A Passivity-Based Regressor-Free Adaptive Controller for Robot Manipulators With Combined Regressor/Parameter Estimation

2018 ◽  
Author(s):  
Donald Ebeigbe ◽  
Dan Simon
Keyword(s):  
Function Approximation ◽  
Equations Of Motion ◽  
Adaptive Controller ◽  
Dynamics Simulation ◽  
Approximation Technique ◽  
Simultaneous Estimation ◽  
Robot Dynamics ◽  
Gravity Vector ◽  
Inertia Matrix ◽  
Function Approximation Technique

This paper develops a new function approximation technique (FAT)-based adaptive controller for the control of rigid robots called the adaptive passivity function approximation technique (APFAT) controller. This controller utilizes the passivity-based approach and simplifies the FAT controller design by eliminating the need for simultaneous estimation of the robot’s inertia matrix, Coriolis matrix, and gravity vector. The controller achieves its simplicity by treating the product of the regressor matrix and parameter vector as an unknown time-varying function to be approximated. The controller can be implemented in robots where the dynamic equations of motion are unknown. The stability of the controller is verified with Lyapunov functions by taking advantage of the passivity property of the robot dynamics. Simulation results on a three degree-of-freedom (DOF) PUMA500 robot demonstrate the ability to track reference trajectories using reasonable control signals when the inertia matrix, Coriolis matrix, and gravity vector are unavailable.

A FAT-based adaptive controller for robot manipulators without regressor matrix: theory and experiments

Robotica ◽  
2005 ◽  
Vol 24 (2) ◽  
pp. 205-210 ◽  
Author(s):  
An-Chyau Huang ◽  
Shi-Chang Wu ◽  
Wen-Fa Ting
Keyword(s):  
Function Approximation ◽  
Matrix Theory ◽  
Robot Manipulator ◽  
Nonlinear Differential Equations ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Approximation Technique ◽  
Control Scheme ◽  
Approximation Errors ◽  
Theory And Experiments

In this paper, an adaptive control scheme is proposed for an n-link rigid robot manipulator without using the regressor. The robot is firstly modeled as a set of second-order nonlinear differential equations with the assumption that all of the matrices in that model are unavailable. Since these matrices are time-varying and their variation bounds are not given, traditional adaptive or robust designs do not apply. The function approximation technique (FAT) is used here to represent uncertainties in some finite linear combinations of orthonormal basis. The dynamics of the output tracking can thus be proved to be a stable first order filter driven by function approximation errors. Using the Lyapunov stability theory, a set of update laws is derived to give closed loop stability with proper tracking performance. Experiments are also performed on a 2-D robot to test the efficacy of the proposed scheme.

Position and Attitude Control of Underactuated Drones Using the Adaptive Function Approximation Technique

2020 ◽  
Author(s):  
Azin Shamshirgaran ◽  
Donald Ebeigbe ◽  
Dan Simon
Keyword(s):  
Disturbance Rejection ◽  
Function Approximation ◽  
Control Method ◽  
System Stability ◽  
Linear Feedback ◽  
Approximation Technique ◽  
Adaptive Function ◽  
Edge Tracking ◽  
Highly Nonlinear ◽  
Function Approximation Technique

Abstract Despite the popularity of drones and their relatively simple operation, the underlying control algorithms can be difficult to design due to the drones’ underactuation and highly nonlinear properties. This paper focuses on position and orientation control of drones to address challenges such as path and edge tracking, and disturbance rejection. The adaptive function approximation technique control method is used to control an underactuated and nonlinear drone. The controller utilizes reference attitude signals, that are derived from a proportional derivative (PD) linear feedback control methodology. To avoid analytic expressions for the reference attitude velocities, we employ a continuous-time Kalman filter based on a model of the measurement signal — which is derived by passing the reference attitude position through a low-pass signal differentiator — as a second-order Newtonian system. Stability of the closed loop system is proven using a Lyapunov function. Our design methodology simplifies the control process by requiring only a few tuning variables, while being robust to time-varying and time-invariant uncertainties with unknown variation bounds, and avoids the requirement for the knowledge of the dynamic equation that governs the attitude of the drone. Three different scenarios are simulated and our control method shows better accuracy than the proportional-derivative controller in terms of edge tracking and disturbance rejection.

Adaptive Multiple-surface Sliding Control of Hydraulic Active Suspension Systems Based on the Function Approximation Technique

2005 ◽  
Vol 11 (5) ◽  
pp. 685-706 ◽  
Author(s):  
P. C. Chen ◽  
A. C. Huang
Keyword(s):  
Function Approximation ◽  
Ride Quality ◽  
Approximation Technique ◽  
Hydraulic Actuator ◽  
Tracking Errors ◽  
Suspension Systems ◽  
Car Suspension ◽  
Mismatched Uncertainties ◽  
Adaptive Laws ◽  
Function Approximation Technique

In this paper we propose an adaptive multiple-surface sliding controller (AMSSC) to control a non-autonomous quarter-car suspension system with hydraulic actuator. Due to the spring nonlinearities, the system property becomes asymmetric under the system’s own weight. Besides, because precise parameters of practical systems are hard to obtain, the system uncertainties should be dealt with. In this paper, these uncertainties are assumed to be lumped into three unknown functions such that the system model has both matched and mismatched uncertainties. Because the bounds of some of time-varying uncertainties are unavailable, traditional adaptive schemes or robust strategies are infeasible. To deal with this problem, a function approximation based adaptive multiple-surface sliding controller (AMSSC) is proposed in this paper. The multiple-surface sliding controller (MSSC) is used to cope with mismatched uncertainties while the function approximation technique is used to represent those uncertainties as finite combinations of basis functions. Adaptive laws for the approximating series can thus be derived based on the Lyapunov-like approach to ensure the closed-loop stability. Convergent performance of tracking errors can be obtained to improve the ride quality. Because the state measurements of the unsprung mass are lumped into the uncertainties, there is no need to feed back these signals with the proposed method. Therefore, the hardware structure can be simplified in the actual implementation. Computer simulations are performed to verify the effectiveness of the proposed strategy.

A regressor-free adaptive controller for robot manipulators without Slotine and Li's modification

Robotica ◽  
2013 ◽  
Vol 31 (7) ◽  
pp. 1051-1058 ◽  
Author(s):  
Chen-Yu Kai ◽  
An-Chyau Huang
Keyword(s):  
Function Approximation ◽  
Closed Loop ◽  
Controller Design ◽  
Robot Manipulators ◽  
Adaptive Controller ◽  
Approximation Technique ◽  
Simple Method ◽  
Acceleration Vector ◽  
Acceleration Feedback ◽  
Joint Acceleration

SUMMARYSimilar to the traditional adaptive strategies for robot manipulators, the regressor-free adaptive controller design also requires applying Slotine and Li's modification to avoid the feedback of joint accelerations. In this paper, a simple method is proposed to construct a regressor-free adaptive controller for robot manipulators without Slotine and Li's modification. In the new design, the joint acceleration vector is lumped into an unknown time-varying function and the function approximation technique is utilized to cover its effect; therefore, its implementation is free from joint acceleration feedback. The closed-loop stability and boundedness of internal signals are justified by the Lyapunov-like technique. Both simulation and experimental results for a two-link robot are presented to show the effectiveness of the proposed design.

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