Function approximation technique-based adaptive virtual decomposition control for a serial-chain manipulator

Abstract

The virtual decomposition control (VDC) is an efficient tool suitable to deal with the full-dynamicsbased control problem of complex robots. However, the regressor-based adaptive control used by VDC to control every subsystem and to estimate the unknown parameters demands specific knowledge about the system physics. Therefore, in this paper, we focus on reorganizing the equation of the VDC for a serial chain manipulator using the adaptive function approximation technique (FAT) without needing specific system physics. The dynamic matrices of the dynamic equation of every subsystem (e.g. link and joint) are approximated by orthogonal functions due to the minimum approximation errors produced. The control, the virtual stability of every subsystem and the stability of the entire robotic system are proved in this work. Then the computational complexity of the FAT is compared with the regressor-based approach. Despite the apparent advantage of the FAT in avoiding the regressor matrix, its computational complexity can result in difficulties in the implementation because of the representation of the dynamic matrices of the link subsystem by two large sparse matrices. In effect, the FAT-based adaptive VDC requires further work for improving the representation of the dynamic matrices of the target subsystem. Two case studies are simulated by Matlab/Simulink: a 2-R manipulator and a 6-DOF planar biped robot for verification purposes.

Adaptive coordinated control of multi-mobile manipulator systems

“…o F ∈ R 6 is the vector of forces applied on the object, M o ∈ R 6×6 is the mass matrix, C o ∈ R 6×6 represents the centrifugal and Coriolis matrix and G o ∈ R 6 is the vector of gravity, Y o ∈ R 6×13 is the dynamic regressor matrix, and θ o ∈ R 13 is known parameter vector, defined in Zhu et al (1997), Al-Shuka et al (2014) andZhu, W-H. (2010).…”

“…The control equation of the j th rigid body of the i th manipulator (10), based on its required velocity and its estimated parameters, is given in linear form by the following equation: The vector of resulting forces/moments acting on the j th rigid body is given by an iterative process (Al-Shuka et al, 2014).…”

“…The global stability of the system using the VDC approach is proven through the virtual stability of each subsystem (Brahmi et al, 2016;Al-Shuka et al, 2014).…”

“…Based on the preceding observations, in this paper, we intend to extend the work proposed in Brahmi et al (2016) by using the adaptive decentralised control of a single MMR based on virtual decomposition control (VDC) (Zhu et al, 1997;Al-Shuka et al, 2014;Zhu, 2010;Luna et al, 2015) originally designed for fixed-base robotic systems with high degrees of freedom. Furthermore, diverging from what is seen in the available works in the literature, we propose an adaptive coordinated control based on the VDC approach.…”

“…An object is a rigid body and an open chain consists of a series of rigid links connected one-by-one by a hinge, and having a certain degree of freedom. The dynamic coupling between the subsystems can be represented by the flow of virtual power (FVP) at the cutting point; this is the principle of virtual work (Zhu et al, 1997;Al-Shuka et al, 2014;Zhu, 2010). The decomposition is illustrated in Figure 2 as follows: Figure 2 Virtual decomposition of the robotic system (see online version for colours)…”