IMU: Inertial sensing of vertical CoM movement

doi:10.1016/j.jbiomech.2009.03.049

Journal of Biomechanics

Volume 42, Issue 10, 22 July 2009, Pages 1578-1581

https://doi.org/10.1016/j.jbiomech.2009.03.049 Get rights and content

Abstract

The purpose of this study was to use a quaternion rotation matrix in combination with an integration approach to transform translatory accelerations of the centre of mass (CoM) from an inertial measurement unit (IMU) during walking, from the object system onto the global frame. Second, this paper utilises double integration to determine the relative change in position of the CoM from the vertical acceleration data. Five participants were tested in which an IMU, consisting of accelerometers, gyroscopes and magnetometers was attached on the lower spine estimated centre of mass. Participants were asked to walk three times through a calibrated volume at their self-selected walking speed. Synchronized data were collected by an IMU and an optical motion capture system (OMCS); both measured at 100 Hz. Accelerations of the IMU were transposed onto the global frame using a quaternion rotation matrix. Translatory acceleration, speed and relative change in position from the IMU were compared with the derived data from the OMCS. Peak acceleration in vertical axis showed no significant difference (p⩾0.05). Difference between peak and trough speed showed significant difference (p<0.05) but relative peak-trough position between the IMU and OMCS did not show any significant difference (p⩾0.05). These results indicate that quaternions, in combination with Simpsons rule integration, can be used in transforming translatory acceleration from the object frame to the global frame and therefore obtain relative change in position, thus offering a solution for using accelerometers in accurate global frame kinematic gait analyses.

Introduction

Optical motion capture systems (OCMS) are used for kinematic analyses of an object in a three-dimensional calibrated volume and seen as the gold standard (Wong et al., 2007). These systems are relatively expensive, time consuming and not easily applicable outside laboratory conditions (Mayagoitia et al., 2002). Accelerometers offer an alternative way to obtain kinematic data in a variety of environments (Refshauge et al., 1995; Schneck, 2000). However certain methodological problems need to be addressed (Kavanagh and Menz, 2008). During circular movements, such as in human gait, the 3D axes rotate.

Commercially available systems combining accelerometers, gyroscopes and magnetometers into an algorithm, known as inertial measurement units (IMU), can transpose translatory acceleration from the object system to the global system using a rotation matrix (Luinge, 2002; Roetenberg, 2006).

Conventional rotation matrices use Euler angle matrices to perform their rotations, but show singularities when using certain sequences of rotations (Pfau et al., 2006).

Quaternions are geometrical operators which represent rotations by using complex numbers forming an algebra (Gravelle, 2006).

This study investigated a lower spine point estimate of centre of mass (CoM), as a simple reference that indicates global gait quality (Meichtry et al., 2007). IMU over the lower spine has an increased risk of showing singularities using Euler angles, therefore quaternions have been chosen as rotation matrix operators (Moe-Nilssen and Helbostad, 2004). Quaternions allow fast computation and simple expressions to be developed for complex rotations and rotating reference frames (Spring, 1986; Hanson, 2006).

This study will investigate the application of an IMU and quaternion-based rotation matrix compared to an OMCS to measure the estimated CoM translatory acceleration during human walking. It also examines double integration of translatory acceleration to obtain relative change in position.

Section snippets

Materials and methods

Five subjects (age: 23.4±3.8 years, weight: 80.5±14.3 kg and height: 181±5.4 cm) participated. The IMU (MTx, Xsens, Netherlands) was fixed with adhesive tape, in an angle of ±90° (due to sensor design), over the fourth lumbar vertebra. A reflective marker was placed on the middle of the IMU to measure the displacement with the OMCS (Proflex, Qualisys, Sweden). Both systems were synchronized and measured at 100 Hz.

Baseline gravitational measurements were recorded before the subjects walked three

Results

Table 1 shows the average difference and standard deviation over three walks for five healthy subjects in the z-axis. Error between both systems of a random participant is plotted in Fig. 1

The data between IMU and OMCS acceleration shows good agreement. Z-axis amplitudes from IMU and OMCS were not significantly different (p⩾0.05). In addition ICC=0.952 and random error 0.176 ms⁻² demonstrated strong agreement between systems.

A paired sample t-test between the relative change in speed (peak to

Discussion

We found that the mathematical transformation using quaternions in combination with double integration applied to IMU data resulted in accurate speed and relative position in the global z-axis during SSWS for short measurements. To the authors knowledge this technique provides more accurate CoM displacement data than previously obtained using Euler angles and step-by-step analysis method described in previous publications (Pfau et al., 2005, Pfau et al., 2006). For this method, the IMU used in

Conflict of interest

None.

Acknowledgement

The authors wish to acknowledge the UK Department of Health for providing funding through the LIFE program.

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Short CommunicationIMU: Inertial sensing of vertical CoM movement

Abstract

Introduction

Section snippets

Materials and methods

Results

Discussion

Conflict of interest

Acknowledgement

Gait Posture

Gait Posture

J. Biomech.

Gait Posture

J. Biomech.

Mech. Mach. Theory

LabVIEW 8 Student Edition

The static accuracy and calibration of intertial measurement unit for 3D orientation

Comput Methods Biomech. Biomed. Eng.

Dynamic accuracy of inertial measurement units during simple pendulum motion

Comput. Methods Biomech. Biomed. Eng.

The role of gravity in human walking: pendular energy exchange, external work and optimal speed

J. Physiol.

Technical note: comparison of the performance of 3D camera systems

Gait Posture

The Global Positioning System and Intertial Navigation

Visualizing Quaternions

Short Communication
IMU: Inertial sensing of vertical CoM movement