Adaptive Robust Control Based on Moore-Penrose Generalized Inverse for Underactuated Mechanical Systems

Chen, Xiaolong; Zhao, Han; Sun, Hao; Zhen, Shengchao

doi:10.1109/access.2019.2950211

Cited by 14 publications

(9 citation statements)

References 39 publications

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“…we have to apply the well-known unique Moore-Penrose Tpseudoinverse marked as (CB) δ [33]. Based on the so-called skeleton factorization we can explicitly obtain its general expression…”

Section: Non-full Rank Imc Structurementioning

confidence: 99%

A New Non-Full Rank Algorithm for the IMC-Derived d-Step MIMO Structures in the Pole-Free State Space

Feliks

Hunek

2020

IEEE Access

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In this paper, the powerful issue of a non-full rank inverse model control investigation is provided. It is broadly known, that the inverse-based methodology is associated with the full-rank control systems only. However, following the recently obtained authors' results in this matter, it should be concluded, that for single-delayed non-full rank state-space plants, the inverse model control-related perfect control expression can also be established. It is shown here, that for all right-and left-oriented multivariable LTI non-full rank systems, including the square ones, governed by the discrete-time statespace domain arranging the zero-reference value, the maximum-speed pole-free instance of such inverse model control strategy can be achieved. Thus, the new non-full rank algorithm does not coincide with the z-transfer-function scenario, which additionally sounds the intriguing peculiarity. The innovative content of the manuscript, that has never been seen before, is strongly supported by the numerical examples. Henceforth, the presented methodology covers the entire set of LTI MIMO state-space-oriented plants in the discrete-time domain, which is also a consequence of conducted research investigation in the past. INDEX TERMS Non-full rank, perfect control procedure, Moore-Penrose inverse, generalized inverses, skeleton factorization, pole-free delayed plants, discrete-time state-space MIMO structures

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“…we have to apply the well-known unique Moore-Penrose Tpseudoinverse marked as (CB) δ [33]. Based on the so-called skeleton factorization we can explicitly obtain its general expression…”

Section: Non-full Rank Imc Structurementioning

confidence: 99%

A New Non-Full Rank Algorithm for the IMC-Derived d-Step MIMO Structures in the Pole-Free State Space

Feliks

Hunek

2020

IEEE Access

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“…Yu et al [24] extend U-K method to automated guided vehicle in order to solve the trajectory tracking control issue. For underactuated system with nonholonomic constraints, Chen et al [25] present a novel control approach utilizing U-K approach, which is proved by Lyapunov approach. The practicality of U-K theory has been fully demonstrated.…”

Section: Introductionmentioning

confidence: 99%

Constrained control methods for lower extremity rehabilitation exoskeleton robot considering unknown perturbations

et al. 2022

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In this paper, trajectory tracking control is investigated for lower extremity rehabilitation exoskeleton robot. Unknown perturbations are considered in the system which are inevitable in the reality. The trajectory tracking control is constructively treated as constrained control issue. To obtain the explicit equation of motion and analytical solution of lower extremity rehabilitation exoskeleton robot, Udwadia-Kalaba theory is introduced. Lagrange multipliers and pseudo variables are not needed in Udwadia-Kalaba theory, which is more superior than Lagrange method. On the basic of Udwadia-Kalaba theory, two constrained control methods including trajectory stabilization control and adaptive robust control are proposed. Trajectory stabilization control applies Lyapunov stability theory to modify the desired trajectory constraint equations. A leakage-type of adaptive law is designed to compensate unknown perturbations in adaptive robust control. Finally, comparing with nominal control and control method in [32], simulation results demonstrate the superiority of trajectory stabilization control and adaptive robust control in trajectory tracking control.

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“…The work [18] applied a proportional integral derivative (PID) control and active disturbance rejection control to balance and steer a two-wheeled selfbalancing robot modeled by Lagrange formula. In [19], an adaptive robust control of a self-balancing two-wheeled underactuated robot to estimate uncertainty bound information, using deterministic system performance by Lyapunov method, was reported. In [20], a navigational two-wheeled self-balancing robot control using a PD-PI controller based on the Kalman filter algorithm was reported.…”

Section: Introductionmentioning

confidence: 99%

Rolling Biped Polynomial Motion Planning

Ortíz¹,

Martínez‐García²

2022

Motion Planning

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This work discloses a kinematic control model to describe the geometry of motion of a two-wheeled biped’s limbs. Limb structure is based on a four-bar linkage useful to alleviate damping motion during self-balance. The robot self-balancing kinematics geometry combines with user-customized polynomial vector fields. The vector fields generate safe reference trajectories. Further, the robot is forced to track the reference path by a model-based time-variant recursive controller. The proposed formulation showed effectiveness and reliable performance through numerical simulations.

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Adaptive Robust Control Based on Moore-Penrose Generalized Inverse for Underactuated Mechanical Systems

Cited by 14 publications

References 39 publications

A New Non-Full Rank Algorithm for the IMC-Derived d-Step MIMO Structures in the Pole-Free State Space

A New Non-Full Rank Algorithm for the IMC-Derived d-Step MIMO Structures in the Pole-Free State Space

Constrained control methods for lower extremity rehabilitation exoskeleton robot considering unknown perturbations

Rolling Biped Polynomial Motion Planning

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