On the Interpretation of 3D Gyroscope Measurements

We demonstrate that the common interpretation of angular velocities measured by a 3D gyroscope as being sequential Euler rotations introduces a systematic error in the sensor orientation calculated during motion tracking. For small rotation angles, this systematic error is relatively small and can be mistakenly attributed to different sources of sensor inaccuracies, including output bias drift, inaccurate sensitivities, and alignments of the sensor sensitivity axes as well as measurement noise. However, even for such small angles, due to accumulation over time, the erroneous rotation interpretation can have a significant negative impact on the accuracy of the computed angular orientation. We confirm our findings using real-case measurements in which the described systematic error just worsens the deleterious effects typically attributed to an inaccurate sensor and random measurement noise. We demonstrate that, in general, significant improvement in the angular orientation accuracy can be achieved if the measured angular velocities are correctly interpreted as simultaneous and not as sequential rotations

On-Manifold Preintegration for Real-Time Visual-Inertial Odometry

Current approaches for visual-inertial odometry (VIO) are able to attain highly accurate state estimation via nonlinear optimization. However, real-time optimization quickly becomes infeasible as the trajectory grows over time, this problem is further emphasized by the fact that inertial measurements come at high rate, hence leading to fast growth of the number of variables in the optimization. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes into single relative motion constraints. Our first contribution is a \emph{preintegration theory} that properly addresses the manifold structure of the rotation group. We formally discuss the generative measurement model as well as the nature of the rotation noise and derive the expression for the \emph{maximum a posteriori} state estimator. Our theoretical development enables the computation of all necessary Jacobians for the optimization and a-posteriori bias correction in analytic form. The second contribution is to show that the preintegrated IMU model can be seamlessly integrated into a visual-inertial pipeline under the unifying framework of factor graphs. This enables the application of incremental-smoothing algorithms and the use of a \emph{structureless} model for visual measurements, which avoids optimizing over the 3D points, further accelerating the computation. We perform an extensive evaluation of our monocular \VIO pipeline on real and simulated datasets. The results confirm that our modelling effort leads to accurate state estimation in real-time, outperforming state-of-the-art approaches.Comment: 20 pages, 24 figures, accepted for publication in IEEE Transactions on Robotics (TRO) 201

Development of an analytical model for rotational vector of a sphere using MEMS inertial sensors

Microelectromechanical Systems (MEMS) based inertial sensors are finding greater applications in sensing position, orientation and motion in automotives, aerospace and consumer electronics [1]-[2]. One particular MEMS inertial sensor is an inertial measurement unit (IMU), which is an integrated chip consisting of a tri-axis gyroscope and tri-axis accelerometer. A gyroscope can sense rate of rotation in a particular axis while an accelerometer can measure the acceleration in an axis. IMUs are used to find the complete motion data which can be processed with appropriate algorithm to find orientation or navigation [3]. The focus of this research is to use a MEMS IMU to find the rotational velocity of a sphere and its axis of rotation. This research aims to build a model using detected motion data from the IMU then use it to calculate the rotation vector (speed and orientation) of an object, so that a great quantity of applications could be achieved. One of these applications we are researching is to detect the rotation of a sphere. Rotation about an arbitrary axis had been researched, however, to calculate the rotation axis from the detected IMU motion data is challenging and has not been addressed in the literature. To solve the problem, we used linear algebra as the tool to calculate the rotation matrix by dividing a 3-D rotation into several pieces of 2-D rotation [4]. The rotation motions were represented as a matrix, which could simplify the process of calculation. Simultaneous orthogonal rotation angle (SORA) concept was also important in this research because it is well-suited to calculate real-time rotation vectors [5]. As 3-D rotations in general are not commutative, the results of an improper sequential addition of the 3 rotation motions in 3-D would lead to a wrong orientation. However, only if the rotation angle is infinitely small, then the error could negligible because they are nearly commutative. Therefore, we divided the rotation angles into infinitesimally small rotations then we integrated the three rotations together. In the experiments, an IMU was placed on a spherical object and mounted on top of a rotating table. The information from IMU was sampled at 375Hz and was collected by a coupled microprocessor. The IMU data provided raw information about dynamic motion in all three axes. Using the IMU data and SORA algorithm the rotational axis and velocity of a moving rotational sphere was found. The outcome of this research achieved to detect rotation axis based on IMU sensors, which was impossible in the past. Key words: MEMS, IMU, SORA, Gyroscop

