FAT-based adaptive sliding control for flexible arms: Theory and experiments

A Regressor-free Adaptive Control for Flexible-joint Robots based on Function Approximation Technique

“…Consider the n-rigid link flexible-joint robot (1) and (2) with unknown parameters D, C, and g then desired transmission torque (14), control input (16) and update law (25) www.intechopen.com (ii) the bound of the tracking error vectors for 0 t t  can be derived as the form of (33), if the Lyapunov-like function candidates are chosen as (23).…”

“…Once it is obtained, we may find that, for most robots, elements in the unknown vector are simple combinations of system parameters such as link mass, link length and moment of inertia, and these are sometimes relatively easy to measure. 13 Huang and Chen 14 proposed an adaptive backstepping-like controller based on FAT [15][16][17][18][19][20][21][22][23][24][25][26][27][28] for single-link flexible-joint robots with mismatched uncertainties. Similar to most backstepping designs, the derivation is too complex to robots with more joints.…”

Function Approximation-based Sliding Mode Adaptive Control for Time-varying Uncertain Nonlinear Systems

“…J. Wu et al, 2007;Fang et al, 2006;Chiang et al, 2007). These research problems are hotspot in the control realm, and some results have been obtained through years of hard work of researchers Chen & Huang, 2005;Huang & Liao, 2006;Liang et al, 2008). These research works adopt a common technique named function approximation technique (FAT) despite of their different design methods.…”

“…Utilizing the FAT, the nonlinear time-varying uncertainty can be transformed into a finite combination of basis functions, and Lyapunov direct method can thus be used to find adaptive laws for updating time-invariant coefficients in the approximating series. Using Fourier series, Huang proposed an adaptive sliding control strategy for a class of nonlinear system with unknown bound time-varying uncertainty satisfying the Dirichlet condition, and further obtained the updating law of coefficients in Fourier series by Lyapunov direct method (Chen & Huang, 2005;Huang & Liao, 2006). The Section 2 proposed a FAT-based adaptive sliding mode control method.…”

Design of a Fat-Based Adaptive Visual Servoing for Robots with Time Varying Uncertainties

“…The unknown camera parameters, kinematics, and dynamics of visual servoing system can be considered as time varying uncertainties and does not need to be linearly parameterized. The function approximation technique (FAT) (Huang and Kuo 2001;Ge et al 2001;Spooner et al 2002;Chien and Huang 2004;Huang and Chen 2004a,b;Huang 2005, 2006;Huang, Wu, and Ting 2006;Huang and Liao 2006;Chien andHuang 2007a,b, 2009) is employed to deal with these uncertainties, which plays an important role in the construction of the update laws. The close loop stability and boundedness of internal signals are proved by using the Lyapunovlike technique with consideration of the approximation error.…”