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

Bayesian Optimization for Automatic Tuning of Torque-Level Nonlinear Model Predictive Control Gabriele Fadini∗⋆, Deepak Ingole∗, Tong Duy Son†, Alisa Rupenyan∗ ∗ZHAW Centre for Artificial Intelligence, Z¨urich University of Applied Sciences, Winterthur, Switzerland † Siemens Digital Industries Software, Leuven, Belgium 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. Index Terms— Torque Control, Nonlinear Model Predictive Control, Trajectory Tracking, Real-Time Control, Bayesian Optimization, Robot Control, Digital Twin. I. INTRODUCTION Torque-based Model Predictive Control (MPC) has emerged as a powerful framework for robot control, enabling the direct selection of joint torques while planning opti- mal control sequences over a receding horizon [1]. Unlike kinematic controllers that rely on cascaded control loops, torque MPC computes optimal torque commands respecting actuator limits and dynamic constraints [2–4]. The practical success of torque MPC depends critically on tuning its many parameters, such as the weights in the optimization problem, solver tolerances, and the low- level controller feedback gains. Each combination creates different trade-offs between tracking accuracy, computational efficiency, and robustness. While MPC provides a solid foun- dation for optimal control, realizing its full potential requires systematic refinement of these parameters [5]. Manual tuning of this high-dimensional space is tedious, often suboptimal, and highly task-dependent. Unlike kinematic control, torque- level MPC enables higher compliance, making it suitable for contact-rich tasks and impedance control [6], but this formu- lation can potentially increase complexity and the chance of ⋆Corresponding Author This work was supported as a part of NCCR Automation, a National Centre of Competence in Research, funded by the Swiss National Science Foundation (grant number 51NF40 225155). {fadi,inge,rupn}@zhaw.ch, son.tong@siemens.com Fig. 1: UR10e robot executing torque-based MPC leveraging a digital twin for real-time optimization. system modeling error. Hence, torque-level MPC requires accurate dynamics modeling to ensure successful sim-to- real transfer [7]. We address this challenge by leveraging a system’s digital twin for safe MPC parameter exploration (Fig. 1), combined with automated tuning methods [8–10]. Recent advances in Bayesian Optimization (BO) provide promising avenues for automated parameter tuning [5, 11– 13]. In particular, Sparse Axis-Aligned Subspace Bayesian Optimization (SAASBO) [14, 15] has shown remarkable performance in high-dimensional problems (hundreds of parameters) by exploiting low-dimensional structure, making it well-suited for robotic applications. This paper’s contributions are the following: • Implementation of a torque-level nMPC interfaced with an extensible digital twin of the UR10e robot arm. • Automated parameter optimization framework using high-dimensional Bayesian Optimization to balance real-time execution and control performance. • Comprehensive testing demonstrating improvement over baselines in simulation and the real system. II. PROBLEM FORMULATION A. Robot Dynamics Building upon prior force control methodologies [16, 17], we augment the classical MPC formulation with an explicit model of the robot’s actuation dynamics. We consider a robot manipulator operating under torque control, where the control input u ∈Rnu consists of joint torque commands and nu is the number of joints. The state of the robot is represented by x = [q; v] ∈Rnq+nv, where the joint arXiv:2512.03772v1 [cs.RO] 3 Dec 2025 positions q ∈Rnq and velocities v ∈Rnv. The robot dynamics follow the standard manipulator equation: M(q) ˙v + C(q, v)v + g(q) = u, (1) where M(q) ∈Rnv×nv is the joint inertia matrix, C(q, v) represents Coriolis and centrifugal terms, g(q) is the gravity vector, and u are the applied joint torques. B. Model Predictive Control Solver Description We formulate the torque-based MPC optimal control prob- lem at each time step t

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