scholarly journals Immersion and Invariance Adaptive Control for Spacecraft Pose Tracking via Dual Quaternions

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Xiaoping Shi ◽  
Xuan Peng ◽  
Yupeng Gong
Keyword(s):  
Relative Motion ◽  
Direction Cosine ◽  
Dual Quaternion ◽  
Unknown Parameters ◽  
Estimation Errors ◽  
Performance Improvements ◽  
Pose Tracking ◽  
Immersion And Invariance ◽  
Dual Quaternions ◽  
Control Scheme

This paper addresses the simultaneous attitude and position tracking of a target spacecraft in the presence of general unknown bounded disturbances in the framework of dual quaternions, which provides a concise and integrated description of the coupled rotational and translational motions. By virtue of the newly introduced dual direction cosine matrix, the dimension of the dual quaternion-based relative motion dynamics written in vector/matrix form can be lowered to six. Treating the disturbances as unknown parameters, a modular adaptive pose tracking control scheme composed of two separately designed parts is then derived. One part is the adaptive disturbance estimator designed based on the immersion and invariance theory. Driven by the disturbance estimation errors, it can realize exponential convergence of the estimations and has the nice “parameter lock” property, which can hardly be expected in the conventional certainty equivalent adaptive controllers. The other part is a proportional-derivative-like pose tracking controller where the estimated disturbances are directly used. The closed-loop stability of the relative motion system under different kinds of disturbances is proven by Lyapunov stability analysis. Simulations and comparisons with two previous dual quaternion-based controllers demonstrate the novel features and performance improvements of the proposed control scheme.

scholarly journals Synchronization of Coupled Different Chaotic FitzHugh-Nagumo Neurons with Unknown Parameters under Communication-Direction-Dependent Coupling

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Iqbal ◽  
Muhammad Rehan ◽  
Abdul Khaliq ◽  
Saeed-ur- Rehman ◽  
Keum-Shik Hong
Keyword(s):  
Gap Junctions ◽  
Chaotic Behavior ◽  
Coupled System ◽  
Parametric Estimation ◽  
Unknown Parameters ◽  
Estimation Errors ◽  
System A ◽  
Control Scheme ◽  
Control Methodology ◽  
The Impact

This paper investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN) neurons with unknown parameters under external electrical stimulation (EES). The coupled FHN neurons of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as the increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme, to cope with the infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via numerical simulations.

Extended state observer–based output feedback control for spacecraft pose tracking with control input saturation

2021 ◽  
pp. 095441002110177
Author(s):  
Kejie Gong ◽  
Ying Liao ◽  
Yafei Mei
Keyword(s):  
Feedback Control ◽  
Output Feedback ◽  
Finite Time ◽  
Output Feedback Control ◽  
State Observer ◽  
Extended State Observer ◽  
Control Input ◽  
Extended State ◽  
Pose Tracking ◽  
Control Scheme

This article proposed an extended state observer (ESO)–based output feedback control scheme for rigid spacecraft pose tracking without velocity feedback, which accounts for inertial uncertainties, external disturbances, and control input constraints. In this research, the 6-DOF tracking error dynamics is described by the exponential coordinates on SE(3). A novel continuous finite-time ESO is proposed to estimate the velocity information and the compound disturbance, and the estimations are utilized in the control law design. The ESO ensures a finite-time uniform ultimately bounded stability of the observation states, which is proved utilizing the homogeneity method. A non-singular finite-time terminal sliding mode controller based on super-twisting technology is proposed, which would drive spacecraft tracking the desired states. The other two observer-based controllers are also proposed for comparison. The superiorities of the proposed control scheme are demonstrated by theory analyses and numerical simulations.

