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The TianQin project is a space gravitational wave detection program proposed by China, imposing strict requirements on inertial sensors. This paper introduces the basic principle and development progress of the TianQin project inertial sensor. At present, key technologies such as test mass, capacitance displacement sensing, and charge management have been developed, with some performance exceeding requirements. Ground-based test systems utilizing torsion pendulums have initially investigated the patch effect, magnetic field effect, residual gas damping, and temperature gradient effect. The inertial sensor is currently undergoing system integration and ground performance tests, and will be tested on TQ-2.

As the key measurement load of Taiji-1 satellite, inertial sensor detects the acceleration disturbance of test mass (TM) under nonconservative force in line with the basic principle of capacitive sensing, while keeping the TM in equilibrium position through electrostatic drive. In order to ensure the smooth progress of the mission, it is necessary to test and evaluate the performance of inertial sensor on the ground. In this paper, a torsion pendulum system is designed to eliminate the influence of the Earth’s gravity so as to meet the requirements of ground test. The experimental results show that the inertial sensor in closed-loop control mode can stably keep the TM at equilibrium position. At the same time, the ground detection of acceleration resolution of inertial sensor is greatly affected by ground vibration noise. If the inertial sensor operates normally in space, its acceleration resolution can reach$3.96\times {10}^{-9}\mathrm{\text{m}}/{\mathrm{\text{s}}}^2/\sqrt{\mathrm{\text{Hz}}}$, thus meeting the requirement of Taiji-1.

The electrostatic suspension control system (ESCS) is the core component of the inertial sensor in space gravitational wave detection. To adapt to the changes in orbit environment and satellite platform vibration, the test mass stable is kept in the center of the electrode cage, the ESCS requires high-precision parameters calibration and high-stability verification of the control system. This paper studied the ESCS method, an adaptive controller with variable preload was proposed, and the stability conditions of the control system are given to provide a theoretical basis for the design of the controller. The structure and working principle of the system were also introduced. The electrostatic control system model was derived, and the performance of adaptive preload controller was analyzed. Finally, a simulation was conducted under different disturbance conditions. The results show that the control method proposed in this paper can achieve stable control in difference disturbance, and the preload voltage will change with the conditions. Compared with the traditional fixed preload method, we can see that our method has significantly improved the stability margin and the control quality during the process of dynamic response. This paper provides a solid foundation for the future exploration of space gravitational waves in China and clears the optimization direction for the next step.

This paper proposes a fusing system consisting of a camera, a line laser, and an inertial measurement unit (IMU) for spatial circle and trunk parameter estimation. The line laser provides a stripe on the object surface that is captured by the camera. When using the system to scan an object, the 3D coordinate points on the surface of the scanned object are calculated with respect to a world coordinate frame by fusing the system movement and laser point coordinates, where the system movement is estimated from the IMU data by solving a smoothing optimization problem. Based on the information from the scanning process, algorithms are derived for detecting the spatial circle’s diameter and the trunk’s parameters. We also performed experiments to verify the feasibility of the system in real applications.

An electrostatically controlled torsion pendulum has been constructed to investigate the performance of the ASTROD I inertial sensor on the ground. The twist motion of the pendulum is monitored by a capacitive transducer and controlled by an electrostatic actuator. The preliminary experimental results show that the torque resolution of the pendulum is 2 × 10^-12 N m Hz^-1/2 at 3 mHz. Further improvements under consideration for the inertial sensor are discussed.

In space-based gravitational wave detection, charge management is used to reduce unwanted electrostatic noise by controlling the absolute charge of the test mass (TM). However, the charge management process will cause periodic interruptions in the scientific measurements. In order to minimize the frequency and influence of the interruptions, this paper proposes a method to optimize the electrostatic noise by adding a common voltage to all the actuation electrodes, to precisely adjust the potential difference between the TM and the electrodes. Theoretical analyses and simulation evaluations indicate that the permissible limit of accumulated charge on the TM can be extended from $10^7$ e to $10^8$ e, while maintaining the same electrostatic noise requirement level of $4\times 10^{-16}$ m/s²/Hz${}^{1/2}$. This approach shows that it allows a tenfold extension of the charge management period, significantly reducing interruptions in gravitational wave detection.

