Tackling Sim-to-Real Mismatch Through Sampling-Based Disturbance Observers: From Analytical Models to Learned World Models

• Unmeasured disturbances and model discrepancies can degrade tracking and closed-loop stability, while classical DOB formulations estimate them using explicit plant or low-dimensional state-space models.Sampling-based MPC instead evaluates candidate action sequences through rollouts and scalar trajectory costs.Source: §1 · p. 1
• Modern rollout and cost-query interfaces can lack an invertible plant representation or a defined input-equivalent disturbance channel, exposing mismatch through feedback-state deviations or changing costs at queried states.Such effects may become observable after contact, perception updates, or obstacle motion.Source: §1 · p. 1
• SDOB estimates deployment mismatch from feedback for analytical models, simulators, and learned predictors accessed through rollouts or cost queries.Its state channel fits feedback transitions to a task-defined disturbance parameterization, while its cost channel models local transport of environment-dependent costs; it targets locally persistent, task-relevant mismatch rather than complete gap identification.Source: §1 · pp. 1–2
• SDOB estimates both disturbance channels online and incorporates them into future state propagation and cost evaluation without plant inversion or model retraining.The paper validates the framework across diverse simulation environments and real-robot platforms, including analytical-model compensation, navigation, and learned-world-model planning.Source: §1 · p. 2

2 Related Work

• Classical DOB estimates input disturbances from nominal plants, while the broader related work connects DOB, MPC, dynamic-environment estimation, sim-to-real adaptation, and world models.The review identifies explicit plant models and predefined disturbance channels as assumptions that are difficult to retain with image, latent-state, or rollout-distribution interfaces.Source: §2 · p. 2, §2.1 · p. 2

2.1 DOB-Based Control

• Classical DOB, ADRC, and ESO methods estimate disturbances or lumped uncertainty, but many formulations assume an explicit plant model and predefined disturbance channel.DOB-enhanced predictive control incorporates disturbance estimates into prediction and optimization (Yang et al. 2015).Source: §2.1 · p. 2

2.2 Sampling-Based MPC

• Sampling-based MPC ranks, weights, or refits candidate action sequences using forward rollouts and trajectory costs, making it suitable for nonlinear, nonsmooth, and black-box models.Related robust variants include Tube-MPPI, RMPPI, parameter-uncertainty path integral control, and Shield-MPPI.Source: §2.2 · p. 2

2.3 Dynamic Environment Estimation and Cost Prediction

• Dynamic-environment methods estimate occupancy, motion, or trajectory costs, while treating cost changes at fixed query states as a distinct disturbance channel receives less emphasis.Examples include dynamic occupancy grids, Occupancy Flow Fields, ImplicitO, neural motion planners, and QuAD.Source: §2.3 · p. 2

2.4 Sim-to-Real Adaptation

• Sim-to-real adaptation changes training distributions, system models, or representations, but remains tied to variations represented during training or adaptation.Greater simulator fidelity does not guarantee that method rankings or task outcomes transfer to hardware (Kadian et al. 2020).Source: §2.4 · pp. 2–3

2.5 World Models for Prediction and Planning

• World models learn action-conditioned representations for imagined futures, but nominal replanning does not usually preserve recurring execution mismatch as an explicit disturbance.Actuator bias, contact mismatch, object drift, and environmental change can therefore reappear as rollout error at each control cycle.Source: §2.5 · p. 3

3.1 Disturbance Observer

• The classical formulation considers an unknown disturbance entering through the same channel as the control input and uses a nominal plant model for estimation.The nominal inverse maps measured output to an input-equivalent quantity, compared with applied input and filtered before compensation.Source: §3.1 · p. 3
• A stable low-pass filter processes the disturbance estimate, which is applied against the baseline controller output to form the compensated input.The baseline output is the controller output before disturbance compensation.Source: §3.1 · p. 3
• In the discrete-time integrator example, the one-step prediction error equals the disturbance when the nominal model is exact and measurement noise is ignored.The residual is filtered, and the observer uses the filtered prediction error to compensate for disturbance in the next control step.Source: §3.1 · p. 3

4 Sampling-Based Disturbance Observer

• SDOB extends classical disturbance observation to rollout- or cost-query models, using the mismatch between a model query and subsequent feedback to estimate a correction.Its estimates target locally persistent, task-relevant mismatch rather than complete identification of the sim-to-real gap.Source: §4 · p. 3

4.1 Model and Forward Equations

• The rollout interface evaluates candidate state-effect disturbances, while cost queries evaluate the same task-mapped query state in the current perceived environment.The selected disturbance-enabled rollout interface determines which state-side effects can be estimated.Source: §4.1 · p. 4

