control gains on K1 remain limited.

  • Problem

    When nuisance parameters are estimated imperfectly, coupling between parameters can let their errors leak into the estimate of the parameter of interest.

    Source: A. Motivation: Parameter Coupling in… · p. 4

  • Method

    IDTD normalizes per-parameter Schur-complement scores and combines each parameter’s best trajectory-segment score through logarithmic aggregation.

    Source: §I · p. 2, §VI · p. 8

  • Results

    Across Go2 and G1, IDTD achieves the lowest overall identification error; on Go2, it reduces error from 10.28% to 7.31% versus SPI-ACTIVE.

    Source: B. Physics-Based Simulation · p. 6

  • Takeaways & Limitations

    On the Booster K1, IDTD-identified parameters predict unseen real trajectories more accurately, while downstream control improvements remain limited.

    Source: §VI · p. 8

    On the real K1, downstream control improvements remain limited, possibly because only a restricted parameter space is identifiable from onboard data.

    Source: §VI · p. 8

Abstract

from arXiv · show

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.

I. INTRODUCTION

The section motivates sampling-based system identification and identifies trajectory design that separates parameter effects as a key challenge. IDTD addresses it by designing complementary excitation and is evaluated in simulation and on a real humanoid.

A. Sim-to-Real Transfer and System Identification

  • Domain randomization trains across a parameter distribution to include real-system dynamics, but covering a wide range tends to produce conservative policies that trade away performance for robustness.Its randomization ranges also require tuning.Source: §I · p. 1, A. Sim-to-Real Transfer and System… · p. 2
  • Sampling-based identification tunes simulator parameters to match real trajectories, retaining physically interpretable parameters while avoiding differentiation through contact and actuator dynamics.Prior sampling-based methods use black-box search over physical parameters, made practical by massively parallel GPU simulation.Source: §I · p. 1

I. INTRODUCTION

  • When parameter effects remain coupled, different parameter combinations can match observed trajectories, making low trajectory-matching cost insufficient evidence of accurate identification.In the mass-and-damping example, more energetic excitation can increase aggregate information while leaving sensitivities nearly collinear.Source: §I · p. 1
  • IDTD uses normalized Schur-complement scores and parameter-wise trajectory coverage to design motions that expose each parameter distinctly somewhere along the trajectory.It evaluates normalized scores across multiple segments to encourage complementary excitation rather than more excitation alone.Source: §I · pp. 1–2
  • IDTD improves parameter identification, target-system prediction, and downstream policy transfer in simulations, and its identified parameters better capture dynamics on a real Booster K1 humanoid.The evaluations include a linear-dynamics system, Unitree Go2, Unitree G1, and Crazyflie.Source: §I · p. 2

A. Sim-to-Real Transfer and System Identification

  • IDTD follows sampling-based identification but focuses on designing exploration so each physical parameter leaves a distinct trajectory effect.The paper presents this as the complementary problem to searching for parameters that match recorded trajectories.Source: A. Sim-to-Real Transfer and System… · p. 2

B. Active Exploration and Optimal Experimental Design

Prior trajectory-design objectives often summarize information across parameters, while IDTD explicitly targets per-parameter separability and coverage. The section situates this objective among sampling-based identification and Fisher-information-based exploration.

B. Active Exploration and Optimal Experimental Design

  • IDTD uses per-parameter separability to enforce coverage of all physical parameters, unlike prior objectives that address separation only implicitly through aggregate criteria.QOED improves distinguishability for a selected subset, whereas system identification requires all physical parameters to be identifiable.Source: B. Active Exploration and Optimal… · p. 2

A. Sampling-Based System Identification

  • Sampling-based system identification tunes simulator parameters to minimize mismatch between simulated and recorded real-world trajectories, using a black-box optimizer rather than differentiating through the simulator.The paper uses CMA-ES to optimize the trajectory-matching objective.Source: A. Sampling-Based System Identification · p. 3

