## 1 Introduction  
As satellite-communication-related technologies continue to prosper, spaceborne antennas (usually deployable) are confronted with great challenges regarding the increasing demand for higher frequency in diverse fields, which involve but are not limited to telemetry, tracking and control (TT&C), remote sensing, radio astronomy, etc. During the past several decades, cable network antennas (CNAs) [1, 2, 3, 4, 5, 6, 7, 8, 9], represented by AstroMesh [10], have been dominating among several deployable antenna concepts due to their distinctive advantages of being lightweight and having a high stowing efficiency. According to the existing studies, the surface accuracy of these antennas usually stays at the millimeter level [1, 11, 12, 13, 14, 15, 16], corresponding to the L-S operating frequency band. If adopting various delicate structures (such as an umbrella-type structure [17, 18, 19, 20]) or sophisticated adjustment approaches [11, 12, 13, 16, 21, 22, 23, 24], small-aperture CNAs are capable of achieving an accuracy of 0.3-1 mm, with which its maximum operating frequency can reach the Ka band. However, the requirement for antenna operating frequency has been increasing invariably, which has far exceeded the Ka band, and even increased to the terahertz band. According to [PERSON]'s formulation [25], if the antenna operating frequency exceeds the Ka band with 5% gain loss, the antenna surface accuracy shall be no less than 0.125 mm and/or even reach the micron level if the operating frequency is in the terahertz band. As a result, the CNAbecomes inappropriate for higher frequency beyond the Ka band. In view of the above challenges, the long-neglected rigid-reflector spaceborne antennas (RRSAs) perfectly fit this situation since the accuracy of the panels composing their reflectors can be machined to the micrometer level using modern processing techniques. This extraordinary accuracy guarantees the highest operating frequency attaining the terahertz band [26; 27]. Several kinds of RRSAs had been proposed since the 20 th century, which differ in the segmentation of their reflective surfaces. Specifically, their types can be categorized as the sunflower [28], the solid surface deployable antenna (SSDA) [29; 30] and the petal-type deployable antenna (PTDA) [26; 31; 32; 33; 34; 35; 36; 37; 38], respectively. Among them, the former two types, ever since they were first proposed, drew little interest due to their various intrinsic structural deficiencies involving but not limited to complicated structures, lack of back frame, etc. In contrast to those two types, the third one has been most widely adopted owing to its maintainability, element universality and mutual dynamic balance in deployment [39]. Regarding its segmentation scheme, the reflector of the PTDA is segmented into multiple identical parts (usually known as petals) in the radial direction, with the rest in the center functioning as the central hub. Despite several companies and universities proposing their exclusive PTDAs and manufacturing the corresponding experimental prototypes, respectively [28; 31; 32; 40], none of them had been implemented in practical application scenarios so far. In 2011, Russia successfully launched the Spektr-R satellite (RadioAstron) [34; 41; 42] to conduct interferometer observation tasks. Combined with the global ground radio telescope network, the satellite can achieve extraordinarily high angular resolution to obtain images, coordinates, motions and evolution of the angular structure of different radio-emitting objects in the Universe. The antenna of the satellite is characterized with a 10 m diameter and 3.33 deploy/fold ratio, and was the largest space-based rigid-reflector antenna ever recorded. In addition, its reflector is composed of 27 carbon-fiber petals together with a central dish, and its 0.3 mm surface accuracy enables its operating frequency to reach up to the Ka band. According to the related literature, its deployment is conducted by rotating all the petals around their respective skew axis [39].