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Interpreting Control Latents for System Identification via Conditional Flow Matching

Dingqi Zhang, Ruiqi Zhang, Mark W. Mueller

arXiv:2608.23887v1cs.RO

TL;DR

Latent-conditioned adaptive policies adapt across changing dynamics but leave their physical meaning opaque, while non-identifiability makes a single latent-to-parameter mapping under-specified. This paper uses conditional flow matching to decode operational latents into distributions of quadrotor models, enabling tuning and robustness analysis around a frozen policy. Under stressed actuator dynamics, decoded-model tuning reduced position RMSE by 23% and heading RMSE by 45% relative to Baseline, while ensembles predicted lateral tracking-error evolution under Gaussian force disturbances.

  • Problem

    Adaptive-control latents lack inspectable physical meaning, and multiple physical systems can produce similar closed-loop behavior.

  • Method

    Conditional flow matching decodes each operational latent into a distribution of physically consistent quadrotor models instead of a single parameter estimate.

  • Results

    Under stressed actuator dynamics, decoded-model tuning reduced position RMSE by 23% and heading RMSE by 45% relative to Baseline.

  • Takeaways & Limitations

    Decoded-model ensembles support controller tuning and robustness analysis around the fixed policy, including calibrated lateral-error prediction under Gaussian force disturbances.

  • Takeaways & Limitations

    Validation is limited to a quadrotor platform and structured parametric model, and decoded parameters are sensitive to observation and state-estimation noise.

Abstract

from arXiv · show

Latent-conditioned adaptive policies can control robots across changing dynamics, but their learned latents remain internal representations of the policy rather than physical models that can be inspected, rolled out, or used by other control modules. This limits closed-loop analysis, diagnosis, and further improvement of a fixed policy. A direct mapping from latent to physical parameters is also under-specified, because multiple systems can induce similar closed-loop behavior. We therefore decode each operational latent into a distribution of quadrotor models using conditional flow matching. The decoded distribution enables two downstream uses without modifying the policy: online predictive tuning of a high-level controller around the fixed low-level policy, and robustness analysis under specified disturbances. Under perturbed actuator dynamics, decoded-model predictive tuning reduces position tracking RMSE by $23\%$ and heading RMSE by $45\%$ relative to fixed gains. Under Gaussian force disturbances, decoded-model ensembles closely predict the lateral tracking-error evolution. Together, these results show that control latents can be converted into physical model ensembles for tuning, robustness analysis, and diagnosis of frozen adaptive policies.

I. INTRODUCTION

Latent-conditioned policies adapt to changing dynamics but do not expose grounded physical meaning, and behavior-to-parameter inversion can be non-unique. The framework addresses this gap by decoding each latent into a distribution of physically consistent models for downstream analysis and control.

  • Motivation: Latent-conditioned policies infer compact representations from sensorimotor history for online adaptation, but those representations lack grounded physical meaning.The paradigm has been applied across legged locomotion, dexterous manipulation, and quadrotor flight.
  • Motivation: Many physically distinct systems can produce indistinguishable behavior under the same trajectories, making the inverse mapping from behavior to physical parameters ill-posed.A heavier quadcopter with weaker actuation can match a lighter vehicle’s closed-loop motion.
  • Motivation: Single-parameter regression cannot represent the physical non-identifiability captured by equivalence classes of plausible dynamics models.The proposed viewpoint replaces one-to-one latent-to-parameter mappings with distributions over compatible models.
  • Approach: Conditional flow matching decodes each latent into a continuous distribution over physically distinct, dynamically consistent models rather than a single estimate.The framework uses these decoded models in parallel simulations whose predictive rollouts can be compared with real responses.
  • Downstream uses: The decoded distributions support controller tuning and robustness analysis around the deployed policy without modifying it.The framework recovers a family of reference models from the latent rather than tuning toward one fixed reference model.

III. METHODOLOGY

The methodology jointly trains a latent-based adaptive controller and decodes its history-recovered latent into a distribution of dynamically consistent models. Alignment, scheduled substitution, and regularization make the latent recoverable, policy-consistent, and resistant to collapse.

  • Framework: The framework jointly learns a latent-based adaptive controller and a conditional flow-matching decoder for dynamically consistent models.The decoder conditions on the latent representation produced from recent sensorimotor history.
  • History-based adaptation: At deployment, the policy uses a latent estimated from recent sensorimotor history because physical parameters are unavailable.The operational latent is inferred from a history window of states and actions.
  • Unified training: Scheduled substitution gradually replaces the privileged latent with the history-based estimate, coupling the adaptation module to the policy.The substitution probability increases after an initial warmup period.
  • Unified training: Alignment and regularization terms prevent latent collapse, promote observability, and stabilize the joint objective.The auxiliary objectives include variance regularization and reconstruction from the privileged latent to physical parameters.
  • Unified training: Joint optimization aligns privileged and history-based latents, reducing their mismatch and keeping the representation recoverable for system identification.The history-based estimate is the latent used throughout deployment-stage decoding.

