1 Introduction In the study of biomimetic propulsion mechanisms, accurate measurement of fish tail fin flapping parameters is of great significance for the research and engineering application of fish biomimetic propulsion mechanisms; however, most researchers currently use observation methods to obtain parameters by analyzing images captured by high-speed cameras. This method is limited by the environment and equipment, resulting in poor accuracy. This design is a micro-inertial measurement device for biological motion based on MEMS devices. Using this device, the accurate measurement of the tail fin flapping parameters of the SPC-III robotic fish was achieved, laying the foundation for the first domestic experiment using MEMS devices to measure the tail fin flapping parameters of live fish, and providing support for the design theory of biomimetic propulsion for robotic fish. Based on the biological characteristics of live fish and the characteristics of the experiment itself, the micro-inertial measurement device should meet the following design requirements: small size, light weight, low power consumption, high acquisition frequency and accuracy, and good waterproof sealing performance. To achieve these requirements, the hardware of the micro-inertial measurement device consists of two parts: ① a microprocessor unit; ② a micro-inertial sensor unit. The microprocessor unit mainly includes a microprocessor, an A/D conversion chip, and Flash memory. The microprocessor, as the core unit, connects to the A/D converter chip via the SP1 port to complete data acquisition, connects to the Flash memory via the SP10 port to complete data storage, and communicates with the host computer via a serial port. The micro inertial sensor unit consists of a MEMS accelerometer and a MEMS gyroscope, which completes the task of acquiring raw acceleration and angular velocity information. After the acquired raw information is processed by A/D conversion, it is written into the Flash chip for storage, or sent directly to the host computer for processing via the serial port. The simplified system principle diagram is shown in Figure 1. 2 Microprocessor Unit 2.1 LPC2129 Processor This device requires the microprocessor to have certain processing power while also requiring low power consumption and small size, so Philips' LPC2129 was selected. The LPC2129 is based on a 16/32-bit ARM7TDMI-S CPU that supports real-time simulation and tracking, and has 16 KB of on-chip SRAM and 256KB of embedded high-speed on-chip Flash memory. The LPC2129 features a small LQFP64 package, extremely low power consumption, multiple 32-bit timers, four 10-bit ADCs, nine external interrupts, and up to 46 GPIOs. In its software design, the LPC2129 does not use the uC/OS-II or uClinux operating systems commonly found on ARM processors, but instead employs a foreground/background timer/interrupt architecture. This foreground/background architecture is more suitable for control systems with high real-time requirements, ensuring that control loop delays remain within a defined range, and that the priority relationships between modules are clearly defined, making it easier to use. 2.2 A/D Conversion and Acquisition Chip ADS1256 The A/D conversion chip used is the 24-bit serial analog-to-digital converter ADS1256 from Texas Instruments (TI). It provides up to 23 bits of noise-free accuracy and a data rate of up to 30 ksps. The ADS1256 uses a four-wire SPI communication method, connecting to the LPC2129's SPI1 interface for flexible and convenient communication. The ADS1256 employs a multi-channel cyclic acquisition mode. After the data preparation signal DRDY indicates that data can be extracted, the current acquisition channel is first changed to the next acquisition channel, a new acquisition and conversion begins, and then the data in the A/D conversion register is immediately extracted (this data is actually the data converted in the previous round). This method performs new data acquisition and conversion simultaneously with data extraction, making it a highly efficient working method. 2.3 Flash Chip AT45DB041B The Flash chip used is the Atmel AT45DB041B programmable serial access chip. The main memory unit is divided into 2048 pages, each page being 264 bytes; it has two 264-byte static random access memories as data buffers. The AT45DB041B is connected to the SPI0 interface of the LPC2129. The acquired data is first written to the Flash buffer 2, and then the data in the buffer is written to the Flash main memory page for storage, to be processed offline. 3 Micro Inertial Sensor Unit The MEMS sensor unit of the micro inertial measurement device consists of a micro-mechanical gyroscope and a micro accelerometer, which can accurately measure one axial angular velocity and one axial acceleration of the carrier. 