Algorithms for spacecraft formation flying navigation based on wireless positioning system measurements

Spacecraft formation flying navigation continues to receive a great deal of interest. The research presented in this dissertation focuses on developing methods for estimating spacecraft absolute and relative positions, assuming measurements of only relative positions using wireless sensors. The implementation of the extended Kalman filter to the spacecraft formation navigation problem results in high estimation errors and instabilities in state estimation at times. This is due tp the high nonlinearities in the system dynamic model. Several approaches are attempted in this dissertation aiming at increasing the estimation stability and improving the estimation accuracy. A differential geometric filter is implemented for spacecraft positions estimation. The differential geometric filter avoids the linearization step (which is always carried out in the extended Kalman filter) through a mathematical transformation that converts the nonlinear system into a linear system. A linear estimator is designed in the linear domain, and then transformed back to the physical domain. This approach demonstrated better estimation stability for spacecraft formation positions estimation, as detailed in this dissertation. The constrained Kalman filter is also implemented for spacecraft formation flying absolute positions estimation. The orbital motion of a spacecraft is characterized by two range extrema (perigee and apogee). At the extremum, the rate of change of a spacecraft’s range vanishes. This motion constraint can be used to improve the position estimation accuracy. The application of the constrained Kalman filter at only two points in the orbit causes filter instability. Two variables are introduced into the constrained Kalman filter to maintain the stability and improve the estimation accuracy. An extended Kalman filter is implemented as a benchmark for comparison with the constrained Kalman filter. Simulation results show that the constrained Kalman filter provides better estimation accuracy as compared with the extended Kalman filter. A Weighted Measurement Fusion Kalman Filter (WMFKF) is proposed in this dissertation. In wireless localizing sensors, a measurement error is proportional to the distance of the signal travels and sensor noise. In this proposed Weighted Measurement Fusion Kalman Filter, the signal traveling time delay is not modeled; however, each measurement is weighted based on the measured signal travel distance. The obtained estimation performance is compared to the standard Kalman filter in two scenarios. The first scenario assumes using a wireless local positioning system in a GPS denied environment. The second scenario assumes the availability of both the wireless local positioning system and GPS measurements. The simulation results show that the WMFKF has similar accuracy performance as the standard Kalman Filter (KF) in the GPS denied environment. However, the WMFKF maintains the position estimation error within its expected error boundary when the WLPS detection range limit is above 30km. In addition, the WMFKF has a better accuracy and stability performance when GPS is available. Also, the computational cost analysis shows that the WMFKF has less computational cost than the standard KF, and the WMFKF has higher ellipsoid error probable percentage than the standard Measurement Fusion method. A method to determine the relative attitudes between three spacecraft is developed. The method requires four direction measurements between the three spacecraft. The simulation results and covariance analysis show that the method’s error falls within a three sigma boundary without exhibiting any singularity issues. A study of the accuracy of the proposed method with respect to the shape of the spacecraft formation is also presented.

REAL TIME FUZZY CONTROLLER FOR QUADROTOR STABILITY CONTROL

In this report, we develop an intelligent adaptive neuro-fuzzy controller by using adaptive neuro fuzzy inference system (ANFIS) techniques. We begin by starting with a standard proportional-derivative (PD) controller and use the PD controller data to train the ANFIS system to develop a fuzzy controller. We then propose and validate a method to implement this control strategy on commercial off-the-shelf (COTS) hardware. An analysis is made into the choice of filters for attitude estimation. These choices are limited by the complexity of the filter and the computing ability and memory constraints of the micro-controller. Simplified Kalman filters are found to be good at estimation of attitude given the above constraints. Using model based design techniques, the models are implemented on an embedded system. This enables the deployment of fuzzy controllers on enthusiast-grade controllers. We evaluate the feasibility of the proposed control strategy in a model-in-the-loop simulation. We then propose a rapid prototyping strategy, allowing us to deploy these control algorithms on a system consisting of a combination of an ARM-based microcontroller and two Arduino-based controllers. We then use a combination of the code generation capabilities within MATLAB/Simulink in combination with multiple open-source projects in order to deploy code to an ARM CortexM4 based controller board. We also evaluate this strategy on an ARM-A8 based board, and a much less powerful Arduino based flight controller. We conclude by proving the feasibility of fuzzy controllers on Commercial-off the shelf (COTS) hardware, we also point out the limitations in the current hardware and make suggestions for hardware that we think would be better suited for memory heavy controllers.