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Robustifying Model-Based Locomotion by Zero-order Stochastic Nonlinear Model Predictive Control with Guard Saltation Matrix

Sotaro Katayama, Noriaki Takasugi, Mitsuhisa Kaneko, Norio Nagatsuka, and Masaya Kinoshita

TL;DR

This paper presents a stochastic/robust nonlinear model predictive control to enhance the robustness of model-based legged locomotion against contact uncertainties and achieves fast stochastic/robust NMPC computation by utilizing the zero-order algorithm with additional improvements in computational efficiency concerning the feedback gains.

Abstract

This paper presents a stochastic/robust nonlinear model predictive control (NMPC) to enhance the robustness of model-based legged locomotion against contact uncertainties. We integrate the contact uncertainties into the covariance propagation of stochastic/robust NMPC framework by leveraging the guard saltation matrix and an extended Kalman filter-like covariance update. We achieve fast stochastic/robust NMPC computation by utilizing the zero-order algorithm with additional improvements in computational efficiency concerning the feedback gains. We conducted numerical experiments and demonstrate that the proposed method can accurately forecast future state covariance and generate trajectories that satisfies constraints even in the presence of the contact uncertainties. Hardware experiments on the perceptive locomotion of a wheeled-legged robot were also carried out, validating the feasibility of the proposed method in a real-world system with limited on-board computation.

Robustifying Model-Based Locomotion by Zero-order Stochastic Nonlinear Model Predictive Control with Guard Saltation Matrix

TL;DR

This paper presents a stochastic/robust nonlinear model predictive control to enhance the robustness of model-based legged locomotion against contact uncertainties and achieves fast stochastic/robust NMPC computation by utilizing the zero-order algorithm with additional improvements in computational efficiency concerning the feedback gains.

Abstract

This paper presents a stochastic/robust nonlinear model predictive control (NMPC) to enhance the robustness of model-based legged locomotion against contact uncertainties. We integrate the contact uncertainties into the covariance propagation of stochastic/robust NMPC framework by leveraging the guard saltation matrix and an extended Kalman filter-like covariance update. We achieve fast stochastic/robust NMPC computation by utilizing the zero-order algorithm with additional improvements in computational efficiency concerning the feedback gains. We conducted numerical experiments and demonstrate that the proposed method can accurately forecast future state covariance and generate trajectories that satisfies constraints even in the presence of the contact uncertainties. Hardware experiments on the perceptive locomotion of a wheeled-legged robot were also carried out, validating the feasibility of the proposed method in a real-world system with limited on-board computation.
Paper Structure (20 sections, 21 equations, 14 figures, 1 algorithm)

This paper contains 20 sections, 21 equations, 14 figures, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Related Works
  3. Contribution
  4. HYBRID SYSTEM AND GUARD SALTATION MATRIX
  5. STOCHASTIC/ROBUST MODEL PREDICTIVE CONTROL WITH SALTATION MATRIX
  6. Problem Settings
  7. Covariance Propagation Between a Contact Event
  8. A priori covariance update using Guard Saltation Matrices
  9. A posteriori covariance update using output-feedback MPC
  10. Stochastic/Robust Optimal Control Problem
  11. EFFICIENT STOCHASTIC/ROBUST MODEL PREDICTIVE CONTROL ALGORITHM
  12. Zero-Order Algorithm for Covariance Propagation
  13. Interior Point Method and Feedback Gain
  14. Algorithm Summary
  15. EXPERIMENTS
  16. ...and 5 more sections

Figures (14)

  • Figure 1: Simulations utilizing the proposed stochastic nonlinear model predictive control. Top row: Tachyon 3, a six-telescopic-wheeled-legged robot, ascends stairs under terrain height estimation errors. Bottom row: EVAL-03, a miniature humanoid robot, traverses a rough terrain area.
  • Figure 2: Discretization of the optimal control problem.
  • Figure 3: A priori and a posteriori covariance updates (\ref{['eq:multipleJumpCovarianceEquation']})--(\ref{['eq:outputCovarianceEquation_P']})
  • Figure 4: A priori covariance update (\ref{['eq:multipleJumpCovarianceEquation']})
  • Figure 5: Dynamics-based covariance update (\ref{['eq:constantJumpCovariance']})
  • ...and 9 more figures