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.
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.
This paper investigates the problem of controlling a chasing spacecraft (chaser) to track and rendezvous with an uncontrolled target. Based on the actual situation, the torque-free motion of an axisymmetric prolate rigid body is employed to represent the short-term attitude motion of the tumbling target. By taking advantage of the dual quaternion's compact and efficient description of the general rigid motion, the coupled and integrated model of the 6-degree-of-freedom (6-DOF) relative motion between the chaser and the tumbling target is derived in the chaser's body fixed frame after taking full consideration of coordinate transformation. Based on the logarithm of dual quaternion, a sliding mode control (SMC) law based on the exponential reaching law and the continuous relay function is brought forward to address the problem of synchronization control of the 6-DOF relative motion. Simulation results illustrate the effectiveness of the proposed method.
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