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

The virtual decomposition control (VDC) is an efficient tool suitable to deal with the full-dynamics-based 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.