### Inhalt des Dokuments

# Magnetometer-free motion tracking in connected multi-body systems

### From Fachgebiet Regelungssysteme TU Berlin

### Abstract

In motion tracking of connected muti-body systems Interial Measurement Units (IMUs) are used in a wide variety of applications. They provide a low-cost and easy-to-use method for orientation tracking and need no direct interaction with the object they are attached to. Inertial orientation estimation is based on the information-fusion of the measurements of the gyroscope, accelerometer and magnetometer within the IMU. This common approach is called 9D sensor fusion, since each sensor yields measurements in all 3 cartesian axes. However, in indoor environments the magnetic field can be heavily disturbed and inhomogenous. This leads to inaccurate orientations and makes traditional 9D sensor fusion inapplicable in those cases. Our research focuses on developing methods for 6D sensor fusion that omit the magnetometer and only use the gyroscope and accelerometer in combination with the exploitation of the kinematic relationships between the individual objects in the system. We propose methods for a wide variety of different joint configurations that can be applied to numerous biomedical or mechanical applications.

### People involved

## Description

In motion tracking we often encounter multi-body systems. They are characterized by multiple bodies connected to each other by joints that allow for relative motion between two connected bodies. Those systems are called Kinematic Chains. For example, the human leg, arm or the fingers can be modelled as such kinematic chain.

To know the orientation of each individual body with respect to a common reference frame is necessary to calculate joint angles, relative orientations or positional relationships between the individual bodies. The estimation of the orientation is done by placing an IMU on each segment of the kinematic chain. However, in indoor environments, the magnetic field measurements are corrupted by an inhomogenous and disturbed magnetic field. This results in an inaccurate orientation estimation and is therefore not applicable for a multitude of biomedical and robotic applications.

One approach to overcome this is to omit the magnetometer measurements and only use the gyroscope and accelerometer measurements from the IMU. This is called 6D sensor fusion and yields an orientation with an accurate inclination but with an unknown heading component. This results in an unknown relative heading offset of each connected kinematic pair. This offset is initially unknown and slowly changing over time. Knowing this heading offset for each kinematic pair at each time step allows us to transform each orientation into a common, known reference frame.

To account for the missing information of the magnetometer we incorporate the kinematic models of the joints connecting each kinematic pair into the estimation. Rotational joints with differing degrees of freedom (see Fig. 3) limit the possible relative orientation of the two connected bodies to a subset of all possible orientations. This is exploited to formulate a minimization problem which is used to estimate the heading offset of each kinematic pair continiously in real time. This then yields the orientations of all connected bodies with respect to a reference frame fixed to the system. This allows us to calculate relative orientations, joint angles or positional relationships needed for various kinds of applications.
The detailed explanations of the estimation problems can be found in the corresponding publications, each focusing on a special type of rotational joint
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## Experimental validation

The methods were evaluated experimentally using different experimental setups.

We used rigid, mechanical test objects with well-known joints and a defined sensor positions and orientations to evaluate the methods for different joint configurations. As ground-truth, an optical motion capture was used for all experiments to provide a highly accurate base for evaluation.

We further evaluated the methods with less-rigid biological joints. For this we used the developed hand sensor system and estimated the orientations of all finger segments. With this system, an IMU is placed on each finger segment and on the back of the hand. We used a simplified model of the complex kinematics of the hand for the application of the developed methods as explained in
^{[4]}.

### Results

With the mechanical objects, a mean error of less than 2° between the true and estimated orientation can be achieved over all experiments. Even for long experiments, the orientations remain stable and do not experience drift. In comparison, with traditional 9D sensor fusion incorporating the magnetometer, only mean errors of around 6° with maximum errors of more than 22° are achieved for the same experiments. In comparison to non-optimization based 6D sensor fusion method, this method also does not need any knowledge of the initial orientation of the objects and converges towards the true orientations within less than 3 seconds for all experiments after starting the measurement.

For the motion tracking of the human hand we can achieve a high repeatability of defined poses and a drift-free estimation without the use of magnetometers. Long-term stability is one of the key improvements over other 6D sensor fusion methods. Also the plug&play approach without prior knowledge of the initial orientation makes the method and system universally applicable for different kinds of applications where no predefined initial poses can be taken.

### Publications

- ↑
- D. Laidig, D. Lehmann, and T. Seel.
**Magnetometer-free Realtime Inertial Motion Tracking by Exploitation of Kinematic Constraints in 2-DOF Joints**. In*41st IEEE International Engineering in Medicine and Biology Conference (EMBC)*, Berlin, Germany, 2019. - Bibtex
**Author :**D. Laidig, D. Lehmann, and T. Seel**Title :**Magnetometer-free Realtime Inertial Motion Tracking by Exploitation of Kinematic Constraints in 2-DOF Joints**In :**In*41st IEEE International Engineering in Medicine and Biology Conference (EMBC)*,**Date :**2019

- D. Laidig, D. Lehmann, and T. Seel.
- ↑
- D. Lehmann, D. Laidig, and T. Seel.
**Magnetometer-free motion tracking of one- dimensional joints by exploiting kinematic constraints**. In Berlin, Germany, 2020. - Bibtex
**Author :**D. Lehmann, D. Laidig, and T. Seel**Title :**Magnetometer-free motion tracking of one-dimensional joints by exploiting kinematic

constraints**In :**In**Date :**2020

- D. Lehmann, D. Laidig, and T. Seel.
- ↑
- D. Lehmann, D. Laidig, R. Deimel, and T. Seel.
**Magnetometer-free inertial motion tracking of arbitrary joints with range of motion constraints**. In Berlin, Germany, 2020. - Bibtex
**Author :**D. Lehmann, D. Laidig, R. Deimel, and T. Seel**Title :**Magnetometer-free inertial motion trackingof arbitrary joints with range of motion

constraints**In :**In**Date :**2020

- D. Lehmann, D. Laidig, R. Deimel, and T. Seel.
- ↑
- C. Salchow-Hömmen, L. Callies, D. Laidig, M. Valtin, T. Schauer, and T. Seel.
**A Tangible Solution for Hand Motion Tracking in Clinical Applications**.*Sensors*, 19 (1):208, 2019. - Bibtex| DOI
**Author :**C. Salchow-Hömmen, L. Callies, D. Laidig, M. Valtin, T. Schauer, and T. Seel**Title :**A Tangible Solution for Hand Motion Tracking in Clinical Applications**In :***Sensors*,**Date :**2019

- C. Salchow-Hömmen, L. Callies, D. Laidig, M. Valtin, T. Schauer, and T. Seel.