IMU-based joint angle measurement for gait analysis

Abstract

This contribution is concerned with joint angle calculation based on inertial measurement data in the context of human motion analysis. Unlike most robotic devices, the human body lacks even surfaces and right angles. Therefore, we focus on methods that avoid assuming certain orientations in which the sensors are mounted with respect to the body segments. After a review of available methods that may cope with this challenge, we present a set of new methods for: (1) joint axis and position identification; and (2) flexion/extension joint angle measurement. In particular, we propose methods that use only gyroscopes and accelerometers and, therefore, do not rely on a homogeneous magnetic field. We provide results from gait trials of a transfemoral amputee in which we compare the inertial measurement unit (IMU)-based methods to an optical 3D motion capture system. Unlike most authors, we place the optical markers on anatomical landmarks instead of attaching them to the IMUs. Root mean square errors of the knee flexion/extension angles are found to be less than 1° on the prosthesis and about 3° on the human leg. For the plantar/dorsiflexion of the ankle, both deviations are about 1°.

Figures

Figure 1.

The placement of inertial sensors on the human body, the definition of joint angle and a model of a hinge joint. (a) The local sensor coordinate axes are not aligned with the physiological axes and planes by which the joint angle, α, is defined; (b) the coordinates of the joint axis direction (green arrows) and the joint position (blue arrows) in the local coordinate systems of the sensors characterize the sensor-to-segment mounting.

Figure 2.

Examples for calibration motions that are used in the literature [14,15,17-19] to determine the coordinates of physiologically meaningful axes, e.g., the knee joint axis, in the local coordinate systems of the sensors. In such methods, the precision depends on how accurately the subject performs the motion. In contrast, the present approach uses arbitrary motions and identifies the sensor-to-segment mounting by exploiting kinematic constraints.

Figure 3.

Sum of squares ψ(j1, j2) of the error in the kinematic constraint (3). The two minima represent the true local coordinates, j1 and — j1, of the joint axis direction vector.

Figure 4.

Projection of the measured angular rates of both sensors into the joint plane (defined by the coordinates in Equation (13)) for a motion with little flexion/extension. In both plots, the projections have the same length at each moment in time, cf. Equation (3). However, when the joint axis signs match, the two curves are congruent up to some rotation around the origin, while in the case of opposite signs, they are mirror images of each other.

Figure 5.

Two algorithms for IMU-based knee angle calculation are considered. (Left) Sensor orientation estimates are used to calculate the orientational difference (i.e., the joint angle) around a given axis. (Right) The problem is reduced to one dimension immediately by integrating the difference of the angular rates around the joint axis. Then, an acceleration-based joint angle estimate is used to remove drift.

Figure 6.

Sensor fusion of the gyroscope-based and the accelerometer-based knee angle of a leg prosthesis. The noisy, but driftless, angle, αacc(t), is combined with the very precise, but drifting, angle, αgyr(t), using the complementary filter (15). The resulting angle, αacc+gyr(t), is accurate on small and on large time scales.

Figure 7.

Placement of inertial measurement units and optical markers on the legs of a transfemoral amputee. The optical markers are placed at the typical physiological landmarks. The IMUs are attached using body straps without restricting their position or orientation.

Figure 8.

Comparison of the two IMU-based knee flexion/extension angle measurements (αacc+gyr+mag(t) and αacc+gyr(t)) with the result of an optical gait analysis system (αopt(t)). On the prosthesis side, there is no significant deviation (epr < 0.6°). However, on the contralateral side, skin and muscle motion effects, which are strongest during push-off and heel-strike, lead to RMS errors ecl of almost 4°.

Figure 9.

Comparison of the two IMU-based ankle plantar/dorsiflexion angle measurements (αacc+gyr+mag(t) and αacc+gyr(t)) with the result (αopt(t)) of an optical gait analysis system. Both on the prosthesis side and on the contralateral side, the deviation is about 1°.