## 1 Introduction
The only data available from the determination section is the angle of the Sun with respect to the solar arrays normal, and the control direction is guessed by a properly sequenced and pulsed control modulation algorithm. The purpose of the research is to have a very basic ADCS, capable to work with a minimal hardware set, in a way to sustain the spacecraft power generation even in the worst-case survival mode scenario. This is motivated by the need to increase the spacecraft reliability, especially when many redundant components cannot be installed on-board, such as in small satellite platforms [1; 2]. The problem of spacecraft ADCS is technologically mature, and existing literature contains many references and dedicated handbooks [3; 4]. Classical attitude determination methods are based on vector measurements of known physical quantities and celestial objects locations [5]. At least two vector measurements are needed to determine the complete three-dimensional attitude state [6; 7], with different estimation methods [8]. This is well established in-flight applications [9; 10], even with very basic sensor components [11]. Analogously, attitude control has an endorsed heritage since the 70's of the last century [12]. Various control methods have been proposed [13; 14; 15], and applications to small spacecraft have become very common [16]. Moreover, diverse actuation methods have been deeply investigated [17; 18; 19; 20]. However, according to previous literature, a spacecraft with only Sun angle and angular rates measurements would be not capable to align its solar arrays to the Sun. Existing works already exploited solar cells as sources of Sun direction information [21; 22], and even common industrial applications retrieve the Sun angles in body reference frame from the electric power data to have a coarse Sun direction estimation. This is commonly accomplished by exploiting solar cells oriented towards all the six reference frame directions (i.e., positive, and negative axes directions). In this way, by combining all the independent power measurements, the complete three-dimensional Sun direction unit vector is easily available, and a standard attitude determination and control subsystem can be implemented. Indeed, solar cells data have been exploited to implement a complete attitude determination subsystem [23], but incomplete Sun direction information always introduced complexity in the mathematical formulation of the attitude determination problem [24]. The application of the proposed algorithm to a non-nominal operative scenario, or to extremely simple small satellites, cannot rely on computationally expensive estimation techniques. Furthermore, the attitude determination problem could not be completely solved with respect to the full attitude state, if only mono-directional solar array data are available, as assumed in this research work. Namely, the incomplete Sun direction estimation is the single output of the proposed determination algorithm, to be used by the control section. The solar arrays and angular rates only ADCS algorithm presented in this work has been also included in a complete multi-mode ADCS for small satellite platforms developed by the authors [25; 26], which underwent a complete validation, verification, and testing campaign to assess the performance of the proposed methods. The paper briefly introduces the mathematical formulation behind attitude dynamics, determination, and control for spacecraft orbiting around planetary bodies in Section 2. This is done to support the discussion of the proposed algorithms with a larger audience of readers, who can refer to classic spacecraft attitude books for further references [3; 4]. The proposed attitude determination and control architecture is then described in Section 2.1, with a specific focus on the developed solar arrays pointing attitude determination and control algorithms, which are detailed in Section 3. The Sun pointing performance is first outlined in Section 3.3 for the ideal case, without measurement noise and actuation errors.