A New Adaptive RISE Feedforward Approach based on Associative Memory Neural Networks for the Control of PKMs
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A New Adaptive RISE Feedforward Approach based on Associative Memory Neural Networks for the Control of PKMs 1 · Hipolito ´ ´ Jonatan Mart´ın Escorcia-Hernandez Aguilar-Sierra2 · Omar Aguilar-Mejia3 · Ahmed Chemori4 · 1 ˜ Jose´ Humberto Arroyo-Nu´ nez
Received: 9 December 2019 / Accepted: 29 July 2020 © Springer Nature B.V. 2020
Abstract In this paper, a RISE (Robust Integral of the Sign Error) controller with adaptive feedforward compensation terms based on Associative Memory Neural Network (AMNN) type B-Spline is proposed to regulate the positioning of a Delta Parallel Robot (DPR) with three degrees of freedom. Parallel Kinematic Manipulators (PKMs) are highly nonlinear systems, so the design of a suitable control scheme represents a significant challenge given that these kinds of systems are continually dealing with parametric and non-parametric uncertainties and external disturbances. The main contribution of this work is the design of an adaptive feedforward compensation term using B-Spline Neural Networks (BSNNs). They make an on-line approximation of the DPR dynamics and integrates it into the control loop. The BSNNs’ functions are bounded according to the extreme values of the desired joint space trajectories that are the BSNNs’ inputs, and their weights are on-line adjusted by gradient descend rules. In order to evaluate the effectiveness of the proposed control scheme with respect to the standard RISE controller, numerical simulations for different case studies under different scenarios were performed. Keywords Delta parallel robot · RISE control · B-spline neural network · Trajectory tracking · On-line learning
1 Introduction PKMs have gained significant interest in recent decades thanks to their desired features provided by their construction based on several closed-loop kinematic chains [1]. This configuration provides some advantages to PKMs over their serial counterparts. For instance, the overall stiffness in PKMs is higher than concerning serial manipulators owing to several limbs joined to a fixed base to support the traveling plate where the end-effector is located, generating more resistance against the deflections caused by external forces or moments exerted on the end-effector [2]. Besides, this arrangement allows to PKMs to obtain absolute greater accuracy, better repeatability, more capacity to carry heavier loads, and the ability to execute faster and more precise movements [3]. These features make PKMs attractive solutions for tasks that require high positioning accuracy and precision, and for these reasons are widely used in product transportation and classification tasks, haptic devices, Hip´olito Aguilar-Sierra
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agricultural applications, machine tools, laser cutting, 3D printers, among others [4], [5], [6]. One of the most studied PKM in the literature is the DPR developed in the 80’s by Reymond Clavel. [7]. The main distinction of the DPR other existing PKMs concepts is the use of
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