A novel relative motion mode, which represents the noncircularity of the reference orbit a parameter uncertainty, is raised in this article. A guaranteed cost tracking controller with input saturation is designed via a linear matrix inequality method, which is more concise and less conservative compared with the previous works. Sufficient conditions for the existence of this robust tracking controller are given, and the numerical examples are provided for both time-invariant and time-variant reference signals to illustrate the effectiveness of the proposed control scheme when applied to the terminal rendezvous and other astronautic missions with scheduled states signal.
The following video is a demonstration for the tracking controller when applied to track a Epitrochoid-shpae reference orbit , the tracking position and velocity signals are given below:
The video shows the relative motion trajectory on the reference orbit as well as the chaser’s control output of the thrusters along the x- and y- axis of the relative coordinate system.
 Lawrence, J. Dennis. A catalog of special plane curves. Courier Corporation, 2013.
This post will give a brief review on the project RoboNaVi*, Robot Navigation & Vision System, which was started in Sep 2010 and was ended in Oct 2012. A lite presentation introducing and reviewing this project can be found in the link below:
The following video is a demonstration of RoboNaVi, which adopts a PID controller and my first-generation objective tracking system. I have posted a thread introducing the second-generation objective tracking system a few days ago, which has significant improvements compared with the one used in this video. However, due to some reasons, this project was cut in Oct 2012 with my leaving the Department of Aerospace Engineering, HIT and no further funds and equipment supporting any more innovative experiments.
To rebuild this system is always a prior thing on my schedule. Therefore, if you are interested in joining, investing or providing any support on this program. Please feel free to contact me.
*RoboNaVi is an integrated guidance, navigation and control system for autonomous robots (LEGO MINDSTORMS NXT), and is developed with NI LabVIEW. RoboNaVi has realized the functions of camera calibration, pattern learning, pattern matching and tracking, feature extraction, trajectory planning, obstacle avoiding, vision-based navigation, robot control, etc.
By using the feature extraction technique, I built a object tracking system for indoor GPS. This tracking system is able to measure the position as well as the orientation (or attitude) information of the object of interest. The object tracking system is one of the modules for the RoboNaVi (Robot Navigation Vision System), an indoor autonomous robot test bed, which is intended to verify some new ideas in control theory, computer vision and operation research, such as the path planning problem. The whole system is built, embedded and driven by NI LabVIEW.
With the help of NI LabVIEW, I realized a camera calibration system for an indoor GPS system. This calibration system needs a set of pictures with calibration grid in them to operate, and is able to give out the external and internal parameters of the lens, which are some crucial parameters for camera calibration and picture correction.