A Dual Quaternion Feedback Linearized Approach for Maneuver Regulation of Rigid Bodies

Antonello, Alessandro; Michieletto, Giulia; Oboe, Roberto; Cenedese, Angelo

doi:10.1109/lcsys.2018.2834300

Cited by 3 publications

(5 citation statements)

References 8 publications

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“…Later in the same decade, the works of control using dual quaternions appeared as kinematic control [78]. After that, the number of works in this area increased rapidly, featuring dual quaternion PID [79], kinematic control [24,80,81], feedback linearization [82][83][84][85][86], model predictive control [69,87,88], adaptive control [47,89] (ref. [90] used adaptive control to perform kinematic-model-free control, in which no previous knowledge of the kinematic model or even joint variables is required to move the end-effector to the desired pose), sliding modes [91,92], H ∞ [46] and backstepping [93,94].…”

Section: General Overviewmentioning

confidence: 99%

“…Kinematic control aims to control the position and orientation of a system by imposing its linear and angular velocity. In the case of the kinematics given by a dual quaternion, kinematic control involves controlling the pose q by using the equation ˙q = 1 2 ω q, (84) where the controller will act by imposing the dual velocity ω.…”

Section: Kinematic Controlmentioning

confidence: 99%

“…Adaptations to the controller developed in this section are made by [83,85] to use it in a whole-body application consisting of a robotic arm mounted in an omnidirectional vehicle, and shows the experimental results of the applied control. Antonello et al [84] uses a Feedback Linearization controller for the maneuver regulation of a free rigid-body.…”

Section: Feedback Linearizationmentioning

confidence: 99%

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A Review on the Applications of Dual Quaternions

Farias,

De Pieri,

Martins

2024

Machines

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This work explores dual quaternions and their applications. First, a theoretical construction begins at dual numbers, extends to dual vectors, and culminates in dual quaternions. The physical foundations behind the developed theory lie in two important fundamentals: Chasles’ Theorem and the Transference Principle. The former addresses how to represent rigid-body motion whereas the latter provides a method for operating on it. This combination presents dual quaternions as a framework for modeling rigid mechanical systems, both kinematically and kinetically, in a compact, elegant and performant way. Next, a review on the applications of dual quaternions is carried out, providing a general overview of all applications. Important subjects are further detailed, these being the kinematics and dynamics of rigid bodies and mechanisms (both serial and parallel), control and motion interpolation. Discussions regarding dual quaternions and their applications are undertaken, highlighting open questions and research gaps. The advantages and disadvantages of using dual quaternions are summarized. Lastly, conclusions and future directions of research are presented.

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Section: General Overviewmentioning

confidence: 99%

Section: Kinematic Controlmentioning

confidence: 99%

Section: Feedback Linearizationmentioning

confidence: 99%

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A Review on the Applications of Dual Quaternions

Farias,

De Pieri,

Martins

2024

Machines

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“…These are generally linear solutions based on proportionalderivative schemes or linear quadratic regulators, see, e.g., [2,20,31]. Hovering non-linear controllers are instead not equally popular and mainly exploit feedback linearization [3,22], sliding mode and backstepping techniques [1,5] and/or geometric control approaches [9,16].…”

Section: Introductionmentioning

confidence: 99%

“…The derivative of ω ω ω d in (28) results from the sum of three components, namelyω ω ω d =ω ω ω d,1 +ω ω ω d,2 +ω ω ω d, 3 witḣ…”

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confidence: 99%

Hierarchical nonlinear control for multi-rotor asymptotic stabilization based on zero-moment direction

et al. 2020

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We consider the hovering control problem for a class of multi-rotor aerial platforms with generically oriented propellers. Given the intrinsically coupled translational and rotational dynamics of such vehicles, we first discuss some assumptions for the considered systems to reject torque disturbances and to balance the gravity force, which are translated into a geometric characterization of the platforms that is usually fulfilled by both standard models and more general configurations. Hence, we propose a control strategy based on the identification of a zero-moment direction for the applied force and the dynamic state feedback linearization around this preferential direction, which allows to asymptotically stabilize the platform to a static hovering condition. Stability and convergence properties of the control law are rigorously proved through Lyapunov-based methods and reduction theorems for the stability of nested sets. Asymptotic zeroing of the error dynamics and convergence to the static hovering condition are then confirmed by simulation results on a star-shaped hexarotor model with tilted propellers.

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