Attitude control is an essential subsystem of most spacecraft buses, therefore attitude determination plays a very important role as it is the feedback system for any closed-loop attitude control system. Of all attitude determination sensors star trackers are usually the most accurate ones. Unfortunately, the star trackers usually used on classical, large spacecrafts are too big, heavy and power hungry. For pico-satellites, which can only carry a limited amount of volume and mass and provide only limited power, these sensors obviously cannot be used. Consequently, miniaturized star trackers have been developed in recent years, but so far the available star trackers are not sufficiently miniaturized to be feasible for the use on pico-satellites, including STELLA, a miniaturized star tracker developed at the University of Würzburg. Therefore, further miniaturization is necessary, which is why the University of Würzburg is active on the research of star trackers for small satellites. A first prototype for a new star tracker for pico-satellites, called PicoStar, has been developed in the scope of this thesis. Using a simpler system design and new image sensors, its volume could be reduced by two-thirds and the mass by about half compared to STELLA. The expected performance is kept reasonably. There is still room for further reduction of the power consumption, as it is currently up to 30% higher than required. As this Master thesis focuses on the implementation of the embedded system and the optimization of the software of the star tracker, the prototype is not finalized. So far, the star tracker algorithm has been implemented and the attitude determination is running. First test results have shown that the next steps in the PicoStar development, among other things, have to be further calibration and testing. / Validerat; 20151109 (global_studentproject_submitter)

