Modeling and Control for Spacecraft Relative Pose Motion by Using Twistor Representation

Deng, Yifan; Wang, Zhigang

doi:10.2514/1.g001522

Cited by 17 publications

(14 citation statements)

References 29 publications

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“…Up next, we introduce a range of findings derived from utilizing a set of fractional Cayley transforms. Notably, these fractional Cayley transforms differ from those previously documented in [20,21,[56][57][58].…”

Section: Higher-order Fractional Modified Cayley Transformcontrasting

confidence: 68%

A Minimal Parameterization of Rigid Body Displacement and Motion Using a Higher-Order Cayley Map by Dual Quaternions

Condurache,

Popa

2023

Symmetry

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The rigid body displacement mathematical model is a Lie group of the special Euclidean group SE (3). This article is about the Lie algebra se (3) group. The standard exponential map from se (3) onto SE (3) is a natural parameterization of these displacements. In technical applications, a crucial problem is the vector minimal parameterization of manifold SE (3). This paper presents a unitary variant of a general class of such vector parameterizations. In recent years, dual algebra has become a comprehensive framework for analyzing and computing the characteristics of rigid-body movements and displacements. Based on higher-order fractional Cayley transforms for dual quaternions, higher-order Rodrigues dual vectors and multiple vectorial parameters (extended by rotational cases) were computed. For the rigid body movement description, a dual tangent operator (for any vectorial minimal parameterization) was computed. This paper presents a unitary method for the initial value problem of the dual kinematic equation.

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Section: Higher-order Fractional Modified Cayley Transformcontrasting

confidence: 68%

A Minimal Parameterization of Rigid Body Displacement and Motion Using a Higher-Order Cayley Map by Dual Quaternions

Condurache,

Popa

2023

Symmetry

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“…is a dual MRP and is used to relate the Cayley transform to the exponential function. Insertion of the real and dual parts ofμ into (9) gives cay(μ) =q whereq is given by (5). This means that…”

Section: Cayley Transformmentioning

confidence: 99%

“…and corresponds to the dual MRP representation ofq. This representation is called a twistor in [9]. The expression (12) can be written as…”

Section: Cayley Transformmentioning

confidence: 99%

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Dual Quaternion Particle Filtering for Pose Estimation

Sveier

Egeland

2021

IEEE Trans. Contr. Syst. Technol.

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This article presents a particle filter for pose estimation using unit dual quaternion kinematics. The eight-parameter unit dual quaternion is used for global representation of the pose, whereas the six parameters of the dual modified Rodrigues parameters (MRPs) are used for local pose representation in the state-space model. The dual MRPs enable estimates of the mean and the covariance to be calculated from the particles without violating the algebraic constraint of the unit dual quaternion. For verification of the filter and comparison with state of the art, we consider pose measurements available in the form of unit dual quaternions. Angular velocity and specific force measurements from a body-mounted inertial measurement unit are also considered in the filtering. We show through simulations that the suggested particle filter has comparable accuracy with a previously proposed unscented Kalman filter based on unit dual quaternions. We also consider a practical application where the pose of an arbitrary rigid object is estimated using a sequence of point clouds from a 3-D camera. A model point cloud of the object is displaced with the unit dual quaternion associated with each particle, and a fitting score is calculated between the displaced model point cloud and the measured point cloud from the 3-D camera. The likelihoods of the fitting scores are calculated from an exponential distribution and are used to update the weights of the particles. The system was verified in an experiment where the motion of a swinging payload hanging from a crane was estimated using a 3-D camera.

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“…A time-varying sliding mode-based fault-tolerant controller was designed in [27], but the proposed model was the same as the traditional tracking model for one spacecraft so that the model couplings between the target and chaser in rendezvous and docking missions were ignored. To describe the relative pose motion between two spacecraft in a unified way, the dual quaternion-based relative pose motion model was reported recently, and some corresponding controllers were also designed, such as the non-certainty-equivalence adaptive controller in [28], output feedback controllers in [29] and [30], proportional-derivative controller in [31], and adaptive sliding mode controller in [32]. The aforementioned state feedback control approaches are able to achieve the prescribed relative pose control objectives.…”

mentioning

confidence: 99%

Saturated Adaptive Relative Motion Coordination of Docking Ports in Space Close-Range Rendezvous

Sun

Jiang

2020

IEEE Trans. Aerosp. Electron. Syst.

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An adaptive relative pose controller for docking ports of two uncertain spacecraft in autonomous rendezvous and docking is developed. A novel relative translational and rotational model represented in the chaser body-fixed frame is derived firstly based on the classical Newton-Euler equations. Based on the proposed model, a six-degrees-of-freedom adaptive control law is presented based on norm-wise estimations for the unknown parameters of two spacecraft to decrease the online computational burden. Meanwhile, an adaptive robust control input is designed by introducing an exponential function of states to improve the response performance with respect to the traditional adaptive robust control. Moreover, a linear anti-windup compensator is employed to ensure the bounded performance of the control inputs. The explicit tuning rules for designing parameters are derived based on the stability analysis of the closed-loop system. It is proved in Lyapunov framework that all closed-loop signals are always bounded and the pose tracking error ultimately converges to a small neighborhood of zero. Simulation results validate the performance of the proposed robust adaptive control strategy. Index Terms-Space rendezvous and docking, docking ports, motion coordination, adaptive control, saturated control, model uncertainty. I. INTRODUCTION M ANY important space missions, such as establishment of the space station, on-orbit servicing, space debris removing, and satellite networking [1] require spacecraft rendezvous and docking technique. In the process of the in-orbit rendezvous and docking, two spacecraft, named the active chaser and the passive target, are involved in the scenario. The chaser should conduct large-angle attitude maneuvers and complicated orbital maneuvers approaching to the passive target. Specifically, the close-range rendezvous and docking operations between two spacecraft require highly accurate translational and rotational controllers, since the chaser should fly around the target to track its docking port precisely [2]. In the last few decades, many problems in rendezvous and docking missions have been considered in the control

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Modeling and Control for Spacecraft Relative Pose Motion by Using Twistor Representation

Cited by 17 publications

References 29 publications

A Minimal Parameterization of Rigid Body Displacement and Motion Using a Higher-Order Cayley Map by Dual Quaternions

A Minimal Parameterization of Rigid Body Displacement and Motion Using a Higher-Order Cayley Map by Dual Quaternions

Dual Quaternion Particle Filtering for Pose Estimation

Saturated Adaptive Relative Motion Coordination of Docking Ports in Space Close-Range Rendezvous

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