3.1 ADXRS300 Single Angular Velocity Gyroscope The ADXRS300 is an angular velocity sensor based on MEMS technology manufactured by Analog Devices. The ADXRS300 is powered by a +5V power supply, measures yaw angular velocity within a range of ±300 rad/s, has a sensitivity of 5 mV/(rad·s⁻¹), and a zero-point output voltage of 2.5V. The measurement range, bandwidth, and zero-point output voltage can be set using external resistors and capacitors. It uses BGA-32 packaging technology, with external dimensions of only 7mm × 7mm × 3mm and a weight of only 0.5g. Let the measured angular velocity be αv (°/s); the output voltage be Uo (mV); the sensitivity K be 5 mV/(°·s⁻¹); and the zero-point output voltage be 2.5V, then the following relationship exists: 3.2 ADXL150 Single-Axis Accelerometer The ADXL150 is a single-axis micro-accelerometer based on MEMS technology manufactured by Analog Devices. The main performance characteristics of ADXL150 are: zero-position output bias voltage of Us/2, measurement range of ±50g, sensitivity coefficient of 38mV/g, nonlinearity of 0.2%, and zero acceleration drift of 0.2g; it can operate with a power supply of 4-6V; it has very low power consumption, with a static current of only 1.8-3.5mA. Let the measured acceleration be av (g); the output voltage be Uo (mV); the sensitivity be K (mV/g); and the power supply voltage be Vs (mV), then the following relationship exists: 4. Measurement Principle of Velocity, Angle, and Displacement After integrating and processing the angular velocity and acceleration information, information such as angle, velocity, and displacement can be obtained. Therefore, based on the ability to measure the angular velocity and acceleration information of the carrier, this device can realize the measurement of various motion state information of the carrier. Let the sampling period be T, v(k) be the velocity at time kT, x(k) be the displacement at time kT, a(k) be the acceleration at time kT, and a(k) be the continuous true value of the acceleration. Then, we have the following integral formula for solving the velocity: The area enclosed within the interval [kT, (k+1)T]. Given that the sampled values ​​of the acceleration at times kT and (k+1)T are a(k) and a(k+1), we can approximate the shape enclosed by the acceleration a(t) within the time interval [kT, (k+1)T] as a rectangle or trapezoid. Using a trapezoid is more accurate, as shown in Figure 2. Therefore, the above formula can be approximated as: Given that the A/D sampling period is t, and at a certain time T1, the angular velocity of the carrier is w1, the linear acceleration is a1, and the linear velocity is v1. After one sampling period t, at time T1+t, the angular velocity of the carrier is w2, the linear acceleration is a2, and the linear velocity is v2. During this sampling period t, the angle through which the carrier rotates is α, and the displacement of the carrier is s. Therefore, the angle, velocity, and displacement of the carrier can be obtained through integration. 5. Application 5.1 System Integration The micro inertial measurement device consists of a processor unit module and a sensor unit module. The two modules are connected via an inter-board bus and are staggered to maximize space utilization and achieve miniaturization. The device is powered by a 7.2V lithium battery. The final packaged device weighs only 25g. Upper computer data processing software was developed using NI's LabWindows/CVI software. The data processing software reads the velocity information collected by the micro inertial measurement device, generates velocity/angle and displacement curves, and obtains the carrier's swing angle and amplitude values. 5.2 SPC-III Robotic Fish Tail Fin Flapping Parameter Measurement Experiment The micro inertial measurement device was used to conduct a measurement experiment on the tail fin flapping parameters of the SPC-III robotic fish developed by the ITM Laboratory of the Robotics Institute of Beijing University of Aeronautics and Astronautics. A micro-inertial measurement device was installed at the caudal peduncle of the robotic fish's tail fin, and the acquisition frequency of the device was set to 1 kHz. When the SPC-III robotic fish was stably flapping at a frequency of 1 Hz, the acquired data was processed by the host computer's data processing software to obtain the tail fin flapping parameters of the SPC-III robotic fish: flapping frequency 1 Hz, swing angle amplitude 41.70°, amplitude 97.368 mm, and maximum angular velocity 124.264 (°)/s. The angular velocity curves are shown in Figures 3 and 4. Table 1 shows that the measured data are not significantly different from the theoretical design values. Possible causes of error include: inherent error biases in the gyroscope and accelerometer, including zero-position error and dynamic error; and the tail fin flapping mechanism of the robotic fish is not very precise, resulting in deviations. Based on the estimation method for fish tail fin thrust, the average thrust generated by the tail fin of the SPC-III robotic fish when flapping at a frequency of 1 Hz was estimated to be 10 N, as listed in Table 2. The SPC-III robotic fish employs a two-jointed parallel mechanism tail fin thruster that generates tens of Newtons of thrust. The actual thrust largely matches the estimated thrust, preliminarily validating the tail fin thrust estimation method based on ideal thruster theory and the momentum theorem. Even without water tunnel model testing or CFD hydrodynamic simulation, this method can quickly and easily obtain an estimate of the tail fin thrust or inversely solve for the tail fin's motion parameters. This thrust estimation method has been successfully applied to the design and experimental work of the SPC series robotic fish at the ITM Laboratory of Beijing University of Aeronautics and Astronautics. Conclusion A micro-inertial measurement device based on MEMS devices can be used to accurately measure the tail fin flapping parameters of the SPC-III robotic fish. The micro-inertial measurement device is small, lightweight, and low-power, and can obtain motion information such as acceleration, angular velocity, velocity, displacement, and angle of the carrier. It can be applied to various fields such as biological motion measurement, sports measurement, and human health monitoring.