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Adaptive-MHE : A Sampling-Based Adaptive MPC for Legged Loco-Manipulation via Moving Horizon Estimation

Hossein Keshavarz, Alejandro Ramirez-Serrano, Majid Khadiv

arXiv:2609.17832v1cs.RO

TL;DR

Unknown and changing object and terrain parameters, together with the difficulty of applying differentiable-dynamics system identification to contact-rich legged systems, challenge loco-manipulation control. Adaptive-MHE estimates physical parameters online through sampling-based moving horizon estimation and couples those estimates with sampling-based MPC. Simulation and hardware experiments report performance comparable to a ground-truth-parameter controller and better than the baseline.

  • Problem

    Object and terrain parameters can be unknown or change, while classical system identification often assumes differentiable dynamics that contact-rich legged systems do not provide.

    Source: §I · p. 1

  • Method

    Adaptive-MHE samples candidate parameters to match simulated and observed trajectories over a moving horizon, then couples online estimates with sampling-based MPC.

    Source: §I · p. 1, B. SPI · pp. 2–3

  • Results

    In simulation and hardware experiments, Adaptive-MHE performed comparably to the True mode and better than Baseline, with substantially lower final goal error.

    Source: §VI · p. 6

  • Takeaways & Limitations

    The results demonstrate Adaptive-MHE’s potential for robust legged loco-manipulation in unstructured environments.

    Source: §VI · p. 6

Abstract

from arXiv · show

Legged robots have demonstrated a remarkable ability to traverse various terrains, yet generating effective loco-manipulation behaviors remains challenging. A key difficulty is that object and terrain parameters are typically unknown to the robot, and mismatches between these parameters and their simulated counterparts introduce a sim-to-real gap that degrades control performance. Classical system identification (Sys-ID) methods often assume differentiable dynamics, an assumption that does not hold for contact-rich legged systems. Sampling-based Sys-ID avoids this restriction by directly matching simulated and recorded state trajectories through massively parallel rollouts, but existing approaches are typically applied offline and do not adapt as environmental conditions change. We present Adaptive-MHE an online sampling-based Sys-ID framework, based on moving horizon estimation (MHE), that estimates the physical parameters of objects and terrain in the environment (e.g., mass, friction) and couples this estimate with a sampling-based model predictive controller, enabling adaptive loco-manipulation in changing and uncertain environments. In simulation and hardware experiments, our framework consistently outperforms baselines and matches the performance of a controller with access to ground-truth parameters.

I. INTRODUCTION

Loco-manipulation must cope with object and terrain parameters that are unknown and can vary across tasks. Adaptive-MHE estimates these parameters online and couples estimation with sampling-based MPC.

I. INTRODUCTION

  • Unknown and changing object or terrain parameters challenge loco-manipulation, while existing methods often assume accurate prior knowledge or training-time dynamics.Learning-based policies trained over fixed parameter distributions may require retraining or fine-tuning to adapt outside those distributions.Source: §I · p. 1, A. Loco-Manipulation for quadruped… · p. 2
  • Adaptive-MHE estimates unknown interaction parameters from recent observations and couples sampling-based MHE with sampling-based MPC for legged loco-manipulation.The estimates include object mass and inertia and terrain friction; the framework is presented as the first sampling-based adaptive MPC formulation for this setting.Source: §I · p. 1
  • The paper’s contributions include online system identification from interaction data without differentiable simulation or specialized touch or force sensors.Source: §I · p. 1
  • The authors report improved performance under object and terrain uncertainty across simulation and hardware experiments.Source: §I · p. 2

A. Loco-Manipulation for quadruped Robots

B. System Identification and Parameter Adaptation

Prior system-identification methods face difficulties in contact-rich locomotion, while SPI offers sampling-based identification and MPOPI combines sampling strategies for whole-body control.

B. System Identification and Parameter Adaptation

  • Optimization-based system identification often needs dynamics derivatives, and contact-switch methods may rely on precise event detection that limits use in whole-body loco-manipulation.Source: B. System Identification and Parameter… · p. 2
  • SPI [21] uses offline sampling-based identification and was demonstrated for locomotion, whereas Adaptive-MHE estimates object and environment parameters online during loco-manipulation.The paper couples the online estimator with sampling-based MPC to control under unknown and changing object properties.Source: B. System Identification and Parameter… · p. 2

A. MPOPI

  • MPOPI combines MPPI and CMA-ES [23], repeatedly updating sampling mean and covariance via CMA-ES for L cycles to generate improved samples and a refined subset of robot-motion trajectories.Source: A. MPOPI · p. 2

B. SPI

SPI identifies parameters by sampling candidates and matching simulated rollouts to recorded trajectories. Adaptive-MHE extends sampling-based estimation to online interaction data using a moving window.

