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

Summary

Abstract Summary

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.

Key Points

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.

Preliminaries

Let $\theta\in\mathbb{R}^{N}$ denote the vector of parameters to identify (e.g., base inertial properties, per-joint PD gains, and friction coefficients), and let $\pi$ be a policy pretrained in simulation, conditioned on a command $c_{t}$ (e.g., base velocity and gait parameters).

A dataset $\mathcal{D}=\{\tau=(s_{0},a_{0},s_{1},\cdots)\}$ of trajectories is collected on the target system by rolling out $\pi$ under a command sequence $\mathbf{c}=(c_{1},\ldots,c_{T})$, recording states and executed actions.

Preliminaries — Informationally Decoupled Trajectory Design for Sim-to-Real System Identification — 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.

Methods

We analyze a two-parameter linear system to illustrate how parameter coupling allows estimation errors in one parameter to be absorbed by another, motivating an explicit characterization of parameter separability.

Consider a scalar state governed by a discrete-time mass-damper system, in which the control input $u_{t}$ drives the state through a compliance $\theta^{\star}$ and the velocity $\dot{x}_{t}$ resists it through a damping $\phi^{\star}$, where $w_{t}$ is i.i.d. Gaussian noise. By Eq.

Methods — Informationally Decoupled Trajectory Design for Sim-to-Real System Identification — Fig. 2: Trajectory matching loss and parameter estimation error over CMA-ES iterations. Shaded regions indicate $95\%$ confidence intervals.

Experiments

We evaluate IDTD on the linear-dynamics system, in physics-based simulation, and on a real Booster K1 robot. To validate the analysis of Sec. IV-A , we manually construct two excitation trajectories on the mass-damper system that differ in how strongly the two parameters are coupled. Specifically, we collect sequences of states $x_{t}$ and inputs $u_{t}$ following the dynamics in Eq. ( 5 ).

Sources and Demonstrations

Figures are reproduced from Shin et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.