This dissertation addresses novel techniques in determining gyroless micro-satellite attitude and attitude rate. The main objective of this thesis is to explore the possibility of using commercially available low cost micro-light star sensor as a stand-alone sensor for micro-satellite attitude as well as attitude rate determination. The objective is achieved by developing accurate and computationally efficient algorithms for the realization of onboard operation of a low fidelity star sensor. All the algorithms developed here are tested with the measurement noise presented in the catalog of the sensor array STAR-1000. A novel accurate second order sliding mode observer (SOSMO) is designed for discrete time uncertain linear multi-output system. Our design procedure is effective for both matched and unmatched bounded uncertain ties and/or disturbances. The bound on uncertainties and/or disturbances is assumed to be unknown. This problem is addressed in this work using the second order multiple sliding modes approach. Second order sliding manifold and corresponding sliding condition for discrete time system is defined similar on the lines of continuous counterpart. Our design is not restricted to a particular class of uncertain (matched) discrete time system. Moreover, it can handle multiple outputs unlike single out-put systems. The observer design is achieved by driving the state observation error and its first order finite difference to the vicinity of the equilibrium point (0,0) in a finite steps and maintaining them in the neighborhood thereafter. The estimation synthesis is based on Quasi Sliding Mode (QSM) design. The problem of designing sliding mode observer for a linear system subjected to unknown inputs requires observer matching condition. This condition is needed to ensure that the state estimation error is a asymptotically stable and is independent of the unknown input during the sliding motion. In the absence of a matching condition, asymptotic stability of the reduced order error dynamics on the sliding surface is not guaranteed. However, unknown bounded inputs guarantee bounded error on state estimation. The QSM design guarantees an ultimate error bound by incorporating Boundary Layer (BL) in its design procedure. The observer achieves one order of magnitude improvement in estimation accuracy than the conventional sliding mode observer (SMO) design for an unknown input. The observer estimation errors, satisfying the given stability conditions, converge to an ultimate finite bound (with in the specified BL) of O(T2), where T Is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The robustness of the proposed observer with respect to measurement noise is also analyzed. The design algorithm is very simple to apply and is implemented for two examples with different classes of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results show the robustness with respect to the measurement noise for SOSMO. Second order sliding mode observer gain can be calculated off-line and the same gain can work for large band of disturbance as long as the disturbance acting on the continuous time system is bounded and smooth. The SOSMO is simpler to implement on board compared to the other traditional nonlinear filters like Pseudo-Linear-Kalman-filter(PLKF); Extended Kalman Filter(EKF). Moreover, SMO possesses an automatic adaptation property same as optimal state estimator(like Kalman filter) with respect to the intensity of the measurement noise. The SMO rejects the noisy measurements automatically, in response to the increased noise intensity. The dynamic performance of the observer on the sliding surface can be altered and no knowledge of noise statistics is required. It is shown that the SOSMO performs more accurately than the PLKF in application to micro-satellite angular rate estimation since PLKF is not an optimal filter. A new method for estimation of satellite angular rates through derivative approach is proposed. The method is based on optic flow of star image patterns formed on a star sensor. The satellite angular rates are derived directly from the 2D-coordinates of star images. Our algorithm is computationally efficient and requires less memory allocation compared to the existing vector derivative approaches, where there is also no need for star identification. The angular rates are computed using least square solution method, based on the measurement equation obtained by optic flow of star images. These estimates are then fed into discrete time second order sliding mode observer (SOSMO). The performance of angular rate estimation by SOSMO is compared with the discrete time First order SMO and PLKF. The SOSMO gives the best estimates as compared to the other two schemes in estimating micro-satellite angular rates in all three axes. The improvement in accuracy is one order of magnitude (around1.7984 x 10−5 rad/ sec,8.9987 x 10−6 rad/ sec and1.4222 x 10−5 rad/ sec in three body axes respectively) in terms of standard deviation in steady state estimation error. A new method and algorithm is presented to determine star camera parameters along with satellite attitude with high precision even if these parameters change during long on-orbit operation. Star camera parameters and attitude need to be determined independent of each other as they both can change. An efficient, closed form solution method is developed to estimate star camera parameters (like focal length, principal point offset), lens distortions (like radial distortion) and attitude. The method is based on a two step procedure. In the first step, all parameters (except lens distortion) are estimated using a distortion free camera model. In the second step, lens distortion coefficient is estimated by linear least squares (LS) method. Here the derived camera parameters in first step are used in the camera model that incorporates distortion. However, this method requires identification of observed stars with the catalogue stars. But, on-orbit star identification is difficult as it utilizes the values of camera calibrating parameters that can change in orbit(detector and optical element alignment get change in orbit due to solar pressure or sudden temperature change) from the ground calibrated value. This difficulty is overcome by employing a camera self-calibration technique which only requires four observed stars in three consecutive image frames. Star camera parameters along with lens (radial and decentering) distortion coefficients are determined by camera self calibration technique. Finally Kalman filter is used to refine the estimated data obtained from the LS based method to improve the level of accuracy. We consider the true values of camera parameters as (u0,v0) = (512.75,511.25) pixel, f = 50.5mm; The ground calibrated values of those parameters are (u0,v0) =( 512,512) pixel, f = 50mm; Worst case radial distortion coefficient affecting the star camera lens is considered to be k1 =5 x 10−3 .Our proposed method of attitude determination achieves accuracy of the order of magnitude around 6.2288 x 10−5 rad,3.3712 x 10−5 radand5.8205 x 10−5 rad in attitude angles φ,θ and ψ. Attitude estimation by existing methods in the literature diverges from the true value since they utilize the ground calibrated values of camera parameters instead of true values. To summarize, we developed a formal theory of discrete time Second Order Sliding Mode Observer for uncertain multi-output system. Our methods achieve the desired accuracy while estimating satellite attitude and attitude rate using low fidelity star sensor data. Our methods require lower on-board processing requirement and less memory allocation; thus are suitable for micro-satellite applications. Thus, the objective of using low fidelity star sensor as stand-alone sensor in micro-satellite application is achieved.

Attitude and position determination systems in satellites are absolutely necessary to keep the desired trajectory. A very accurate, reliable and most used sensor for attitude determination is the star tracker, which orient itself in space by observing and comparing star constellations with known star patterns. For on earth tests of movements and docking maneuvers of spacecrafts, the new Spacecraft Maneuvering and Docking (SMD) facility at the chair of Aerospace Information Technology at the University of Würzburg has been built. Air bearing systems on the space ve- hicles help to create micro gravity environment on a smooth surface and simulate an artificial space-like surrounding. A new star tracker based optical sensor for indoor application need to be developed in order to get the attitude and position of the vehicles. The main objective of this thesis is to research on feasible star tracking algorithms for the SMD facility first and later to implement a star detection software framework with new developed voting methods to give the star tracker system its fully autonomous function of attitude determination and position tracking. Furthermore, together with image processing techniques, the software framework is embedded into a controller board. This thesis proposes also a wireless network system for the facility, where all the devices on the vehicles can uniquely communicate within the same network and a devel- opment of a ground station to monitor the star tracker process has also been introduced. Multiple test results with different scenarios on position tracking and attitude determination, discussions and suggestions on improvements complete the entire thesis work.

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