Compensation for inertial and gravity effects in a moving force platform

Abstract

Force plates for human movement analysis provide accurate measurements when mounted rigidly on an inertial reference frame. Large measurement errors occur, however, when the force plate is accelerated, or tilted relative to gravity. This prohibits the use of force plates in human perturbation studies with controlled surface movements, or in conditions where the foundation is moving or not sufficiently rigid. Here we present a linear model to predict the inertial and gravitational artifacts using accelerometer signals. The model is first calibrated with data collected from random movements of the unloaded system and then used to compensate for the errors in another trial. The method was tested experimentally on an instrumented force treadmill capable of dynamic mediolateral translation and sagittal pitch. The compensation was evaluated in five experimental conditions, including platform motions induced by actuators, by motor vibration, and by human ground reaction forces. In the test that included all sources of platform motion, the root-mean-square (RMS) errors were 39.0 N and 15.3 N m in force and moment, before compensation, and 1.6 N and 1.1 N m, after compensation. A sensitivity analysis was performed to determine the effect on estimating joint moments during human gait. Joint moment errors in hip, knee, and ankle were initially 53.80 N m, 32.69 N m, and 19.10 N m, and reduced to 1.67 N m, 1.37 N m, and 1.13 N m with our method. It was concluded that the compensation method can reduce the inertial and gravitational artifacts to an acceptable level for human gait analysis.

Introduction

Force plates and instrumented treadmills are commonly used to measure ground reaction forces (GRF) for clinical movement analysis, sports performance, or research on human movement. The combination of motion capture and force plate data allow for the calculation of joint moments through inverse dynamic analysis. Recently, instrumented treadmills have become equipped with actuators to translate and rotate the walking surface, for either virtual reality applications or for testing human response to perturbations. Acceleration of the force plate creates large inertial artifacts in the GRF measurement, because a large moving mass is located between the force of interest (foot/ground interface) and the load cells. Additionally, when the frame is tilted, its gravitational mass starts contributing to the horizontal GRF signals. The problem is especially severe in an instrumented treadmill, where the moving mass includes the treadmill frame, motor, and belts. These large errors in GRF data make it impossible to perform standard inverse dynamics in these conditions because the joint moment calculations are based on inaccurate force measurements. The same problem also occurs when the force plate foundation is not sufficiently rigid, or in a moving vehicle in order to study the biomechanics of driving.

Although the problem is noteworthy in human movement analysis, it exists in any load measurement system where the force of interest and the load cells are separated by a moving mass. This includes certain applications in high-speed material testing and in force-controlled robots (Hessling, 2009, Dixon, 1990). The work presented in this paper will be applicable in those fields as well.

In principle, the inertial and gravitational forces can be estimated and compensated using rigid body dynamics. This requires knowledge of the mass, inertia matrix, acceleration, angular acceleration, angular velocity, and orientation of the frame. This has been successfully done for one-dimensional linear motion such as in materials testing or a sliding force plate (Hessling, 2009, Dixon, 1990, Pagnacco et al., 2000, Yang and Pai, 2006). While it is straightforward to extend this approach into a six degree of freedom (DOF) load measurement, it becomes impractical due to the requirement to estimate full 3D motion relative to an inertial reference frame, and the use of nonlinear models (Berme and Guler, 2012a, Berme and Guler, 2012b, Hou et al., 2009, van den Bogert et al., 1996). Furthermore, mass and inertial properties of the frame must be known (Preuss and Fung, 2004). Some of the existing methods neglect the effect of rotation and are limited to compensating for errors due to vibrations within the building or floor (Boschetti et al., 2013).

In this paper, we introduce a simple linear, accelerometer-based compensation method for a fully general inertial and gravitational compensation of force plate data. The linear model is based on the principle that an accelerometer directly measures the inertial and gravitational force on its internal test mass. With a sufficient number of accelerometers, attached at different locations, the total inertial and gravitational artifact of all mass elements in the moving frame will be a linear combination of accelerometer signals (Zappa et al., 2001). The method will be presented and evaluated on an instrumented treadmill in various experimental conditions.