Safety-Aware Controller Optimization for a Flexure-Joint Biaxial Gantry Robot

Controller tuning and optimization remain fundamental challenges in dynamic control of mechatronic and robotic systems. Traditional model-based methods depend heavily on accurate mathematical representations, which are difficult to obtain for complex real-world systems. This limitation motivates learning-based methods, such as Bayesian optimization (BO), which leverage abundant data to enhance control performance. However, applying BO to mechatronic systems often encounters slow convergence and safety issues. This article proposes <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SafeCtrlBO</small>, designed to safely and efficiently optimize multiple controllers simultaneously. <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SafeCtrlBO</small> addresses conventional BO limitations via two key innovations: first, it integrates additive Gaussian kernels in Gaussian processes, significantly improving the efficiency of Gaussian process updates for unknown functions, reducing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">total iterations</i> needed for convergence; second, it simplifies the safe exploration strategy without compromising exploration effectiveness, reducing computational complexity <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">per</i> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">iteration</i>. The method is validated experimentally on a flexure-joint biaxial gantry robot performing circular and cardioid-shaped contouring tasks. Results show that controllers optimized with <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SafeCtrlBO</small> substantially outperform initial controllers, reducing contouring errors by 74.7% and 72.2%, respectively. Our approach consistently surpasses existing BO methods in optimization performance while ensuring safety, demonstrating its practical potential in complex control systems.