B. SPI

  • SPI [21] formulates system identification as zero-order optimization with GPU-based parallel sampling, avoiding the need for differentiable dynamics.Source: B. SPI · p. 2
  • SPI segments recorded trajectories into short clips of sampled horizon lengths and estimates parameters by matching multi-step simulated rollouts to the data.The optimization uses CMA-ES to sample candidate parameter vectors in parallel and update the sampling distribution; its objective also regularizes parameters toward a nominal prior.Source: B. SPI · p. 3

IV. PROPOSED LOCOMOTION FRAMEWORK

  • Adaptive-MHE extends SPI to recursively re-estimate object and terrain parameters from interaction data collected during task execution.The framework has a moving-horizon estimator and a whole-body controller operating asynchronously on separate CPU threads.Source: §IV · p. 3

A. Moving Horizon Estimator

  • Unlike SPI’s one-time estimate from the complete recorded history, Adaptive-MHE estimates from a short sliding window of recent interaction data.Robot and box states and robot control inputs are recorded during execution; the window is refreshed periodically as further dynamics information becomes available.Source: A. Moving Horizon Estimator · p. 3
  • The proposed estimator runs on the CPU in a separate thread from the controller, allowing estimation to proceed in the background without interrupting real-time control.Source: A. Moving Horizon Estimator · p. 3

B. Whole-body Controller (MPOPI)

The controller reduces MPOPI’s computational burden by refining its sampling distribution only when the reference gait’s contact mode changes.

B. Whole-body Controller (MPOPI)

  • MPOPI refines its sampling distribution only at contact-mode changes and retains the latest refinement to warm-start subsequent control cycles.This reduces computational burden while preserving sampling-based exploration and exploitation; the controller operates continuously as MHE updates dynamics parameters asynchronously.Source: B. Whole-body Controller (MPOPI) · p. 3

C. Adaptive-MHE Formulation

Adaptive-MHE estimates unknown physical parameters by matching predicted and recorded states over a recent observation window. It updates this estimate through sampling and uses it in the concurrent controller.

C. Adaptive-MHE Formulation

  • The estimator and controller share a parameterized dynamics model, and the controller uses the current parameter estimate to generate and evaluate control sequences.The first action in the optimized sequence is applied to the robot.Source: C. Adaptive-MHE Formulation · pp. 3–4
  • The estimator minimizes weighted state-prediction error over a recent window while regularizing the estimate toward the previous parameter estimate.The regularization weights correspond to mass, inertia, and friction.Source: C. Adaptive-MHE Formulation · p. 4
  • Candidate parameter distributions are initialized around the previous estimate and refined by sampling candidates and updating from their trajectory costs.The update uses log-rank-weighted averaging with learning rate α.Source: C. Adaptive-MHE Formulation · p. 4
  • At each update interval, the estimation window advances and the procedure updates the dynamics model while control continues.The most recent H measurements are used when the parameter-update interval is reached.Source: C. Adaptive-MHE Formulation · p. 4

V. EVALUATION

The evaluation uses a Unitree Go1 and compares Adaptive-MHE with ground-truth and fixed offline beliefs. The framework combines online parameter updates with sampling-based control.

V. EVALUATION

  • The evaluation compares Adaptive-MHE with True, which uses fixed ground-truth parameters, and Baseline, which uses an offline-identified belief that remains fixed.Adaptive-MHE initializes its belief through offline probing, then re-identifies parameters online during task execution.Source: §V · p. 4
  • The evaluation runs on a Unitree Go1 using a ROS-based Python controller in real time on an AMD Ryzen 9 7950X3D CPU with 64 GB of memory.Source: §V · p. 4
  • The control loop samples and parallel-rolls out action sequences under the current estimated dynamics, applies the first optimized action, and stores state-input data for estimation.When an update is triggered, the estimator uses the most recent H measurements and returns an updated parameter estimate.Source: §V · p. 4

A. Task Definitions and setups

Five simulation tasks test pushing under different goals and changing physical conditions. They include both moving the robot while pushing and stationary one-leg manipulation.

