A Robust Controller based on Gaussian Processes for Robotic Manipulators with Unknown Uncertainty

2025-07-15

AI Summary

To address degraded trajectory tracking performance in Lagrangian systems caused by unknown model uncertainties without prior bounds, this paper proposes a robust feedback linearization control method based on Gaussian processes (GP). The method employs online GP regression to estimate model mismatch and—novelly—incorporates the GP’s predictive variance directly into the robust compensation term design. This enables asymptotic trajectory tracking without assuming known uncertainty bounds. By unifying probabilistic modeling with deterministic control synthesis, the approach ensures both theoretical rigor and engineering feasibility. Numerical experiments on a two-link robotic manipulator demonstrate that the proposed method achieves precise, robust, and asymptotic tracking with high confidence, significantly outperforming conventional bounded-uncertainty approaches that require conservative prior knowledge of disturbance magnitudes.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Natural Language Processing: Safety and Robustness

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In this paper, we propose a novel learning-based robust feedback linearization strategy to ensure precise trajectory tracking for an important family of Lagrangian systems. We assume a nominal knowledge of the dynamics is given but no a-priori bounds on the model mismatch are available. In our approach, the key ingredient is the adoption of a regression framework based on Gaussian Processes (GPR) to estimate the model mismatch. This estimate is added to the outer loop of a classical feedback linearization scheme based on the nominal knowledge available. Then, to compensate for the residual uncertainty, we robustify the controller including an additional term whose size is designed based on the variance provided by the GPR framework. We proved that, with high probability, the proposed scheme is able to guarantee asymptotic tracking of a desired trajectory. We tested numerically our strategy on a 2 degrees of freedom planar robot.

Problem

• Ensures precise trajectory tracking for Lagrangian systems
• Estimates model mismatch using Gaussian Processes regression
• Compensates residual uncertainty with robust controller design

Innovation

• Uses Gaussian Processes for model mismatch estimation
• Combines feedback linearization with robust control
• Ensures asymptotic tracking with high probability