Discussion on Maximum Likelihood-Based Methods for Inertial Sensor Calibration

This paper presents a simple but effective method for inertial parameter identification with symmetrical trifilar pendulum and inertial measurement unit (IMU). An improvement upon conventional pendulum method is described by introducing IMU to identify the orientation of specimen by self-alignment, and then complicated equipment and experimental manipulation are not needed any more. Based on the excellent capacity of motion tracking, the IMU is also used for recording the characteristic of periodic movement by collected the information about acceleration and angular velocity. The main sources of identification errors are discussed from a set of examples. Then an experiment is carried out, and Fourier analysis is used to gain the oscillation period, which made the measurement much more convenient and accurate. The identification results are also presented by comparing with reference values computed from geometrical considerations, which proves the effectiveness of such method.

A steady-state sinusoidal and distortion-free excitation source is very important for the accuracy and consistency of the calibration parameters of micro-electro-mechanical systems (MEMS) inertial sensors. To solve the problem that the current MEMS inertial measurement unit (IMU) calibration device is unable to reproduce the spatial motion of linear and angular vibration coupling, research topics on the coupling vibration characteristics and parameter identification for an electromagnetic linear-angular vibration exciter are proposed. This research paper used Ampere’s law and Lorentz force to establish the analytical expressions for the electromagnetic force and electromagnetic torque of the electromagnetic linear-angular vibration exciter. Then, the main purpose of this paper is to establish uniaxial and coupled vibration electromechanical analogy models containing mechanical parameters based on the admittance-type electromechanical analogy principle, and the parameter identification model is also obtained by combining the impedance formula with the additional mass method. Finally, the validity of the coupling vibration characteristics and the parameter identification model are verified by the frequency response simulation and the additional mass method, and the relative error of each parameter identification is within 5% in this paper.

In this paper, we present a real-time method for identification of the inertial parameters of a humanoid robot and an estimation of its center-of-mass (CoM)and linear and angular momentum. CoM and momentum are important for whole-body motion generation of a humanoid robot and can be used as an indicator of motion planning. Because they are affected by modeling errors and inertia changes (e.g., due to object grasping), it is important to estimate them online. The proposed method has the advantage of being based only on the internal sensors. We verified the effectiveness of the proposal method by applying it to a humanoid robot.

According to the urgent need of high-precision navigation system to future fighters, this paper researches on a dynamic error excitation and calibration method for high-precision IMU. The Kalman filter model including installation errors, scale factor errors and random constant errors of the inertial measurement unit (IMU) as state variables for online identification is established. The relationship between IMU errors and aircraft maneuver manner is derived, and the dynamic flight track to incite IMU errors is designed. Simulation results verify the feasibility of the proposed dynamic error parameter excitation and calibration method, which can incite and identify the IMU error effectively. With the error identification results, the IMU errors are compensated and the precision of the INS is improved significantly.

Accurately calibrate the extrinsic parameters between a camera and an Inertial Measurement Unit (IMU) is a prerequisite for achieving sensor data fusion in visual-inertial navigation systems. Due to delays introduced by triggering, transmission, and other factors, the sampled times of the camera and IMU do not align with the system timestamps, leading to a decrease in the accuracy of extrinsic calibration. Existing calibration methods are unable to avoid the temporal misalignment between the camera and IMU. This paper introduces a novel intermittent calibration sampling method to address temporal misalignment challenges. The approach entails detecting motion-stillness transition points in the IMU data as keyframe segmentation criteria, thereby decoupling data acquisition from system timestamps and aligning it with the sensor’s motion process. Subsequently, the robot hand-eye calibration method is applied to the extrinsic calibration of the Camera-IMU, combining the Random Sample Consensus algorithm to filter the poses of the camera and IMU. This process achieves precise calibration of extrinsic parameters. Experimental validation shows that the algorithm proposed in this paper enhances calibration accuracy when compared to the widely used Kalibr Camera-IMU calibration toolbox. The rotational extrinsic parameter accuracy increased by 181.25%, and the translational extrinsic parameter accuracy improved by 168.33%. These findings provide effective technical means for precise measurement of Camera-IMU extrinsic parameters.

