Abstract
It is challenging to accurately judge the actual end position of the manipulator—regarded as a rigid body—due to the influence of micro-deformation. Its precise and efficient control is a crucial problem. To solve the problem, the Hamilton principle was used to establish the partial differential equation (PDE) dynamic model of the manipulator system based on the infinite dimension of the working environment interference and the manipulator space. Hence, it resolves the common overflow instability problem in the micro-deformable manipulator system modeling. Furthermore, an infinite-dimensional radial basis function neural network compensator suitable for the dynamic model was proposed to compensate for boundary and uncertain external interference. Based on this compensation method, a distributed boundary proportional differential control method was designed to improve control accuracy and speed. The effectiveness of the proposed model and method was verified by theoretical analysis, numerical simulation, and experimental verification. The results show that the proposed method can effectively improve the response speed while ensuring accuracy.
Highlights
Dynamic Modeling of Micro-Deformable ManipulatorThe control methods of micro-deformation manipulators were developed based on the ordinary differential equation (ODE) dynamic model in most studies
Differential Control Method of Keywords: micro-deformable manipulator; partial differential equation dynamic model; radial basis function neural network compensator; boundary proportional differential control method
This study completely considered the interference at both ends of the boundary while establishing the partial differential equation (PDE) dynamic model
Summary
The control methods of micro-deformation manipulators were developed based on the ordinary differential equation (ODE) dynamic model in most studies. It cannot accurately describe the distributed parameter characteristics of the micro-deformable structure and may cause overflow instability problems. The Hamilton method was used to derive the PDE dynamic equation of the micro-deformable manipulator system [5,7,9,12]; the corresponding boundary conditions of the system were obtained. The PDE dynamic model of the micro-deformation manipulator system is obtained as Equation (10). The boundary control only needs a small number of thrusters to achieve a better control effect than the discrete distributed control
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