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Adaptive MPC-based quadrupedal robot control under periodic disturbances

Elizaveta Pestova, Ilya Osokin, Danil Belov, Pavel Osinenko

TL;DR

The paper addresses robust quadrupedal locomotion under external disturbances, focusing on periodic disturbances as a gap in existing MPC-based methods. It proposes a lightweight disturbance regressor that decomposes disturbances into stationary and periodic components and integrates this into an adaptive MPC framework, using a convex, discretized model with state augmentation by external forces. Validation in Raisim with a Unitree A1 demonstrates improved reference tracking under periodic disturbances compared with a baseline MPC and static disturbance compensation, using disturbances of the form $d(t)=d_{static}+A\sin(\omega t)$. The approach aims to enable real-time, robust locomotion in dynamic environments, with future work extending to torque disturbances, varying disturbance frequencies, and hardware experiments to close the sim-to-real gap.

Abstract

Recent advancements in adaptive control for reference trajectory tracking enable quadrupedal robots to perform locomotion tasks under challenging conditions. There are methods enabling the estimation of the external disturbances in terms of forces and torques. However, a specific case of disturbances that are periodic was not explicitly tackled in application to quadrupeds. This work is devoted to the estimation of the periodic disturbances with a lightweight regressor using simplified robot dynamics and extracting the disturbance properties in terms of the magnitude and frequency. Experimental evidence suggests performance improvement over the baseline static disturbance compensation. All source files, including simulation setups, code, and calculation scripts, are available on GitHub at https://github.com/aidagroup/quad-periodic-mpc.

Adaptive MPC-based quadrupedal robot control under periodic disturbances

TL;DR

The paper addresses robust quadrupedal locomotion under external disturbances, focusing on periodic disturbances as a gap in existing MPC-based methods. It proposes a lightweight disturbance regressor that decomposes disturbances into stationary and periodic components and integrates this into an adaptive MPC framework, using a convex, discretized model with state augmentation by external forces. Validation in Raisim with a Unitree A1 demonstrates improved reference tracking under periodic disturbances compared with a baseline MPC and static disturbance compensation, using disturbances of the form . The approach aims to enable real-time, robust locomotion in dynamic environments, with future work extending to torque disturbances, varying disturbance frequencies, and hardware experiments to close the sim-to-real gap.

Abstract

Recent advancements in adaptive control for reference trajectory tracking enable quadrupedal robots to perform locomotion tasks under challenging conditions. There are methods enabling the estimation of the external disturbances in terms of forces and torques. However, a specific case of disturbances that are periodic was not explicitly tackled in application to quadrupeds. This work is devoted to the estimation of the periodic disturbances with a lightweight regressor using simplified robot dynamics and extracting the disturbance properties in terms of the magnitude and frequency. Experimental evidence suggests performance improvement over the baseline static disturbance compensation. All source files, including simulation setups, code, and calculation scripts, are available on GitHub at https://github.com/aidagroup/quad-periodic-mpc.
Paper Structure (17 sections, 18 equations, 4 figures, 1 table)

This paper contains 17 sections, 18 equations, 4 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. System Dynamics and Control
  3. Robot Dynamics Model
  4. Floating-Base Dynamics
  5. Equations of Motion
  6. State Representation with External Forces
  7. Model Predictive Control Formulation
  8. System Linearization and Discretization
  9. External Force Estimation
  10. Experimental Setup
  11. Simulation Environment
  12. Testing Scenarios
  13. Performance Metrics
  14. Results and Discussion
  15. Quantitative Results
  16. ...and 2 more sections

Figures (4)

  • Figure 1: A quadrupedal robot under periodic disturbances
  • Figure 2: Block diagram of the adaptive MPC-based control system
  • Figure 3: Simulation setup in Raisim
  • Figure 4: Comparison of commanded (dashed red) and measured linear velocities for different control strategies under a periodic disturbance.