B. Generative System Identification via Conditional Flow Matching

Conditional Flow Matching decodes each operational latent into a distribution over physically distinct models by transporting a Gaussian base distribution to latent-conditioned parameters. The learned vector field is integrated at inference to generate dynamically consistent parameter samples.

  • CFM models the conditional distribution p(θ | ẑt) by transporting a Gaussian base distribution to empirical physical parameters associated with the latent.A neural vector field vψ(θτ, τ, ẑt) governs the transport.
  • Gaussian-smoothed interpolation uses θτ=(1−τ)θ0+τθ1+σε, with θ0 sampled from N(0,I) and θ1 sampled from the physical-parameter dataset.The smoothing perturbation prevents degeneracy and smooths the marginal velocity field.
  • Truncating flow time to [0,τmax] with τmax<1 avoids ill-conditioned regression near τ=1.Near τ=1, smoothing noise becomes comparable to the residual interpolation signal.
  • The flow-matching objective trains vψ to approximate the displacement θ1−θ0 for noisy interpolated parameters conditioned on the operational latent.The target vector field is independent of the noise realization ε.
  • At inference, Euler integration from θ0∼N(0,I) produces samples ˆθ from the learned conditional distribution p(θ|ẑt).The solver integrates the learned vector field from τ=0 to τ=1.

IV. IMPLEMENTATION

The framework is instantiated on quadrotors because they offer accurate first-principles models, standard parametric controllers, and substantial cross-platform variation in physical parameters.

  • Quadrotors provide accurate first-principles models and standard parametric controllers for evaluating decoded parameters against policy actions.
  • Cross-platform quadrotor adaptation spans orders-of-magnitude variation in mass, inertia, and motor constants.
  • The instantiation follows the cross-platform adaptation setting of.

A. Training Setup

Training combines an eight-dimensional adaptive latent policy with extensive simulation randomization, then learns the decoder from 20,000 latent–parameter pairs and evaluates the system in simulation and hardware experiments.

  • A. Training Setup: The policy produces an eight-dimensional latent representation and is trained in simulation with extensive randomization over cross-platform quadrotor parameters.
  • A. Training Setup: The platform-agnostic inner-loop policy receives IMU measurements and high-level commands, then outputs normalized motor-speed commands.Unified training uses scheduled substitution between privileged and history-based latent representations.
  • A. Training Setup: 20,000 parameter–latent pairs train the conditional flow-matching model after policy convergence.The velocity field uses a four-layer residual network with hidden dimension 512 and SiLU activations.
  • B. Parameter Space: The 19-dimensional parameter vector includes mass, arm length, thrust and torque coefficients, inertia, drag, rotor speed, motor effectiveness, motor time constant, and external torque disturbances.
  • C. Experimental Setup: Simulation training and pre-hardware evaluation are conducted in Flightmare with randomized quadrotor dynamics.
  • C. Experimental Setup: The hardware platform’s nominal parameters are measured independently of the latent decoder through direct measurement, bench characterization, and static motor tests.

V. DECODED MODELS FOR CONTROL AND ROBUSTNESS ANALYSIS

The decoded models support online predictive tuning around a frozen low-level policy, improving controller performance in nominal, stressed, and hardware settings.

  • Overview: Decoded models enable online predictive tuning and robustness analysis around the fixed latent-conditioned policy.The low-level policy remains frozen while decoded-model rollouts support high-level controller updates.
  • Nominal Predictive Control: 34% lower position RMSE and 18% lower maximum position error versus Naive were achieved by CFM-tuned in nominal randomized environments.CFM-tuned closed most of the gap to the hand-tuned Baseline using decoded-model rollouts.
  • Hardware Gain Tuning: CFM-tuned was deployed for hardware 3D lemniscate tracking at slow, medium, and fast reference speeds.The tuner started from naive gains and updated them online using decoded-model rollouts.
  • Hardware Gain Tuning: CFM-tuned matched Baseline hardware tracking while reducing peak position error and position-error standard deviation at every tested speed.Mean position errors differed by only a few centimeters, while Figure 4 shows reduced tracking spread at medium speed.

B. Robustness Analysis under Disturbances

Decoded-model ensembles estimate closed-loop robustness under deterministic disturbances, with stronger agreement for lateral than vertical tracking responses.