A Modified Algorithm for the Least Squares Identification

1983 ◽  
Vol 105 (1) ◽  
pp. 50-52
Author(s):  
C. Batur
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Mechanical Systems ◽  
Model Structure ◽  
Input Output ◽  
Unknown Parameters ◽  
Estimation Errors ◽  
Usual Practice ◽  
Unknown Disturbances ◽  
Modified Algorithm

To identify the dynamics of mechanical systems, the usual practice is to assume a certain model structure and try to estimate the unknown parameters of this model on the basis of input output observations. For mechanical systems operating under noisy industrial conditions, the number of unknowns of the problem exceeds the number of equations available. It is then inevitable that certain assumptions must be made on the unknown disturbances. This paper assumes that the only reliable feature of the disturbance is its independence of input. This yields a set of assumptions in excess of the minimal requirements and an endeavor has been made to exploit this excess to minimize the parameter estimation errors. Th resulting algorithm is similar to that of the Two Stage Least Squares method [1].

scholarly journals Relative Status Determination for Spacecraft Relative Motion Based on Dual Quaternion

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jun Sun ◽  
Shijie Zhang ◽  
Xiande Wu ◽  
Fengzhi Guo ◽  
Yaen Xie
Keyword(s):  
Relative Motion ◽  
Dynamic Models ◽  
Attitude Determination ◽  
System State ◽  
Dual Quaternion ◽  
Dynamics Model ◽  
Navigation Problem ◽  
Spacecraft Formation ◽  
Navigation Algorithm ◽  
Relative Status

For the two-satellite formation, the relative motion and attitude determination algorithm is a key component that affects the flight quality and mission efficiency. The relative status determination algorithm is proposed based on the Extended Kalman Filter (EKF) and the system state optimal estimate linearization. Aiming at the relative motion of the spacecraft formation navigation problem, the spacecraft relative kinematics and dynamics model are derived from the dual quaternion in the algorithm. Then taking advantage of EKF technique, combining with the dual quaternion integrated dynamic models, considering the navigation algorithm using the fusion measurement by the gyroscope and star sensors, the relative status determination algorithm is designed. At last the simulation is done to verify the feasibility of the algorithm. The simulation results show that the EKF algorithm has faster convergence speed and higher accuracy.

Logic-Based Switching Adaptive Control of DC-DC Buck Converter

2012 ◽  
Vol 229-231 ◽  
pp. 2209-2212
Author(s):  
Bao Bin Liu ◽  
Wei Zhou
Keyword(s):  
Adaptive Control ◽  
Closed Loop ◽  
Buck Converter ◽  
Uncertain Parameters ◽  
Small Signal ◽  
Closed Loop System ◽  
Unknown Parameters ◽  
Signal Model ◽  
Small Signal Model ◽  
Control Scheme

Logic-based switching adaptive control scheme is proposed for the model of DC-DC buck converter in presence of uncertain parameters and power supply disturbance. All uncertain parameters and the disturbance are estimated together through constructing Lyapunov function. And a switching mechanism is used to ensure global asymptotic stability of the closed-loop system. The results of simulation show that even if there are multiple unknown parameters in the small-signal model, the control system of DC-DC buck converter can estimate unknown parameters quickly and accurately.

A New Airborne Passive DF Method only Based on Frequency Difference

2011 ◽  
Vol 219-220 ◽  
pp. 846-850
Author(s):  
Tao Yu
Keyword(s):  
Direction Cosine ◽  
Doppler Frequency ◽  
Frequency Measurement ◽  
Frequency Difference ◽  
Baseline Length ◽  
Direct Proportion ◽  
Unknown Parameters ◽  
Flight Direction ◽  
Phase Interference ◽  
Circular Functions

If three antenna units are divided into two set and two baselines are placed at right angles to each other in flight plain, in which the direction of one baseline is parallel to the actual flight direction of air vehicle, the sine and cosine function of target bearing respectively in two baseline directions can be simultaneously obtained according to the analysis principle of the direction cosine change rate. The angulations’ formula only based on Doppler frequency difference can be derived after eliminating the unknown parameters including angular velocity and wavelength by the specific value of two circular functions. The analog calculation shows that the relative error is in direct proportion to the baseline length provided that the incident wave is parallel in derivation. But the error analysis depicts that the measurement accuracy is in direct proportion to the baseline length. Moreover, the measurement error relies on mainly the accuracy of frequency measurement. Furthermore, the derived formula has irregularity in airborne axis direction. However, since the new method is not associated with wavelength, this new DF only based on Doppler frequency difference will be more adapted to passive sounding as compared with phase interference method.