T1. Single-goal pushing

T2. Circular-path pushing

T3. Adaptation to mass variation

T4. Adaptation to terrain change

T5. Pushing a box with one leg

B. Ablation and Simulation Study

Across five tasks, Adaptive-MHE nearly matches tracking performance with true parameters, and it improves all reported metrics over the fixed Baseline belief. Hyperparameter defaults are selected for low controller cost while maintaining high success.

Ablation

  • The ablation varies each of seven estimator hyperparameters individually across a small grid, repeating each setting over 15 random seeds.Reported outcomes include mean controller cost and success rate.Source: B. Ablation and Simulation Study · p. 5
  • Hardware defaults are selected for the lowest mean controller cost while maintaining high success, favoring the most conservative setting among comparable configurations.Dashed lines in Fig. 4 mark these defaults.Source: B. Ablation and Simulation Study · p. 5, Figure 4 · p. 6

Simulation Study

C. Real-world demonstration

Real-world tests show Adaptive-MHE adapting to unannounced changes in object mass and surface friction. Across simulation and hardware experiments, it performs better than Baseline and comparably to the ground-truth-parameter True mode.

C. Real-world demonstration

  • The hardware experiments used a Unitree Go1 to push a box or basket toward a goal while object mass or surface friction varied unbeknownst to the policy.The robot ran Adaptive-MHE or Baseline policies.Source: C. Real-world demonstration · p. 6
  • When basket mass rose unexpectedly from 3 kg to 4 kg, Adaptive-MHE re-estimated mass and increased pushing force to reach the target, while Baseline stopped short.The additional 1.0 kg was added mid-push without signaling the policy.Source: C. Real-world demonstration · p. 6
  • Across low-friction concrete and high-friction turf, Adaptive-MHE inferred increased resistance and increased force to reach the target, while Baseline stalled short.Baseline used force calibrated to average friction estimated offline.Source: C. Real-world demonstration · p. 6

VI. CONCLUSIONS

  • Across simulation and hardware experiments, Adaptive-MHE tracked accurately under uncertain object and terrain parameters, performed comparably to True, and outperformed Baseline with substantially lower final goal error.The conclusion identifies this as evidence of potential for robust loco-manipulation in unstructured environments.Source: §VI · p. 6

APPENDIX

Appendix results compare the three control modes across pushing tasks, including circular paths, abrupt mass changes, and single-leg pushing. Adaptive-MHE generally tracks closely to True and outperforms Baseline, though velocity-tracking gains in T4 do not clearly isolate the benefit of friction adaptation.

T2. Circular-path pushing

  • On circular-path pushing, Adaptive-MHE and True tracked the reference path closely, while Baseline drifted; Adaptive-MHE’s cost distribution peaked near zero and Baseline’s was broader and higher-cost.Robot speed tracking also favored Adaptive-MHE and True over Baseline under the continuously changing pushing direction.Source: APPENDIX · p. 7, Figure 6 · p. 7, Figure 7 · p. 7

T3. Adaptation to mass variation

  • After box mass switched from 4 to 6 kg, Adaptive-MHE and True tracked the path closely while Baseline deviated; Adaptive-MHE tracked the true mass and friction coefficient online.The associated cost distributions followed the same pattern.Source: APPENDIX · p. 7, Figure 8 · p. 8, Figure 9 · p. 8

T4

  • For T4, Adaptive-MHE estimated friction more accurately, but its post-switch velocity degradation mirrored a brief estimate re-convergence transient, making the adaptation benefit hard to separate from fixed-parameter control by velocity alone.All modes had comparable pre-switch accuracy, and tracking degraded modestly after the switch.Source: APPENDIX · p. 8, Figure 10 · p. 8

T5. Pushing a box with one leg

  • For a 0.5 m single-leg push, Adaptive-MHE’s final box error was 0.28 m versus True’s 0.12 m and Baseline’s 0.42 m; its zero-velocity RMSE was 0.052 m/s versus True’s 0.051 m/s and Baseline’s 0.149 m/s.Figure 11 shows the final box configuration; Figure 12 shows speed tracking.Source: APPENDIX · p. 8, Figure 11 · p. 8, Figure 12 · p. 8

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