Influence of Radial Basis Activation Functions on Intelligent Controller for Robotic Manipulators

Jul 16, 2026

An intelligent control framework for robotic manipulator trajectory tracking uses radial basis function (RBF) neural networks to estimate and compensate online disturbances. The design fuses model-based nonlinear feedback linearization with an adaptive neural approximator that addresses parametric uncertainty, friction, and unmodeled dynamics. A Lyapunov-based adaptation law with projection ensures bounded closed-loop signals and convergence of tracking error to a compact region. The study analyzes how RBF activation kernels affect transient response, steady-state accuracy, and control smoothness, supported by manipulator experiments.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages8

Reading Time20 min

Introduction

Intelligent Controller

Equations of Motion and Control Formulation

Activation Functions

Experimental Results

Concluding Remarks

arXiv :2607 .02167v1 [ ee ss . SY] 2 Jul 2026 EURODINAME III -An International Symposium on Dynamic Problems of Mechanics June 8-11, 2026-Giens Peninsula, FR EURODINAME-2026-9024036 INFLUENCE OF RADIAL BASIS ACTIVATION FUNCTIONS ON INTELLIGENT CONTROLLER FOR ROBOTIC MANIPULATORS Kimmo Paldanius Gabriel Da Silva Lima Wallace Moreira Bessa Smart Systems Lab, Department of Mechanical Engineering, University of Turku, 20520, Finland. kkpald@utu.fi, gdasil@utu.fi, wmobes@utu.fi Abstract. This paper presents an intelligent control framework for trajectory tracking of robotic manipulators using radial basis function (RBF) neural networks for online disturbance estimation. The proposed control structure combines model based nonlinear control with an adaptive neural approximator that compensates for parametric uncertainties, friction, and unmodeled dynamics. A Lyapunov-based adaptation law with projection guarantees boundedness of the closed-loop signals and convergence of the tracking error to a compact region. The primary objective of this work is to investigate how the choice of activation function within the RBF network influences transient behavior, steady-state accuracy, and control smoothness. The controller is implemented on a robotic manipulator. Experimental results demonstrate that although stability is preserved for all kernels, activation function selection significantly affects adaptation dynamics and practical tracking performance. These findings demonstrate that activation function selection acts as a structural design parameter in intelligent control, directly shaping adaptation dynamics and practical closed-loop performance. Keywords: intelligent control, feedback linearization, radial basis function, neural networks, robotic manipulators 1. INTRODUCTION Trajectory tracking of robotic manipulators is commonly addressed using model-based nonlinear control methods such as feedback linearization (Ccari et al., 2024; Liu et al., 2025) . By exploiting the known system dynamics, these approaches enable systematic cancellation of nonlinearities and precise reference tracking under nominal conditions. In practice, however, accurate tracking can be degraded by parametric uncertainty, friction, unmodeled dynamics, and external disturbances. To mitigate these effects, adaptive and learning-based extensions are often incorporated to enhance robustness while preserving the structure of model-based control (Sveen et al., 2025; Abu-Jassar et al., 2026) . Adaptive control techniques typically address structured parametric uncertainties through online parameter estimation mechanisms, with stability established using tools such as Lyapunov analysis or related adaptive frameworks, thereby ensuring boundedness of the closed-loop signals despite unknown system parameters (Ioannou and Fidan, 2006; Venanzi, 2016; Zhang and Wei, 2017) . In contrast, learning-based approaches, particularly neural-network-based disturbance estimators, aim to approximate unmodeled or unstructured dynamics without requiring explicit parametric representations (Brunke et al., 2022; Zeng et al., 2025) . Owing to their universal approximation capability, neural networks are well suited to compensate for complex nonlinear effects such as friction and residual coupling dynamics. This paper adopts a hybrid perspective that integrates feedback linearization with an online neural disturbance estimator based on radial basis function (RBF) networks. The neural weights are updated through a Lyapunov-based adaptation law, ensuring boundedness of all closed-loop signals and convergence of the tracking error to a neighborhood of the origin while exploiting the approximation capability of neural networks. The primary focus of this work is the influence of the RBF activation (basis) function on closed-loop behavior. Although Lyapunov stability holds for a broad class of bounded activation functions, performance characteristics, such as transien

FAQs

What role do radial basis function (RBF) neural networks play in the proposed controller?

They provide an online disturbance estimation mechanism, with neural weights updated through a Lyapunov-based adaptive law to compensate for uncertainties and unmodeled dynamics.

How is closed-loop stability and tracking performance guaranteed?

A Lyapunov-based adaptation law with projection guarantees boundedness of closed-loop signals and drives the tracking error to converge to a neighborhood of the origin.

Why does the choice of RBF activation function matter?

Although stability is preserved for all considered kernels, kernel selection significantly affects adaptation dynamics and practical tracking performance, including transient behavior, steady-state accuracy, and control smoothness.

Jul 16, 2026

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