Singularity-Free Quaternion Representation to Control a UGV-UAV Formation Performing Trajectory-Tracking Tasks

In this paper, a systematic procedure for controller design is proposed for a class of nonlinear underactuated systems (UAS), which are non-feedback linearizable but exhibit a controllable (flat) tangent linearization around an equilibrium point. Linear extended state observer (LESO)-based active disturbance rejection control (ADRC) is shown to allow for trajectory tracking tasks involving significantly far excursions from the equilibrium point. This is due to local approximate estimation and compensation of the nonlinearities neglected by the linearization process. The approach is typically robust with respect to other endogenous and exogenous uncertainties and disturbances. The flatness of the tangent model provides a unique structural property that results in an advantageous low-order cascade decomposition of the LESO design, vastly improving the attenuation of noisy and peaking components found in the traditional full order, high gain, observer design. The popular ball and beam system (BBS) is taken as an application example. Experimental results show the effectiveness of the proposed approach in stabilization, as well as in perturbed trajectory tracking tasks.

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Control PI difuso de un sistema de levitación magnética mediante un sistema embebido

Ingeniería Investigación y Tecnología ◽

10.22201/fi.25940732e.2019.20n4.043 ◽

2019 ◽

Vol 20 (4) ◽

pp. 1-11

Author(s):

Yair Lozano Hernández ◽

Oscar Octavio Gutiérrez Frías ◽

Mario Villafuerte Bante

Keyword(s):

Mathematical Model ◽

Trajectory Tracking ◽

Magnetic Levitation ◽

Magnetic Bearing ◽

Control Action ◽

Tracking Tasks ◽

Control Scheme ◽

Levitation System ◽

Non Linear ◽

Magnetic Levitation System

In the present work, the design and implementation of a control scheme is presented. The aim of the control scheme is to perform regulation and trajectory tracking tasks in the position of a magnetic levitation system, which acts by electromagnetic repulsion. Such levitation system consists of a beam operated by an active magnetic bearing in pendular configuration. Although the Proportional Integral Derivative (PID) controller shows arithmetic simplicity, ease of use, high robustness and error equal to zero in stable state (Pal & Mudi, 2008), the magnetic levitation system mathematical model is highly non-linear and is subject to uncertainty or variation of its parameters. Therefore, the PID control does not guarantee the fulfillment of trajectory tracking tasks (Precup & Hellendoorn, 2011). In summary, a diffuse PI is used due to the system non-linear dynamics and the hysteresis present in the electromagnet. The controller design was made with the following methodology: the mathematical model and the non-linear characteristics of the system are analyzed; the universes of error discourse (derived from error and control action) are experimentally measured. The experimental data was used for the fuzzification, defuzzification, statement of the rules and controller gains. The implemented rules were designed for a PD-Fuzzy in which a numerical integration of the control action was applied, obtaining a Fuzzy PI. Finally, the implementation was made on the STM32F407G-DISC card, which was programmed with MATLAB-Simulink software tools. The experimental results show that the proposed controller works even below the horizontal, where the behavior can show singularities or physical problems such as magnetization. In compliance with the stated objectives for a range of -5 to 10 radians, these results are maintained even in the presence of disturbances, demonstrating the feasibility of the controller.

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Trajectory Tracking Control for Uncertain Robot Manipulators with Repetitive Motions in Task Space

Mathematical Problems in Engineering ◽

10.1155/2021/8838927 ◽

2021 ◽

Vol 2021 ◽

pp. 1-17

Author(s):

Jiutai Liu ◽

Xiucheng Dong ◽

Yong Yang ◽

Hongyu Chen

Keyword(s):

Trajectory Tracking ◽

Robot Manipulators ◽

Tracking Error ◽

Task Space ◽

Learning Gain ◽

Trajectory Tracking Control ◽

Adaptive Iterative Learning Control ◽

Tracking Tasks ◽

Control Schemes ◽

Composite Energy

This paper aims at the trajectory tracking problem of robot manipulators performing repetitive tasks in task space. Two control schemes are presented to conduct trajectory tracking tasks under uncertain conditions including unmodeled dynamics of robot and additional disturbances. The first controller, pure adaptive iterative learning control (AILC), is based upon the use of a proportional-derivative-like (PD-like) feedback structure, and its design seems very simple in the sense that the only requirement on the learning gain and control parameters is the positive definiteness condition. The second controller is designed with a combination of AILC and neural networks (NNs) where the AILC is adopted to learn the periodic uncertainties that attribute to the repetitive motion of robot manipulators while the add-on NNs are used to approximate and compensate all nonperiodic ones. Moreover, a combined error factor (CEF), which is composed of the weighted sum of tracking error and its derivative, is designed for network updating law to improve the learning speed as well as tracking accuracy of the system. Stabilities of the controllers and convergence are proved rigorously by a Lyapunov-like composite energy function. The simulations performed on two-link manipulator are provided to verify the effectiveness of the proposed controllers. The results of compared simulations illustrate that our proposed control schemes can significantly conduct trajectory tracking tasks.

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