Euler–Rodrigues formula variations, quaternion conjugation and intrinsic connections

This paper proposes a nonlinear adaptive position and attitude-tracking controller for satellite proximity operations between a target and a chaser satellite. The controller requires no information about the mass and inertia matrix of the chaser satellite and takes into account the gravitational acceleration, the gravity-gradient torque, the perturbing acceleration due to Earth’s oblateness, and constant (but otherwise unknown) disturbance forces and torques. Sufficient conditions to identify the mass and inertia matrix of the chaser satellite are also given. The controller is shown to ensure almost global asymptotical stability of the translational and rotational position and velocity tracking errors. Unit dual quaternions are used to simultaneously represent the absolute and relative attitude and position of the target and chaser satellites. The analogies between quaternions and dual quaternions are explored in the development of the controller.

/pdf/adaptive-position-and-attitude-tracking-controller-for-iokwifxjw4.pdf

Adaptive Position and Attitude-Tracking Controller for Satellite Proximity Operations Using Dual Quaternions

6-DOF robust adaptive terminal sliding mode control for spacecraft formation flying

relativetranslationandrotationbetweenthesetwospacecraftis firstintroduced,whichisrequiredtotrackadesired time-varying trajectory given in advance. A six-degrees-of-freedom relative-motion model is proposed by using the dual-quaternion representation, which can describe the coupling effect between the translational motion and the rotational one. A terminal sliding mode-control law is proposed such that the defined dynamical synchronization errorcanconvergetothedesiredtrajectoryin finitetime,basedonwhichamodifiedcontrollerisdesignedtosolvethe ambiguity problem caused by dual-quaternion representation. To alleviate the chattering phenomenon, a continuousterminal sliding mode-control scheme isfurthermore developed, which will enable the tracking errors to converge to a small neighborhood of the origin in finite time. The proposed control strategies are robust to model uncertainties and bounded external disturbances. Finally, numerical simulations are performed to demonstrate the validity of the proposed approaches.

Finite-Time Control for Spacecraft Formation with Dual-Number-Based Description

This paper presents two integrated planar-spherical overconstrained mechanisms that are inspired and evolved from origami cartons with a crash-lock base. Investigating the crash-lock base of the origami cartons, the first overconstrained mechanism is evolved by integrating a planar four-bar linkage with two spherical linkages in the diagonal corners. The mechanism has mobility one and the overconstraint was exerted by the two spherical linkages. This mechanism is then evolved into another integrated planar-spherical overconstrained mechanism with two double-spherical linkages at the diagonal corners. The evolved mechanism has mobility one. It is interesting to find that the double-spherical linkage at the corner of this new mechanism is an overconstrained 6R linkage. The geometry evolution is presented and the constraint matrices of the mechanisms are formulated using screw-loop equations verifying mobility of the mechanisms. The paper further reveals the assembly conditions and geometric constraint of the two overconstrained mechanisms. Further, with mechanism decomposition, geometry and kinematics of the mechanisms are investigated with closed-form equations, leading to comparison of these two mechanisms with numerical simulation. The paper further proposes that the evolved overconstrained mechanism can in reverse lead to new origami folds and crease patterns. The paper hence not only lays the groundwork for kinematic investigation of origami-inspired mechanisms but also sheds light on the investigation of integrated overconstrained mechanisms.

Origami-inspired integrated planar-spherical overconstrained mechanisms

This paper presents a new joint coined as the rT joint and proposes two types of metamorphic parallel mechanisms assembled with this rT joint. In the first type, the mechanism changes its topology by turning the rT joints in all limbs into different configurations. This change in mobility is completed by two cases illustrated by a 3(rT)PS metamorphic parallel mechanism having variable mobility from 3 to 6 and a 3(rT)P(rT) parallel mechanism having various configurations including pure translations, pure rotations, and mobility 4. In the second type, a central strut with the rT joint is added in a parallel mechanism. The variable mobility of the mechanism results from the topological change of the central (rT)P(rT) strut. This is illustrated in a 3SPS-1 (rT)P(rT) metamorphic parallel mechanism, which changes its mobility from 4 to 5. It is demonstrated in mobility analysis that the change in local mobility of each limb results in the change in the platform mobility that a metamorphic process can be achieved. This particular analysis leads to advancement of improved Grubler-Kutzbach criterion by introducing the local mobility factor in the mobility analysis.

Mobility Change in Two Types of Metamorphic Parallel Mechanisms

Constraint analysis on mobility change of a novel metamorphic parallel mechanism

Inverse kinematic analysis of the general 6R serial manipulators based on double quaternions

Closed-form forward kinematics for a symmetrical 6-6 Stewart platform using algebraic elimination

The theory of dual quaternion and its use in serial mechanisms are described in this paper. A closed-form solution to the inverse kinematic analysis of the general 7-link 7R mechanism is presented....

Qizheng Liao

Papers

Mobility Change in Two Types of Metamorphic Parallel Mechanisms

Constraint analysis on mobility change of a novel metamorphic parallel mechanism

Inverse kinematic analysis of the general 6R serial manipulators based on double quaternions

Closed-form forward kinematics for a symmetrical 6-6 Stewart platform using algebraic elimination

Dual quaternion-based inverse kinematics of the general spatial 7R mechanism: