TY - JOUR

T1 - Observability of the relative motion from inertial data in kinematic chains

AU - Kok, Manon

AU - Eckhoff, Karsten

AU - Weygers, Ive

AU - Seel, Thomas

N1 - Funding Information: The conducted human experiments were funded by the European Regional Development Fund – We-lab for HTM [grant number 1047 ]. The inertial, optical and video data of the 3D-printed mechanical joint motions has been recorded and preprocessed by Dustin Lehmann.

PY - 2022/8

Y1 - 2022/8

N2 - Real-time motion tracking of kinematic chains is a key prerequisite in the control of, e.g., robotic actuators and autonomous vehicles and also has numerous biomechanical applications. In recent years, it has been shown that, by placing inertial sensors on segments that are connected by rotational joints, the motion of that kinematic chain can be tracked accurately. These methods specifically avoid using magnetometer measurements, which are known to be unreliable since the magnetic field at the different sensor locations is typically different. They rely on the assumption that the motion of the kinematic chain is sufficiently rich to assure observability of the relative pose. However, a formal investigation of this crucial requirement has not yet been presented, and no specific conditions for observability have so far been given. In this work, we present an observability analysis and show that the relative pose of the body segments is indeed observable under a very mild condition on the motion. We support our results by simulation studies, in which we employ a state estimator that neither uses magnetometer measurements nor additional sensors and does not impose assumptions on the accelerometer to measure only the direction of gravity, nor on the range of motion or degrees of freedom of the joints. We investigate the effect of the amount of excitation and of stationary periods in the data on the accuracy of the estimates. We then use experimental data from two mechanical joints as well as from a human gait experiment to validate the observability criterion in practice and to show that small excitation levels are sufficient for obtaining accurate estimates even in the presence of time periods during which the motion is not observable.

AB - Real-time motion tracking of kinematic chains is a key prerequisite in the control of, e.g., robotic actuators and autonomous vehicles and also has numerous biomechanical applications. In recent years, it has been shown that, by placing inertial sensors on segments that are connected by rotational joints, the motion of that kinematic chain can be tracked accurately. These methods specifically avoid using magnetometer measurements, which are known to be unreliable since the magnetic field at the different sensor locations is typically different. They rely on the assumption that the motion of the kinematic chain is sufficiently rich to assure observability of the relative pose. However, a formal investigation of this crucial requirement has not yet been presented, and no specific conditions for observability have so far been given. In this work, we present an observability analysis and show that the relative pose of the body segments is indeed observable under a very mild condition on the motion. We support our results by simulation studies, in which we employ a state estimator that neither uses magnetometer measurements nor additional sensors and does not impose assumptions on the accelerometer to measure only the direction of gravity, nor on the range of motion or degrees of freedom of the joints. We investigate the effect of the amount of excitation and of stationary periods in the data on the accuracy of the estimates. We then use experimental data from two mechanical joints as well as from a human gait experiment to validate the observability criterion in practice and to show that small excitation levels are sufficient for obtaining accurate estimates even in the presence of time periods during which the motion is not observable.

KW - Inertial sensors

KW - Kinematic chains

KW - Motion estimation

KW - Observability

UR - http://www.scopus.com/inward/record.url?scp=85130331301&partnerID=8YFLogxK

U2 - 10.1016/j.conengprac.2022.105206

DO - 10.1016/j.conengprac.2022.105206

M3 - Article

AN - SCOPUS:85130331301

VL - 125

JO - Control engineering practice

JF - Control engineering practice

SN - 0967-0661

M1 - 105206

ER -