B. Fisher Information for Trajectory Design

  • The Fisher information matrix measures trajectory informativeness because its inverse lower-bounds the covariance of an unbiased parameter estimate.The section assumes additive Gaussian process noise when approximating the trajectory FIM.Source: B. Fisher Information for Trajectory… · p. 3
  • Active exploration optimizes the command sequence while keeping the pretrained policy fixed, evaluating the FIM at nominal parameters because the true parameters are unavailable.The optimized command is executed on the target system to collect a trajectory for parameter estimation.Source: B. Fisher Information for Trajectory… · p. 3

C. Problem Statement

The exploration objective must support recovery of all physical parameters within a fixed collection-time budget. Parameter coupling can let one parameter’s estimation error be absorbed by another, motivating trajectories that separate their effects.

C. Problem Statement

  • A fixed data-collection budget and pretrained command-conditioned policy frame the goal: design an exploration objective that enables accurate recovery of all physical parameters.The proposed objective replaces the existing criterion.Source: C. Problem Statement · p. 3

A. Motivation: Parameter Coupling in System Identification

  • In a two-parameter mass-damper example, error in the estimated damping parameter can propagate into the compliance estimate when their effects are coupled.The example models control input through compliance and velocity resistance through damping.Source: A. Motivation: Parameter Coupling in… · pp. 3–4
  • Reducing off-diagonal coupling limits how much error in the nuisance estimate leaks into the target estimate; the Schur complement measures the information remaining after accounting for that nuisance parameter.The Schur complement reflects both information about the target parameter and its separability from the other parameter.Source: A. Motivation: Parameter Coupling in… · p. 4

B. Per-Parameter Decoupling Factor

The per-parameter Schur complement measures information about a target parameter after accounting for the remaining parameters, distinguishing independently informative sensitivities from effects absorbed by others.

B. Per-Parameter Decoupling Factor

  • For each parameter, the Schur complement gives the information that remains after accounting for all other parameters.It is computed by partitioning the parameter vector and corresponding Fisher information matrix into target and remaining-parameter blocks.Source: B. Per-Parameter Decoupling Factor · p. 4
  • A parameter with sensitivity orthogonal to the others has S_i = F_ii, while a parameter fully absorbed by them has S_i → 0.Source: B. Per-Parameter Decoupling Factor · p. 4
  • Unlike A-optimal design’s aggregate uncertainty criterion, IDTD explicitly uses per-parameter Schur complements and adds controls for information quantity and parameter coverage.The A-optimal trace of the inverse Fisher information is expressed as a sum of reciprocal per-parameter Schur complements.Source: B. Per-Parameter Decoupling Factor · p. 4

C. Two Normalizations for Faithful Decoupling

IDTD normalizes sensitivities and the Schur-complement score so parameter scale and excitation strength do not obscure parameter separability.

C. Two Normalizations for Faithful Decoupling

  • Finite-difference steps scale with each parameter’s search range, avoiding sensitivity distortions caused by one shared absolute step across parameters with different natural scales.The passage contrasts a 10^-3 absolute step that perturbs friction by roughly 0.2% but proportional gain by only 0.001%.Source: C. Two Normalizations for Faithful… · p. 4
  • The raw Schur complement combines diagonal information, which measures excitation strength, with a decoupling ratio measuring the fraction of information remaining after accounting for other parameters.The decoupling ratio corresponds to 1/VIF_i.Source: C. Two Normalizations for Faithful… · p. 4
  • A parameter-specific exponent α_i dampens the diagonal factor; α_i = 1 yields the pure decoupling ratio, while α_i = 0 leaves the score in the diagonal-dominated regime.Experiments use parameter-specific α_i ≥ 0.7.Source: C. Two Normalizations for Faithful… · p. 4

D. Segment-Wise Decoupling Coverage

IDTD partitions the trajectory into segments and scores each parameter by its best decoupling segment, encouraging complementary intervals that cover all parameters.

