Nonlinear Robust Control of Coordinated Electrically Driven Robots—An Adaptive Balázs‐Szabados Operators Approach

ABSTRACT Function approximation methods have emerged as powerful mathematical tools in designing compliant motion controllers for collaborative robotic manipulation without requiring exact system models. However, many existing approaches rely on velocity feedback, which is often unavailable or impractical in real‐world scenarios. This paper presents a nonlinear, robust, and regressor‐free adaptive impedance control scheme for multiple electrically actuated manipulators. The proposed method leverages Balázs‐Szabados operators to estimate dynamic uncertainties with low computational overhead. A voltage‐level controller is formulated to incorporate actuator dynamics directly, enhancing the strategy's practical relevance. Furthermore, a simple observer is integrated to eliminate the need for velocity measurements. Lyapunov‐based analysis guarantees that both tracking and estimation errors are Uniformly Ultimately Bounded (UUB) in the presence of model uncertainties, friction forces, and external disturbances. Extensive simulations on a dual‐arm robotic platform manipulating a rigid object demonstrate the proposed controller's superior performance in terms of tracking precision, energy efficiency, and robustness. Specifically, the proposed method reduces ISE and IAE by up to 96.3% and 85.1%, respectively, compared to the fuzzy controller on a simple path, and achieves up to 89.1% ISE improvement on complex trajectories. Compared with other benchmark schemes—including the Fuzzy, Chebyshev Neural Network (CNN), and B‐spline‐based impedance controllers—the Balázs‐Szabados approach achieves up to 14.2% lower ISV than CNN and approximately 11.5% lower ISV than B‐spline across both manipulators, indicating smoother control efforts and reduced actuator workload.