Robust Adaptive Tracking Control of Autonomous Underwater Vehicle-Manipulator Systems

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Mohan Santhakumar ◽  
Jinwhan Kim
Keyword(s):  
Adaptive Control ◽  
Control Algorithm ◽  
Autonomous Underwater Vehicle ◽  
Underwater Vehicle ◽  
Dynamic Coupling ◽  
Unknown Parameters ◽  
Adaptive Tracking Control ◽  
Control Scheme ◽  
Robust Adaptive ◽  
Model Reference Adaptive

This paper proposes a new tracking controller for autonomous underwater vehicle-manipulator systems (UVMSs) using the concept of model reference adaptive control. It also addresses the detailed modeling and simulation of the dynamic coupling between an autonomous underwater vehicle and manipulator system based on Newton–Euler formulation scheme. The proposed adaptation control algorithm is used to estimate the unknown parameters online and compensate for the rest of the system dynamics. Specifically, the influence of the unknown manipulator mass on the control performance is indirectly captured by means of the adaptive control scheme. The effectiveness and robustness of the proposed control scheme are demonstrated using numerical simulations.

Practical Tracking Control of a Class of Uncertain Surface Vessels Under Weak Assumptions on Uncertainties and Reference Trajectories

2021 ◽  
Author(s):  
Jian Li ◽  
Wenqing Xu ◽  
Zhaojing Wu ◽  
Yungang Liu
Keyword(s):  
Tracking Control ◽  
Broad Class ◽  
Tracking Error ◽  
Reference Trajectory ◽  
Unknown Parameters ◽  
Related Literature ◽  
Surface Vessels ◽  
Control Scheme ◽  
Reference Trajectories ◽  
Theoretical Results

Abstract This paper is devoted to the tracking control of a class of uncertain surface vessels. The main contributions focus on the considerable relaxation of the severe restrictions on system uncertainties and reference trajectory in the related literature. Specifically, all the system parameters are unknown and the disturbance is not necessarily to be differentiable in the paper, but either unknown parameters or disturbance is considered but the other one is excluded in the related literature, or both of them are considered but the disturbance must be continuously differentiable. Moreover, the reference trajectories in the related literature must be at least twice continuously differentiable and themselves as well as their time derivatives must be known for feedback, which are generalized to a more broad class ones that are unknown and only one time continuously differentiable in the paper. To solve the control problem, a novel practical tracking control scheme is presented by using backstepping scheme and adaptive technique, and in turn to derive an adaptive state-feedback controller which guarantees that all the states of the resulting closed-loop system are bounded while the tracking error arrives at and then stay within an arbitrary neighborhood of the origin. Finally, simulation is provided to validate the effectiveness of the proposed theoretical results.

Robust and efficient forward, differential, and inverse kinematics using dual quaternions

2020 ◽  
pp. 027836492093194
Author(s):  
Neil T Dantam
Keyword(s):  
Inverse Kinematics ◽  
Forward Kinematics ◽  
Robot Kinematics ◽  
Dual Numbers ◽  
Dual Quaternion ◽  
Implicit Representation ◽  
Alternative Representation ◽  
Transformation Matrices ◽  
Dual Quaternions ◽  
Efficient Representation

Modern approaches for robot kinematics employ the product of exponentials formulation, represented using homogeneous transformation matrices. Quaternions over dual numbers are an established alternative representation; however, their use presents certain challenges: the dual quaternion exponential and logarithm contain a zero-angle singularity, and many common operations are less efficient using dual quaternions than with matrices. We present a new derivation of the dual quaternion exponential and logarithm that removes the singularity, we show an implicit representation of dual quaternions offers analytical and empirical efficiency advantages compared with both matrices and explicit dual quaternions, and we derive efficient dual quaternion forms of differential and inverse position kinematics. Analytically, implicit dual quaternions are more compact and require fewer arithmetic instructions for common operations, including chaining and exponentials. Empirically, we demonstrate a 30–40% speedup on forward kinematics and a 300–500% speedup on inverse position kinematics. This work relates dual quaternions with modern exponential coordinates and demonstrates that dual quaternions are a robust and efficient representation for robot kinematics.

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