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Bayesian Optimization for Automatic Tuning of Torque-Level Nonlinear Model Predictive Control

Gabriele Fadini, Deepak Ingole, Tong Duy Son, Alisa Rupenyan

TL;DR

The paper tackles the challenge of tuning high-dimensional parameters in torque-based nonlinear MPC for robotic trajectory tracking. It introduces an automated framework that combines Sparse Axis-Aligned Subspace Bayesian Optimization (SAASBO) with a digital twin of the UR10e, enabling efficient exploration of 12-dimensional MPC parameter space and rapid convergence to high-performance configurations. Simulation results show up to 41.9% improvement in tracking error over baselines, with real-robot validation achieving a 25.8% improvement, demonstrating effective sim-to-real transfer. The work highlights the value of sparsity-aware Bayesian optimization for complex, real-time robotic controllers and points to future work on richer physical modeling to further close the sim-to-real gap.

Abstract

This paper presents an auto-tuning framework for torque-based Nonlinear Model Predictive Control (nMPC), where the MPC serves as a real-time controller for optimal joint torque commands. The MPC parameters, including cost function weights and low-level controller gains, are optimized using high-dimensional Bayesian Optimization (BO) techniques, specifically Sparse Axis-Aligned Subspace (SAASBO) with a digital twin (DT) to achieve precise end-effector trajectory real-time tracking on an UR10e robot arm. The simulation model allows efficient exploration of the high-dimensional parameter space, and it ensures safe transfer to hardware. Our simulation results demonstrate significant improvements in tracking performance (+41.9%) and reduction in solve times (-2.5%) compared to manually-tuned parameters. Moreover, experimental validation on the real robot follows the trend (with a +25.8% improvement), emphasizing the importance of digital twin-enabled automated parameter optimization for robotic operations.

Bayesian Optimization for Automatic Tuning of Torque-Level Nonlinear Model Predictive Control

TL;DR

The paper tackles the challenge of tuning high-dimensional parameters in torque-based nonlinear MPC for robotic trajectory tracking. It introduces an automated framework that combines Sparse Axis-Aligned Subspace Bayesian Optimization (SAASBO) with a digital twin of the UR10e, enabling efficient exploration of 12-dimensional MPC parameter space and rapid convergence to high-performance configurations. Simulation results show up to 41.9% improvement in tracking error over baselines, with real-robot validation achieving a 25.8% improvement, demonstrating effective sim-to-real transfer. The work highlights the value of sparsity-aware Bayesian optimization for complex, real-time robotic controllers and points to future work on richer physical modeling to further close the sim-to-real gap.

Abstract

This paper presents an auto-tuning framework for torque-based Nonlinear Model Predictive Control (nMPC), where the MPC serves as a real-time controller for optimal joint torque commands. The MPC parameters, including cost function weights and low-level controller gains, are optimized using high-dimensional Bayesian Optimization (BO) techniques, specifically Sparse Axis-Aligned Subspace (SAASBO) with a digital twin (DT) to achieve precise end-effector trajectory real-time tracking on an UR10e robot arm. The simulation model allows efficient exploration of the high-dimensional parameter space, and it ensures safe transfer to hardware. Our simulation results demonstrate significant improvements in tracking performance (+41.9%) and reduction in solve times (-2.5%) compared to manually-tuned parameters. Moreover, experimental validation on the real robot follows the trend (with a +25.8% improvement), emphasizing the importance of digital twin-enabled automated parameter optimization for robotic operations.

Paper Structure

This paper contains 20 sections, 12 equations, 7 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Robot Dynamics
  4. Model Predictive Control Solver Description
  5. Motivation for Torque-Level Model Predictive Control
  6. Bayesian Optimization Framework
  7. Automatic Tuning Overview
  8. Implementation Details
  9. Digital Twin for Parameter Optimization
  10. Low-Level Joint Controller
  11. MPC Formulation
  12. Solver Configuration and Real-Time Control
  13. High-dimensional Bayesian Optimization Configuration
  14. Experimental Results
  15. Automatic Tuning Results in Simulation
  16. ...and 5 more sections

Figures (7)

  • Figure 1: UR10e robot executing torque-based MPC leveraging a digital twin for real-time optimization.
  • Figure 2: Overview of the Bayesian Optimization, a digital twin is used to evaluate the MPC.
  • Figure 3: Low-level torque control interface for UR10e robot using RTDE library.
  • Figure 4: Tracking MPC trajectories in task-space.
  • Figure 5: Tracking error trend, the baseline is compared with optimized parameters.
  • ...and 2 more figures