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

Abstract

In this paper, we propose a nonlinear adaptive position and attitude tracking controller for satellite proximity operations. This controller requires no information about the mass and inertia matrix of the satellite, and takes into account the gravitational force, the gravitygradient torque, the perturbing force due to Earth's oblateness, and other constant-but otherwise unknown-disturbance forces and torques. We give sufficient conditions on the reference motion for mass and inertia matrix identification. The controller is shown to be almost globally asymptotically stable and can handle large error angles and displacements. Unit dual quaternions are used to simultaneously represent the absolute and relative attitude and position of the satellites, resulting in a compact controller representation.

Fast adaptive pose tracking control for satellites via dual quaternion upon non-certainty equivalence principle

“…All of them take the advantage of the dual quaternion algebra and succeed in stabilizing the system for both rotational and translational motions simultaneously. In [4], the authors emphasize the effectiveness of the dual quaternion in proximity operations between satellites and propose an adaptive controller using the certainty equivalence principle (CE). The CE framework for the adaptive controller design has a well-known major drawback.…”

“…For the spacecraft pose control systems, several algorithms with dual quaternion representation are appeared in [3,4,12]. All of them take the advantage of the dual quaternion algebra and succeed in stabilizing the system for both rotational and translational motions simultaneously.…”

“…It is shown that the unit dual quaternion is the most compact and computationally efficient tool among others [1,5,6]. Due to such efficiency of the unit dual quaternion in 6-DOF rigid body dynamics, it is recently adopted to the controller design problems in [3,4,7,9,12,14,15] to name a few.…”

Integrated 6-DOF Orbit-Attitude Dynamical Modeling and Control Using Geometric Mechanics

“…The integrated 6-DOF orbit-attitude dynamical modeling and control of spacecraft have shown great importance in various space missions, such as formation flying [1][2][3][4][5][6][7], proximity operations [8][9][10][11][12][13][14], and proximity operations about minor celestial bodies [15][16][17].…”

“…The dual quaternion has been widely used as a unified representation of the 6-DOF rigid body motion, but the constraints between its elements need to be dealt with carefully [10,11]. Sanyal et al [8,27] have used the matrix form of the Lie group SE(3) in the dynamical modeling of rigid body motion and achieved controllers with almost global convergence, which is the best that can be achieved for a system evolving on a noncontractible state space, like the 6-DOF rigid body motion, with continuous feedback [6].…”