D. Segment-Wise Decoupling Coverage

  • The trajectory is divided into M equal-length segments, with a Fisher information matrix and decoupling factor computed for each segment.Source: D. Segment-Wise Decoupling Coverage · p. 4
  • Each parameter receives its highest decoupling score across segments, allowing different intervals to specialize in different parameter subsets.Source: D. Segment-Wise Decoupling Coverage · p. 5
  • A logarithmic sum of per-parameter coverage scores penalizes parameters not decoupled in any segment and encourages complementary information across the trajectory.When a parameter’s coverage score approaches zero, its log drives the objective toward negative infinity.Source: D. Segment-Wise Decoupling Coverage · p. 5

V. EXPERIMENTS

The linear-dynamics experiment contrasts trajectories that excite the same system parameters with different degrees of coupling. Although both can fit the identification data, only the decoupled trajectory recovers the parameters and predicts held-out motion accurately.

V. EXPERIMENTS

  • The experiments evaluate IDTD in simulation and on a real Booster K1 robot, while the linear-system example follows mass-damper dynamics.Figure 2 tracks trajectory-matching loss and parameter-estimation error over CMA-ES iterations, with 95% confidence intervals.Source: §V · p. 5, A. Linear-Dynamics System · p. 5, Figure 2 · p. 5

A. Linear-Dynamics System

  • The coupled trajectory uses sustained positive input, while the decoupled trajectory alternates high- and low-input phases to preferentially excite θ and ϕ.Both designs maintain excitation, but the alternating regimes reduce coupling between the parameters.Source: A. Linear-Dynamics System · p. 5
  • The coupled and decoupled trajectories reach similarly low matching costs, but only the decoupled trajectory recovers both parameters and predicts held-out motion near the noise floor.The coupled trajectory retains large parameter-estimation errors and higher held-out prediction error, showing that a low matching cost alone does not establish accurate identification.Source: A. Linear-Dynamics System · p. 5, Figure 2 · p. 5

B. Physics-Based Simulation

In physics-based simulation, IDTD improves identification on Go2 and G1 and remains competitive on Crazyflie, with gains in prediction, transfer, and parameter separation. Ablations and excitation comparisons show how segment coverage and decoupling contribute to its performance.

B. Physics-Based Simulation

  • The evaluation uses Newton simulation with known ground-truth parameters on Go2, G1, and Crazyflie; identification targets 50, 68, and 17 parameters, respectively.Each method uses two pretrained policies and five identification seeds per policy; IDTD optimizes five two-second segments per 10-second episode using separate control points.Source: B. Physics-Based Simulation · pp. 5–6
  • IDTD reduces overall identification error from 10.28% to 7.31% on Go2 and from 3.72% to 1.28% on G1 versus SPI-ACTIVE, while E-OPTIMAL leads on Crazyflie at 1.59% versus IDTD at 2.11%.Figure 3 compares overall identification error by platform and the error ratio of each baseline to IDTD.Source: B. Physics-Based Simulation · p. 6, Table I · p. 6, Figure 3 · p. 6
  • IDTD achieves the lowest forward-dynamics prediction error across Go2 rollout horizons and the lowest Go2 tracking errors, fall rate, and energy consumption among evaluated transfer methods.Transfer policies are retrained under identified dynamics and evaluated on the ground-truth target dynamics; E-OPTIMAL and QOED are excluded because their Go2 identification errors yield unstable policies.Source: B. Physics-Based Simulation · pp. 6–7, Figure 4 · p. 7, Table II · p. 7
  • On G1, IDTD yields a more isotropic wrist-pitch gain covariance ellipse and larger 1 −|ρij| across joints, indicating weaker parameter coupling than competing objectives.SPI-ACTIVE implicitly penalizes correlation but does not separate that effect from information quantity, resulting in weaker parameter separation in practice.Source: B. Physics-Based Simulation · p. 7, Figure 5 · p. 7
  • Relative to SPI-ACTIVE, IDTD raises Go2 arm and leg joint velocities to 1.95× and 1.44× and arm-angle range to 1.30×, while achieving higher decoupling factors across parameter groups.SPI-ACTIVE induces the strongest base and waist motion; E-OPTIMAL improves decoupling over SPI-ACTIVE but under weaker excitation.Source: B. Physics-Based Simulation · p. 7, Figure 6 · p. 7
  • On Go2, mean aggregation raises overall error from 7.31% to 10.47%, unnormalized sensitivity raises it to 8.31%, and removing decoupling normalization raises it to 22.68%.The three ablations respectively weaken coverage of less-excited parameters, overweight foot-friction parameters under a common perturbation scale, and let absolute information magnitude dominate decoupling.Source: B. Physics-Based Simulation · p. 8, Table III · p. 8

C. Real-world Experiments

On the Booster K1 humanoid, IDTD identified parameters from onboard IMU and encoder sensing and achieved the largest reported reduction in held-out open-loop prediction cost. The conclusion notes that downstream control improvements remain limited, possibly because onboard sensing restricts the identifiable parameter space.

C. Real-world Experiments

  • The K1 experiment identified 60 actuator- and joint-level parameters using onboard joint encoders and an IMU, without external motion capture.The parameter groups were torque-lag time constants, velocity-dependent actuator gains, joint-friction coefficients, and joint armatures; floating-base inertial properties were not included.Source: C. Real-world Experiments · p. 8
  • 14.4% cost reduction for IDTD exceeded 11.9% for PASSIVE and 10.0% for SPI-ACTIVE on held-out K1 trajectories.IDTD also achieved the lowest error on most state components; Table IV reports weighted prediction cost and errors for joint position, joint velocity, base angular velocity, and base orientation.Source: C. Real-world Experiments · p. 8, Table IV · p. 8

VI. CONCLUSION

  • Across simulated Go2, G1, and Crazyflie platforms, IDTD improved identification accuracy, dynamics prediction, and parameter decoupling; K1 parameters predicted unseen real trajectories more accurately.Source: §VI · p. 8
  • Downstream control improvements on the real K1 remained limited, possibly because onboard sensing restricted the parameter space that could be identified.The conclusion suggests more accurate state estimation, such as external motion capture, as a way to identify a broader parameter set.Source: §VI · p. 8

APPENDIX

The appendix describes trajectory optimization and Fisher-information estimation used to construct segment-wise information for IDTD. It also reports synchronization and regularization choices for the sensitivity calculations and objective.

A. Trajectory Optimization

  • Exploration commands were optimized with CMA-ES over five 2-second trajectory segments, using degree-5 Bézier curves with six control points per command channel.Optimization ran for up to 3000 generations with early stopping; population sizes and command dimensions varied by platform.Source: A. Trajectory Optimization · p. 9, Table V · p. 9

B. Fisher-Information Estimation

  • Finite-difference sensitivities used a nominal rollout and one perturbed rollout per parameter, with eight parallel groups sharing the Fisher-information parameter vector.Perturbed environments were synchronized with the nominal rollout every five simulation steps, and sensitivities were accumulated within each segment to form segment-wise Fisher information matrices.Source: B. Fisher-Information Estimation · p. 9
  • The Schur-complement nuisance-parameter block was regularized with λSchur = 10^-6, and the logarithmic coverage objective used ε = 10^-6.Source: B. Fisher-Information Estimation · p. 9

C. Decoupling Exponents

The appendix fixes decoupling exponents by parameter group and uses group-specific finite-difference perturbations scaled to each physical parameter. For the real K1 experiment, it also specifies the identified parameter vector and fitting settings.

C. Decoupling Exponents

  • Decoupling exponents α_i ranged from 0.7 to 1.0, with larger values emphasizing the decoupling ratio and smaller values retaining more dependence on excitation strength.The exponent was assigned by parameter group and held fixed throughout each experiment.Source: C. Decoupling Exponents · p. 9

D. Finite-Difference Perturbations

E. Real-World K1 Experiment

  • For K1, fitting used a 60-dimensional parameter vector and CMA-ES with population 100, initial standard deviation 0.5, and MAP-style regularization strengths from 10^-3 to 5 × 10^-2.The vector comprised 8 torque-lag time constants, 8 velocity-dependent actuator gains, 22 joint-friction coefficients, and 22 joint-armature parameters.Source: E. Real-World K1 Experiment · p. 10, Table VIII · p. 10

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