## 1 Introduction  
Aerospace vehicles and the space environment interact to produce vibrations, while the normal operation of the various subsystems (moving parts) within the spacecraft also generates disturbances [1, 2, 3]. These disturbances are transmitted through the structure to the sensitive instruments carried by the spacecraft, which are responsible for navigation, measurement, pointing, imaging, observation, and other tasks. The sensitive instruments include high-precision equipment like space cameras and space telescopes [4, 5]. The minute vibrations can affect the accuracy and reliability of these high-precision sensitive instruments, potentially impacting the entire spacecraft's maneuverability and data transmission capabilities. To ensure that sensitive instruments operate stably and reliably, it is essential to provide them with an ultra-quiet mechanical environment [6, 7]. Appropriate technical measures to reduce the transmission of external vibrations and internal disturbances from the spacecraft to the sensitive instruments are required [8]. During the movement of spacecraft, disturbances are generated from multiple directions simultaneously, which requires a vibration isolation system with the ability of isolating vibrations from multiple directions at the same time [9]. Among the multi-degree-of-freedom vibration isolation systems, the Stewart platform is the most commonly used structural form. Multi-dimensional vibration isolation platforms are mostly three-bar, four-bar, five-bar, six-bar, and eight-bar parallel structures [10; 11]. The parallel platforms that can achieve six-degree-of-freedom vibration isolation are mostly based on the Stewart parallel structure. The Stewart structure was first applied in flight simulation [12]. Compared with its application as a motion platform and parallel operation mechanism, its application in active vibration isolation research is relatively late, and there are significant differences in the control methods [13]. The Free University of Brussels has developed a rigid active damping operation platform that simultaneously uses piezoelectric sensors and piezoelectric actuators, which can perform active vibration isolation and precise directional operation at the same time [14]. In addition, Xi'an Jiaotong University has also developed a soft active vibration isolation platform, with voice coil motors as actuators [15]. The gapless flexible hinges and force sensors are used to measure the main force in real time. The result of weightlessness experiment verified that the vibration isolation performance is excellent, and the active vibration isolation can attenuate resonance peaks, while most of the vibration is suppressed and isolated by passive vibration isolation [16]. The Swiss Center for Electronics and Microtechnology has developed a multi-target active vibration isolation platform MAI for space laser communication [17; 18]. This platform can suppress vibrations from 50 Hz to 500 Hz, but its effect on lower frequency vibrations is poor. Moreover, the system's low load capacity (2.2 kg) also limits its large-scale application. Active and passive hybrid vibration isolation [19] refers to the combination of active and passive vibration isolation. There are many specific combination methods. Researchers have combined active and passive vibration isolation elements in different forms, and designed many different hybrid vibration isolators for application in related fields. [PERSON] [20] proposed a vibration isolator combining an electromagnetic actuator and elastic plate structure. Based on Maxwell normal stress, the vibration isolator can produce negative stiffness characteristics. [PERSON] [21] designed a hybrid vibration isolation system by combining rubber vibration isolation elements and piezoelectric actuators. The robust synovial control method was used to conduct experiments, which could achieve wide frequency isolation in the frequency range of 20-2000 Hz in the uniaxial direction, and the vibration attenuation at the resonance peak reached 22 dB.