We propose a novel self-assisted rehabilitation system for the upper limbs of stroke patients. The system mainly includes two haptic devices (PHANTOM Omni), an advanced inertial sensor (MTx) and a computer. The inertial sensor is used to get the real-time orientation of one of the manipulator's hands, and the haptic devices are used to get the real-time positions of the manipulator's two hands and generate the appropriate forces that act on the two hands. We have built a virtual force model to get the accurate magnitude and orientation of the forces. With the change of the position and orientation of the manipulator's hands, the magnitude and orientation of the forces will change accordingly. The manipulator operates the styluses of the two haptic devices to control the position and orientation of the virtual object m, so that it can track the virtual object m′, which moves and rotates randomly in 4 degree-of-freedoms (DOF). It is expected to improve the agility and strength of manipulator's hands in this way. Furthermore, one hand can be used to assist the other one in the rehabilitation, so the self-assistance character is included in the system. The advantages of high safety, compaction and self-assistance will make the system suitable for home rehabilitation.

The Lunar Gravitational–Wave Antenna is a proposed low–frequency gravitational–wave detector on the Moon surface. It will be composed of an array of high-end cryogenic superconducting inertial sensors (CSISs). A cryogenic environment will be used in combination with superconducting materials to open up pathways to low–loss actuators and sensor mechanics. CSIS revolutionizes the (cryogenic) inertial sensor field with a modelled displacement sensitivity at 0.5 Hz of 3 orders of magnitude better than the current state–of–the–art. It will allow the Lunar Gravitational–Wave Antenna to be sensitive below 1 Hz, down to 1 mHz and it will also be employed in the forthcoming Einstein Telescope—a third-generation gravitational–wave detector which will make use of cryogenic technologies and that will have an enhanced sensitivity below 10 Hz. Moreover, CSIS seismic data could also be employed to obtain new insights about the Moon interior and what we can call the Selene-physics.

We present a new design for the mobile and robust gravimeter GAIN (Gravimetric Atom Interferometer), which is based on interfering ensembles of laser cooled ⁸⁷Rb atoms in an atomic fountain configuration. With a targeted accuracy of a few parts in 10¹⁰ for the measurement of local gravity, g, this instrument would offer about an order of magnitude improvement in performance over the best currently available absolute gravimeters. Together with the capability to perform measurements directly at sites of geophysical interest, this will open up the possibility for a number of interesting applications. We report on important subsystems of this atom interferometer, including a rack-mounted laser system and a compact vacuum chamber. Furthermore, a high flux 2-dimensional Magneto-optical trap capable of providing up to 10¹² atoms/second and a high-power laser system providing 6.4 W at 780 nm are presented.

The Gross Ring G is a ring-laser, it is located in the geodetic observatory of Wettzell. It has demonstrated that a ring laser has a sensitivity and stability such to measure the Earth rotational rate with the relative precision of 5 part in 10⁹ and a long term stability of 3 hours. The GINGER project is intending to take this level of sensitivity further and to improve the long-term stability. A factor of about 10 improvement in sensitivity could allow the observation of the frame dragging produced by the Earth rotating mass (Lense- Thirring effect), and predicted by General Relativity. At the same time GINGER will provide a local measurement of the Earth rotational rate with a sensitivity comparable to that of the International Earth Rotation and Reference Systems Service (IERS). In GINGER the stability of each ring and the relative alignment of the different rings play a crucial role. Therefore the preliminary goal is the demonstration of the feasibility of a larger gyroscope structure, where the mechanical stability is obtained through an active control of the geometry. A ring-laser prototype (GP-2) has been set up in Pisa in order to develop and test the active control of the ring geometry, while a second apparatus (GINGERino) has been installed inside the Gran Sasso underground laboratory in order to investigate the seismic noise of the site in view of an installation of GINGER. The status of both prototypes is presented.

An electrostatic-control led torsion pendulum was constructed to test the in-flight performance of an electrostatic inertial sensor on ground. An electrostatic-controlled torque resolution of 6 × 10^-13 N m Hz^-1/2 and a force resolution of 3.6 × 10^-11 N Hz^-1/2 from 2 mHz to 0.1 Hz were achieved.