Integrated modeling of spacecraft relative motion dynamics using dual quaternion

Abstract

To realize high accurate control of relative position and attitude between two spacecrafts, the coupling between position and attitude must be fully considered and a more precise model should be established. This paper breaks the traditional divide and conquer idea, and uses a mathematical tool, namely dual quaternion to establish the integrated 6 degree-of-freedom (6-DOF) model of relative position and attitude, which describes the coupled relative motion in a compact and efficient form and needs less information of the target. Considering the complex operation rules and the unclarity of the current relative motion model in dual quaternion, necessary mathematical foundations are given at first, followed by clear and detailed modeling process and analysis. Finally a generalized proportion-derivative (PD) controller law is designed. The simulation results show that based on the integrated model established by dual quaternion, this control law can achieve a high control accuracy of relative motion.

Dual-quaternion-based modeling and control for motion tracking of a tumbling target

“…In this section, the control law (40) are numerically simulated. Under the same initial conditions, its antiinterference ability is compared with the generalized proportional differential controller designed in [36].…”

“…The relative attitude and position errors are within 0.05 • and 1 mm at time of 400 s, which indicate the controller can achieve high control precision. The anti-interference capacity of the controller (50) is compared with that of the generalized PD controller in [36], whose control parameters are tuned so that the settling time and control precision are similar to those of the controller (50). The simulation results show that to achieve the same control precision, the magnitudes of the disturbance torque and force that the PD controller can withstand are τ c d,P D = 0.18τ c d and f c d,P D = 0.004f c d , which are much smaller.…”

Dual Attitude Representations and Kinematics for Six-Degree-of-Freedom Spacecraft Dynamics

“…Moreover, control laws based on the dual quaternion involving combined position and attitude intrinsically account for the natural coupling between the rotational and translational motion [1]. The widespread use of dual quaternions can be found in robotics systems [2] [3], rigid body dynamics [4] [5] [6], and in relative spacecraft system dynamics [7] [8]. They are also utilized in field of aerospace engineering involving dual quaternions for powered descent [9] and satellite autonomous rendezvous control [10] [11].…”