A novel viscoelastic model of four-wire suspension structure with damping gel in an optical pickup actuator was identified and validated. A two-stage method was developed for the identification of inertia, damping, and spring parameters in the dynamic model. The inertia and spring parameters were identified from static tests. With the identified parameters in the dynamic model, the damping parameters were identified through sinusoidal excitation tests. The accuracy of utilizing fractional derivative to model the damping of polymer damper was validated by carrying out error analysis. The fractional transfer function with voltage input was identified and compared with the transfer function of classical model.

SUMMARYA manipulator regressor is an n x l matrix function in the dynamic expression τ = Y r or τ = Wr, which linearizes the robotic dynamics with respect to a properly defined inertia parameter vector ζr є R1. Many modern adaptive controllers require on-line computation of a regressor to estimate the unknown inertia parameters and ensure robustness of the closed-loop system.While the computation of Y is studied by Atkeson, An and Hollerbach1 and Khosla and Kanade,2 the computation of W for a general n–link robot has not been reported in the literature. This paper presents an algorithm to compute W for a general n–link robotic manipulator. The variables used to construct the regressor matrix are directly available from the outward iteration of a Newton-Euler algorithm; some additional arithmetic operations and first-order, low-pass filtering are needed. The identification of unknown inertia parameters is also discussed.

In this article we formulate, in a Lie group setting, the equations of motion for a system of n coupled rigid bodies subject to holonomic constraints. A mapping $f: { \cal {M} \rightarrow \cal {N}$ is constructed, where $\cal M$ is the m-dimensional configuration manifold of the system, and $\cal{N} = \rm{SE(3)} \times \cdots \times \rm{SE(3)}$ (n copies) is endowed with the left-invariant Riemannian metric h corresponding to the total kinetic energy of the system, where SE(3) is the special Euclidean group. The generalized inertia tensor of the system is given by the pullback metric $f^*h$ ; the equations of motion are then the geodesic equations on $\cal M$ with respect to this metric. We show how this coordinate-free formulation leads directly to a factorization of the generalized inertia tensor of the form ${\cal S}^T {\cal L}^T {\cal H} {\cal L} {\cal S}$ , where $\cal S$ is a constant block-diagonal matrix consisting only of kinematic parameters, $\Cal H$ is a constant block-diagonal matrix consisting only of inertial parameters, and ${\cal L}$ is a block lower-triangular matrix composed of Adjoint operators on se(3). Such a factorization is useful for various multibody system dynamics applications, e.g., inertial parameter identification, adaptive control, and design optimization. We also show how in many practical situations ${\cal N}$ can be reduced to a submanifold, thereby considerably simplifying the derivation of the equations of motion. Our geometric formulation not only suggests ways to choose the best coordinates for analysis and computation, but also provides high-level insight into the structure of the equations of motion.

A new dynamic calibration method for IMU deterministic errors of the INS on the Hypersonic Cruise Vehicles

Due to the need for providing low-cost, small-size, and high-reliability calibration solution around the clock independently, the Micro-Electro-Mechanical System (MEMS) inertial measurement unit (IMU) is a hot topic currently. In this paper, we propose a new calibration method based on MEMS IMU with the assistance of the FOG IMU. Different from the traditional MEMS IMU calibration, a Four-Position-and-Three-Rotation (FPTR) calibration sequence is designed in the conditions of lacking turntable. The simulation result shows that all 24 calibration parameters converge through the calibration rotation scheme. An experiment result of qualitative analysis is presented, by comparing the traditional method and proposed calibration method, which reveals the repeatability and stability of the proposed method. In practical applications, this FPTR calibration method can effectively reduce the calibration time and improve the experimental efficiency. In summary, the proposed method is suitable for the mass production calibration of MEMS IMU, and possesses the ability to calibrate full parameters of MEMS IMU at once without turntable or other devices. The research outcomes can provide a practical basis for MEMS IMU plus FOG IMU calibration.

A new probability distribution evolution algorithm (PDE) is proposed for inertial parameters identification of space target. Based on the conservation of angular momentum, the number of space target's inertial unknown parameters is reduced from 10 to 4 by using pseudo inverse operation. The pseudo-inverse solution consistency in multiple groups status is proposed as the optimization evaluation index, and identification simulations are carried out using PDE. A evaluation strategy is given to significantly improve identification accuracy while a small increase of calculation consumption. The statistical results of identification simulation examples show that by only using angular momentum measurement data, the proposed PDE and strategy can achieve the high precision identification for the target inertial parameters with large range change. And PDE is equivalent to the optimization ability of typical evolutionary algorithms, such as genetic algorithm (GE) and differential evolution algorithm (DE).