4.2 Two Disturbance Channels

• State-effect disturbances change feedback states; cost disturbances change costs at fixed query states as the perceived environment changes.SDOB requires repeatable rollouts or comparable cost queries, observable disturbance coordinates, and slowly varying disturbances; cost transport additionally assumes local changes are approximated by short-horizon transport.Source: §4.2 · pp. 4–5

4.3 State-Effect Disturbance Estimation

• For sampled or black-box rollouts, SDOB scores candidate state disturbances by feedback-transition mismatch and regularization, then uses their loss-weighted mean as the estimate.Physical-constraint violations can also be penalized; the weighted mean is a practical estimate and need not minimize the fitting objective.Source: §4.3 · p. 5

4.4 Cost Disturbance Estimation

• The cost channel estimates local cost-field motion from before-and-after queries, then backtraces future query states to predict costs without modeling obstacle motion.It uses neighborhood matching and velocity regularization; this can retain task-relevant information without reconstructing the environment or tracking every object.Source: §4.4 · pp. 5–7

4.5 Using SDOB in Control

• In control, the state estimate modifies subsequent rollouts and the cost estimate modifies horizon query costs, while other constraints, goal error, and input smoothness remain separate objective terms.The cost-channel estimate is held fixed over the prediction horizon, and cost motion may be unidentifiable in constant-cost regions or ambiguous along straight obstacle boundaries.Source: §4.5 · p. 7, §4.4 · p. 7

5.1 Simulation Results

• Under a shared sinusoidal torque disturbance, MPPI+SDOB and MPPI+DOB succeeded in all 20 trials, and SDOB reduced disturbance-estimation RMSE from 0.018 to 0.014.Uncompensated MPPI failed in all trials; RMPPI had smaller tail error but more than twice MPPI+SDOB’s P95 planning time.Source: §5.1 · p. 8, Table 2 · p. 9
• All 20 navigation trials succeeded with MPPI+SDOB and RMPPI, while MPPI, MPPI+DOB, and Tube-MPPI collided in every trial; SDOB had a shorter mean path ratio than RMPPI.The task combined a constant input bias with moving obstacles that changed queried costs.Source: §5.1 · p. 8, Table 3 · p. 9
• 19/20 nominally solvable Reacher tasks met the success criterion with MPPI+SDOB under hidden action bias, versus 0.427, 0.185, and 0.176 rad mean tail errors for MPPI, Tube-MPPI, and RMPPI.The 20 tasks were selected because disturbance-free MPPI already achieved a final-20-step mean error no greater than 0.025 rad.Source: §5.1 · pp. 9–10, Table 4 · p. 10
• 7.38 pixels was MPPI+SDOB’s mean touchdown center error, versus 20.49 for MPPI, 14.54 for Tube-MPPI, and 16.61 for RMPPI; all methods reached the deck in 20/20 trials.The task included an unknown horizontal input bias and deck speed at 1.6 times nominal.Source: Table 5 · p. 10, §5.1 · p. 11
• 19/20 Rocket Collect trials succeeded without collisions with MPPI+SDOB, compared with 16/20 for MPPI and Tube-MPPI and 15/20 for RMPPI.Asteroid speed was increased to 1.5 times nominal; control variation was slightly higher than MPPI, while planning time remained comparable.Source: Table 5 · p. 10, §5.1 · pp. 10–11

5.2 Experimental Results

• Across 20 paired PointWorld lifting trials, initial-feedback-calibrated MPPI+SDOB achieved a lower mean final task RMSE than the uncorrected planner.The frozen predictor was too slow for real-time replanning, so the single plan used an initial 50 mm lift for calibration and execution had no replanning or observer updates.Source: Table 7 · p. 12, §5.2 · p. 12
• In representative real-robot demonstrations, MPPI+SDOB completed the car’s shortest route in 9.29 s and began dual-arm obstacle avoidance earlier, avoiding collisions that occurred in comparison runs.The car study inferred cost-field motion from temporal cost queries without separate person detection; the arm study lacked independent velocity or future-trajectory measurements.Source: §5.2 · pp. 11–12

• Simulation and robot studies demonstrated improved task performance across analytical models, simulators, and learned world models.Source: §6 · p. 12
• The state channel estimates corrections to predicted motion, while the cost channel estimates local changes in the cost field.Source: §6 · p. 12
• World-model demonstrations remain limited to relatively simple tasks because repeated planning and disturbance-estimation evaluations add computational burden, and latent representations are difficult to interpret physically.Source: §6 · p. 12