Quaternionic Attitude Estimation with Inertial Measuring Unit for Robotic and Human Body Motion Tracking using Sequential Monte Carlo Methods with Hyper-Dimensional Spherical Distributions

This dissertation examined the inertial tracking technology for robotics and human tracking applications. This is a multi-discipline research that builds on the embedded system engineering, Bayesian estimation theory, software engineering, directional statistics, and biomedical engineering. A discussion of the orientation tracking representations and fundamentals of attitude estimation are presented briefly to outline the some of the issues in each approach. In addition, a discussion regarding to inertial tracking sensors gives an insight to the basic science and limitations in each of the sensing components. An initial experiment was conducted with existing inertial tracker to study the feasibility of using this technology in human motion tracking. Several areas of improvement were made based on the results and analyses from the experiment. As the performance of the system relies on multiple factors from different disciplines, the only viable solution is to optimize the performance in each area. Hence, a top-down approach was used in developing this system. The implementations of the new generation of hardware system design and firmware structure are presented in this dissertation. The calibration of the system, which is one of the most important factors to minimize the estimation error to the system, is also discussed in details. A practical approach using sequential Monte Carlo method with hyper-dimensional statistical geometry is taken to develop the algorithm for recursive estimation with quaternions. An analysis conducted from a simulation study provides insights to the capability of the new algorithms. An extensive testing and experiments was conducted with robotic manipulator and free hand human motion to demonstrate the improvements with the new generation of inertial tracker and the accuracy and stability of the algorithm. In addition, the tracking unit is used to demonstrate the potential in multiple biomedical applications including kinematics tracking and diagnosis instrumentation. The inertial tracking technologies presented in this dissertation is aimed to use specifically for human motion tracking. The goal is to integrate this technology into the next generation of medical diagnostic system

Real-time manhattan world rotation estimation in 3D

Drift of the rotation estimate is a well known problem in visual odometry systems as it is the main source of positioning inaccuracy. We propose three novel algorithms to estimate the full 3D rotation to the surrounding Manhattan World (MW) in as short as 20 ms using surface-normals derived from the depth channel of a RGB-D camera. Importantly, this rotation estimate acts as a structure compass which can be used to estimate the bias of an odometry system, such as an inertial measurement unit (IMU), and thus remove its angular drift. We evaluate the run-time as well as the accuracy of the proposed algorithms on groundtruth data. They achieve zerodrift rotation estimation with RMSEs below 3.4° by themselves and below 2.8° when integrated with an IMU in a standard extended Kalman filter (EKF). Additional qualitative results show the accuracy in a large scale indoor environment as well as the ability to handle fast motion. Selected segmentations of scenes from the NYU depth dataset demonstrate the robustness of the inference algorithms to clutter and hint at the usefulness of the segmentation for further processing.United States. Office of Naval Research. Multidisciplinary University Research Initiative6 (Awards N00014-11-1-0688 and N00014-10-1-0936)National Science Foundation (U.S.) (Award IIS-1318392

An Auto-Calibrating Knee Flexion-Extension Axis Estimator Using Principal Component Analysis with Inertial Sensors

Inertial measurement units (IMUs) have been demonstrated to reliably measure human joint angles—an essential quantity in the study of biomechanics. However, most previous literature proposed IMU-based joint angle measurement systems that required manual alignment or prescribed calibration motions. This paper presents a simple, physically-intuitive method for IMU-based measurement of the knee flexion/extension angle in gait without requiring alignment or discrete calibration, based on computationally-efficient and easy-to-implement Principle Component Analysis (PCA). The method is compared against an optical motion capture knee flexion/extension angle modeled through OpenSim. The method is evaluated using both measured and simulated IMU data in an observational study (n = 15) with an absolute root-mean-square-error (RMSE) of 9.24∘ and a zero-mean RMSE of 3.49∘. Variation in error across subjects was found, made emergent by the larger subject population than previous literature considers. Finally, the paper presents an explanatory model of RMSE on IMU mounting location. The observational data suggest that RMSE of the method is a function of thigh IMU perturbation and axis estimation quality. However, the effect size for these parameters is small in comparison to potential gains from improved IMU orientation estimations. Results also highlight the need to set relevant datums from which to interpret joint angles for both truth references and estimated data.National Science Foundation (U.S.) (GRFP)National Science Foundation (U.S.) (IIS-1453141