# Inertial Sensor Based Solution for Finger Motion Tracking

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## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

- Top level (map level),
- Object level,
- Source level.

#### 1.2. Tracking Approaches

#### 1.2.1. Related Works

- Solutions that use magnetometers cannot operate correctly in a significantly non-homogeneous magnetic field; otherwise, they require a complex calibration procedure,
- Methods that use only 6D data do not provide absolute yaw information, or require a resetting procedure, and suffer from drift,
- Most existing solutions include three inertial sensors on a finger to independently track the orientation of each phalange and, thus, do not take into account some important details of finger movement,
- Mixed solutions can include all limitations listed above or combine some.

#### 1.2.2. Proposed Approach

## 2. Materials and Methods

#### 2.1. Finger Model

#### 2.2. Simple Switching Tracking Algorithm

#### 2.2.1. Algorithm of The Position Estimation of The Single Phalange

#### 2.2.2. Slow Motion Estimation

#### 2.2.3. Fast Movement Estimation

#### 2.2.4. Errors in The Estimation Algorithms for Slow and Fast Motion

#### 2.2.5. Switching Algorithm

- 1.
- receive sensor readings $\widehat{a},\widehat{\omega}$;
- 2.
- calculate ${\Delta \theta}_{g}\left({t}_{i}\right)=\frac{|\tilde{\mu}|\left(\widehat{\omega}\right)}{|{\overrightarrow{g}}_{xy}|}$ and $\Delta \theta \left({t}_{i}\right){|}_{\omega}=\Delta \theta \left({t}_{i-1}\right)+({t}_{i}-{t}_{i-1})\xb7|\Delta \omega |$;
- 3.
- choose the estimation mode:
- if currently in fast motion mode and ${\Delta \theta}_{g}\left({t}_{i}\right)<\Delta \theta \left({t}_{i}\right){|}_{\omega}$, then switch to slow motion mode, and assign $\Delta \theta \left({t}_{i}\right):={\Delta \theta}_{g}\left({t}_{i}\right)$;
- if currently in slow motion mode and $\Delta \theta \left({t}_{i}\right){|}_{\omega}<{\Delta \theta}_{g}\left({t}_{i}\right)$, then switch to fast motion mode, taking $\tilde{\theta}\left({t}_{i-1}\right)$ as the initial estimate, and assign $\Delta \theta \left({t}_{i}\right):=\Delta \theta \left({t}_{i}\right){|}_{\omega}$.

- 4.
- Calculate a new orientation estimate $\tilde{\theta}$ using the currently selected estimation algorithm.

#### 2.3. Madgwick Filter Modification

#### 2.3.1. Finger Rotation Estimation

#### 2.3.2. Combining Filter Algorithm

## 3. Verification of Algorithms Using Numerical Model Data

- a model of a moving finger equipped with inertial sensors,
- a set of parametric descriptors for some groups of finger movements,
- implementations of the simple switching algorithm and the modified Madgwick filter,
- a wrapper program applying logic to conducting tests of estimation algorithms on generated model data.

- A static interval lasting ${t}_{\mathrm{d}}$;
- The extension of a straight finger in the MCPjoint (Joint 0) to a $-{28}^{\circ}$ angle lasting $\frac{1}{3}{t}_{\mathrm{m}}$;
- Simultaneous flexion of the finger in Joint 0 to ${90}^{\circ}$ and in the interphalangeal (1 and 2) joints to an angle of ${85}^{\circ}$ lasting $\frac{2}{3}{t}_{\mathrm{m}}$.

- Initial conditions for the kinematic model of the finger were specified. This position was considered as the known accurate initial estimate.
- The motion and its parameters were specified.
- The modeling of a given movement was performed, during which we collected data with a given sampling rate:
- -
- the readings of virtual sensors were calculated and transferred to the evaluation algorithm with the addition of sensor errors;
- -
- the current true configuration (phase coordinates and speeds) of the finger model and the configuration estimate by the algorithm were recorded.

- After the simulation was completed, a measure of the deviation of the estimate from the actual configuration was calculated.

- with white noise;
- with a zero offset;
- with errors of both kinds.

#### Test Results

## 4. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

IMU | Inertial Measurement Unit |

AVS | Angular Velocity Sensor |

INS | Inertial Navigation System |

RMS | Root-Mean-Square |

VR | Virtual Reality |

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**MDPI and ACS Style**

Lemak, S.; Chertopolokhov, V.; Uvarov, I.; Kruchinina, A.; Belousova, M.; Borodkin, L.; Mironenko, M.
Inertial Sensor Based Solution for Finger Motion Tracking. *Computers* **2020**, *9*, 40.
https://doi.org/10.3390/computers9020040

**AMA Style**

Lemak S, Chertopolokhov V, Uvarov I, Kruchinina A, Belousova M, Borodkin L, Mironenko M.
Inertial Sensor Based Solution for Finger Motion Tracking. *Computers*. 2020; 9(2):40.
https://doi.org/10.3390/computers9020040

**Chicago/Turabian Style**

Lemak, Stepan, Viktor Chertopolokhov, Ivan Uvarov, Anna Kruchinina, Margarita Belousova, Leonid Borodkin, and Maxim Mironenko.
2020. "Inertial Sensor Based Solution for Finger Motion Tracking" *Computers* 9, no. 2: 40.
https://doi.org/10.3390/computers9020040