Modelling and Operator-Based Nonlinear Control for a Miniature Pneumatic Bending Rubber Actuator Considering Bellows

Abstract

Abstract:Recently, many kinds of soft actuators composed of flexible materials, such as silicon rubber, have been studied in the mechatronics field with increasing attention on the artificial muscle in welfare, medical care and biotechnology. Particularly, pneumatic-driven soft actuator moves flexibly and works safely because of not electrical but pneumatic input, so that the actuator could perform effectively in the medical operations. A miniature pneumatic bending rubber actuator is a tiny pneumatic-driven soft actuator which has some chambers connected to only one tube providing compressed air and the chamber has bellows. This actuator can bend circularly in two directions and grab delicate objects such as fish eggs, by inputting pressure into its chambers. The actuator, however, has nonlinear property derived from elastomer in input-output relation. The actuator, therefore, sacrifices some degree of control performance instead of obtaining the passive flexibility to delicate objects. To solve the above problem, previous studies have shown, by the experiments, that the effectiveness of designing the nonlinear feedback control system using robust right coprime factorization based on the operator theory for control of the output angle of the actuator. However, the mathematical model used for designing the system caused modelling error because the bellows were not considered in deriving the model. The mathematical model should fit experimental value as well as possible for system design and there has been no example modelling of the micro hand having bellows. In this research, a new model of the micro hand considering its bellows with elastomer property is proposed. Moreover, a control system using the robust right coprime factorization based on the operator theory is designed for the new model. Finally, the effectiveness is shown in the experiment.

Operator-Based Nonlinear Control for a Miniature Flexible Actuator Using the Funnel Control Method

“…In addition, the elasticity of the bellowed structure is greater than that of fiber-reinforced rubber; therefore, it can be bent more greatly than the fiber-reinforced rubber actuator [12]. Figure 2 shows the bending motion of the actuator [13]. When positive pressure is applied, the bellows side tends to expand, and the flat side does not expand easily; therefore, the actuator bends with its bellows outside (at 60 kPa in Figure 2).…”

“…The model of the actuator has been proposed for controlling the position of the tip (see details in [13]). As shown in Figure 3, it is supposed that the actuator curves in an arc [13]. Additionally, the bending angle θ ∈ [0, 2π], the curvature radius R, and the length of the actuator L are defined.…”

“…The relationship between the input air pressure p and the bending angle θ has been derived from the balance of moments working on bellows by applying neo-Hookean law, which gives the strain-stress property of a single-strand of rubber [13]. The strain-stress property helps modeling to include the nonlinear elasticity of the actuator more exactly than that by Hooke's law.…”

“…The model of the actuator is, however, complicated due to the nonlinearity of silicone rubber, and a classical control theory is difficult to apply. To solve this problem, a control system has been proposed using robust right coprime factorization based on operator theory [13][14][15][16]. Operator theory [17][18][19][20][21] can guarantee the robust stability of the system with uncertainty.…”

Modeling and System Integration for a Thin Pneumatic Rubber 3-DOF Actuator

“…Pneumatic soft actuators mainly have a structure of tubes and balloons which show expanding and bending motions under air pressure. For example, there are McKibben pneumatic artificial muscle [1], a flexible micro actuator [2] and a miniature pneumatic bending rubber actuator [3][4][5].…”