We present a method of extrinsic calibration for a system of multiple inertial measurement units (IMUs) that estimates the relative pose of each IMU on a rigid body using only measurements from the IMUs themselves, without the need to prescribe the trajectory. Our method is based on solving a nonlinear least-squares problem that penalizes inconsistency between measurements from pairs of IMUs. We validate our method with experiments both in simulation and in hardware. In particular, we show that it meets or exceeds the performance—in terms of error, success rate, and computation time—of an existing, state-of-the-art method that does not rely only on IMU measurements and instead requires the use of a camera and a fiducial marker. We also show that the performance of our method is largely insensitive to the choice of trajectory along which IMU measurements are collected.

Low-cost inertial sensors have been in the focus of ongoing research since they enable a low priced and low complex way to increase the robustness and reliability of navigation systems, especially GNSS. In this paper, we analyze a loosely coupled INS/GNSS including evaluation of the inertial error propagation and robustness of the corresponding navigation integrity concept with respect to the inertial system parameters. Moreover, we analyze the system integrity performance in terms of overall system protection level dependent on the inertial sensor error model. We discuss and compare the expected performance of using either typical high-end, middle-grad, low-cost or a network of redundant low-cost IMUs in terms of integrity and GNSS coasting time. We show that a network of four independent and identical distributed and orthogonally mounted low-cost sensors boosts the integrity performance significantly and even outperforms the one of a higher grade sensor. Additionally we discuss the trade-off between inertial networks and increased system complexity with respect to integrity performance in this paper.

Accurate laser positioning system (ALPS) is widely used in large space indoor dynamic positioning. To improve the positioning accuracy and refresh frequency, the inertial measurement unit (IMU) with a high frame rate is used for fusion, so it is necessary to calibrate the external parameters of ALPS and IMU. Based on the analysis of the calculation process and error description of traditional calibration, we propose a calibration method of spatial multipose transformation (SMT). In this calibration method, the target plate performs multiple attitude transformations to obtain the attitude data and process its error. Then, the Lodrigues matrix is introduced in the solution process to reduce the dimension of unknown variables in the equation, and it is optimized combined with SVD decomposition. At the same time, to further adapt to the application of fusion, a more intuitive error description method is proposed to evaluate the influence of calibration results on fusion accuracy. The simulation experiments indicate that the proposed method enables the calibration error to have accuracy within 0.02 mm. Furthermore, the results of the validation experiments show that the proposed calibration solution method improves in accuracy and robustness with respect to the conventional method. It provides a technical basis for realizing higher precision indoor dynamic positioning applications in large space.

Limited by the principle of multi-angle intersection measurement, photoelectric scanning measurement systems such as workshop Measuring and Positioning System (wMPS) and indoor Global Positioning System (iGPS) have systematical positioning errors when measuring moving targets. Fusing target movement information can effectively compensate the positioning error introduced by the relative motion between the target and the transmitter. Inertial measurement systems are capable of high-frequency, all-weather and autonomous rotation and acceleration measurement. They have good measurement complementarity with photoelectric scanning measurement systems. Integrating movement information from inertial measurement unit (IMU) is an effective method to improve the dynamic measurement performance. Inertial information fusion needs two preconditions: the first one is clock synchronization and the second one is spatial alignment. In response to the two problems above, we research on wMPS and propose a wMPS-IMU integrated online calibration method. The time offset of the two systems is precisely calibrated by compensating the delay between the wMPS reference clock and the IMU clock. Due to the fact that wMPS receivers and the IMU are connected as a rigid body, the rotation R and the translation T between the wMPS and the IMU can be easily calibrated through a linear estimation method. Our novel method benefits to achieve real-time online temporal and spatial calibration without the help of any external measurement equipment and prior information and significantly improves the applicability of wMPS. Verification experiments were carried out. A three-axis turntable and a linear guide were utilized as the roundness and straightness references. The calibration experiment shows that the calibration accuracy of our method is at the same level as that achieved from the high accuracy coordinate measuring machine (CMM). The precision evaluation experiment shows that the hybrid wMPS-IMU system calibrated through the proposed method has slightly better dynamic performance than that calibrated on a CMM. This method is fully verified to be effective.