3D Trajectory Calculation in Crash Testing Using Inertial Sensors

Optical motion-tracking systems are an accurate method of capturing motion of a body traveling through a 3-dimensional (3D) space. There are several disadvantages of these systems, including cost, the time consumed in performing the tracking, and especially the requirement of a constant line of sight between the cameras and the tracked object throughout the analyzed event. An alternative to optical based tracking is an approach that utilizes body local acceleration and angular velocity recorded by inertial measurement units (IMUs).
The advancement in the MEMS technology allowed for small, light and inexpensive accelerometers and angular rate sensors to be more accessible. Data from these sensors can be utilized to obtain the position and orientation of the body on which they are attached. Even though sensor-based motion capture offers many benefits, it has been shown to be less accurate than optical motion-tracking due to multiple types of signal and sensor errors and uncertainty associated with the initial orientation of tracked body. In addition, there are multiple numerical formulas (for example the one that is utilized to obtain body’s orientation) that can be used as part of the trajectory calculation algorithm but there is no consensus on how these different methods affect the resulting sensor-based position estimation.
Even though sensor-based tracking has its limitations, research has shown that it can be a promising alternative to optical capture systems under certain conditions. Before the IMU-based position estimation can replace more costly and time-consuming optical motion capture, the accuracy of trajectories obtained from processed IMU data needs to be improved and the reasons behind errors in sensor-based predictions better understood, so that the method can be employed in a way to facilitate its success.
This dissertation presents the development of an algorithm that can be used to compute 3D component trajectories of a rigid body – based on locally-mounted inertial sensors – for applications in vehicle crash tests with anthropomorphic test devices. In addition to the algorithm, this dissertation identifies different correction techniques that could be used to minimize the error in the calculated trajectory when sensor readings are affected by measurement inaccuracies. These goals were accomplished through the following tasks. The first task focused on assembling a training set for verification and validation of the proposed algorithm using data from progressively more complex impact scenarios. Next, from different methods identified in the literature, the most accurate technique of updating body orientation based on body’s angular rate (Task 2) as well as the most accurate method of obtaining body’s local angular acceleration (Task 3) were identified. In Task 4, a comprehensive study investigating the influence of different error types on the IMU-based trajectories was carried out. In the final task, different techniques that could be used to minimize the error in the calculated trajectory were evaluated.
Analysis from Task 2 indicated two algorithms based on the Euler parameters as the most accurate methods of updating body’s orientation. In addition, the analysis showed that the accuracy of the method used to update body’s orientation depends strongly on the accuracy of the numerical integration scheme utilized in the orientation algorithm. Investigation from Task 3 identified the approach based on differentiation of the local angular velocity as the method that gave the smallest deviation from the reference (from an optical motion capture system) position data. The analysis from Task 4 described the errors in the debias values for linear accelerometers and angular rate sensors, the error in accelerometer sensitivity, as well as the error in initial orientation as error types that can have the most substantial effect on the IMU-based trajectory estimation. The error analysis also showed that by adding two redundant angular rate sensors to a standard “3 ACC + 3 ARS” package, an angular rate sensor with errors in its signal can be identified. Similarly, by adding two redundant linear accelerometers, an accelerometer with a faulty response can be pinpointed. When (in Task 5) either optimization of initial orientation angles in combination with the debias values for linear acceleration data was performed, or known information about 3D position of the tracked body was introduced into the trajectory calculation algorithm, a substantial improvement in the accuracy of the computed position of the tracked body was achieved. Even when only three data points with known position were used throughout the analysis, the position error (when compared to a test without these three points) decreased by more than 93% and the maximum absolute difference for all three trajectory components stayed below 5.5 mm when matched against reference data from the optical system. Finally, in Task 5 two techniques of interpolating an optical data gap were investigated.
This dissertation focused on crash scenarios mainly, but its findings and conclusions can be extrapolated and applied in many other fields, ranging from gait and sport studies, through clinical trials and animal motion analysis, to tracking underwater or underground autonomous vehicles.