  • Individual Step-Disturbance Analysis: Decoded models produce uncertainty envelopes by rolling out physically plausible quadrotor models under the fixed policy and matched disturbances.The deterministic step test uses identical initial conditions and disturbance profiles across true and decoded rollouts.
  • Hardware Gain Tuning: Hardware tracking comparisons span slow, medium, and fast 3D lemniscate references, with Table IV reporting position and heading error metrics.Figure 4 focuses on the medium-speed trial and compares CFM-tuned with Baseline.
  • Individual Step-Disturbance Analysis: The decoded lateral response stayed close to the true response under horizontal and vertical constant-force steps.For horizontal force, true lateral error remained inside the predicted envelope; vertical-force lateral error was predicted at the correct scale.
  • Individual Step-Disturbance Analysis: Decoded models captured lateral closed-loop behavior better than vertical behavior in the deterministic step test.Vertical decoded rollouts had wider spreads and larger offsets, while ±20% true-system perturbations produced much larger envelopes in both directions.

2) Monte-Carlo Disturbance Analysis:

Monte Carlo disturbance experiments show that decoded ensembles track lateral error trends across disturbance strengths, while vertical-error spread is less accurate.

  • Monte-Carlo Disturbance Analysis: Temporal error envelopes are emphasized for robustness monitoring because they indicate whether tracking error may exceed tolerance during a rollout.Final tracking-error distributions provide a complementary finite-horizon steady-offset measure.
  • Monte-Carlo Disturbance Analysis: Decoded vertical-error distributions were broader and shifted relative to true distributions, especially at larger σ.The decoded models identified increasing vertical error but overestimated or misplaced part of its spread.
  • Monte-Carlo Disturbance Analysis: The decoded ensemble provides a useful lateral robustness envelope under both deterministic and Gaussian disturbances, while exposing weaker vertical-response reliability.The vertical mismatch indicates where the training distribution or decoded parameter set should be strengthened.

VI. ABLATION OF DISTRIBUTIONAL DECODING

The ablation tests whether operational latents should decode to distributions over physical parameters rather than deterministic point estimates. Across tracking speeds, CFM better reproduces the policy’s motor-command magnitude and temporal structure than regression.

  • The experiment replays recorded hardware state, command, and latent histories while each decoder instantiates a parametric controller for action comparison.
  • CFM updates decoded parameters at 10 Hz while the neural policy outputs normalized motor speeds at 500 Hz during lemniscate tracking.
  • The comparison includes Random parameter perturbations and Regression’s single point estimate, isolating the effect of modeling the latent-to-parameter map as a distribution.
  • CFM produces the lowest motor-command RMSE and highest PCC across all three tracking speeds.
  • 0.032 RMSE and 0.723 PCC: CFM outperforms Regression on the aggressive 5 s trajectory, which records 0.059 RMSE and 0.077 PCC.
  • Distributional decoding preserves both motor-command magnitude and temporal pattern, whereas regression traces oscillate around the policy response.

2) Off-Center Payload Adaptation:

An abrupt off-center payload tests whether decoded parameters can reproduce policy actions after a physical change. CFM achieves the strongest action-prediction result and supports interpreting latents as distributions over dynamically consistent models.

  • The payload is attached during hover, changing effective mass and inertia while introducing a torque bias.
  • CFM decodes parameters online from the measured state and latent history, then evaluates the resulting parametric controller during replay.
  • 0.031 RMSE and 0.812 PCC: CFM achieves the strongest action-prediction result in the 100 g off-center payload experiment.
  • Distributional decoding converts learned control latents into distributions of dynamically consistent physical models rather than single parameter estimates.
  • The decoded distribution supports predictive tuning and robustness analysis around the fixed policy, while remaining sensitive to observation and state-estimation noise.
  • Future active probing would identify weak policy regions by perturbing latents in decoded-model rollouts and feeding decoded weak systems into training.

APPENDIX A PARAMETRIC CONTROLLER

The appendix defines Kθ as a physical-parameterized controller that maps high-level references to normalized rotor-speed commands. Its dynamics and allocation calculations depend explicitly on decoded physical parameters.

  • Kθ maps a high-level reference to rotor-speed commands using inertia-weighted rate feedback and rigid-body thrust/torque allocation.
  • Reference and rate loop: The desired body torque is generated by a proportional rate loop using inertia J, measured body rate ω, and diagonal gains Kω.
  • Thrust/torque allocation: The allocation matrix Balloc(θ) encodes arm length, thrust coefficient, and torque coefficient, together with per-rotor efficiency η.
  • Thrust/torque allocation: Normalized rotor commands are defined as Ωi,norm = Ωi,cmd/Ωmax to match the policy action space.
  • Sampling θ̂ from p(θ | ẑt) produces Kθ̂, the controller evaluated in the experiments.
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