# Foot-Mounted Inertial Measurement Units-Based Device for Ankle Rehabilitation

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## Abstract

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## 1. Introduction

- Grade l: Involves the stretching of any ligament without tearing and slight signs of pain and/or inflammation.
- Grade II: Involves the partial tearing of one or more ligaments and moderate pain and inflammatory signs.
- Grade III: Involves full tear of ligaments and joint instability; pain and inflammatory signs are significant, and there is a loss of ankle function and mobility.

## 2. Materials and Methods

#### 2.1. Inertial Sensor

#### 2.1.1. Inertial Measurement Units

#### 2.1.2. Estimation of the Inertial Measurement Variable

**ω**= (ωx, ωy, ωz), is directly provided by the three-axis gyroscope in the IMU, but the angular position

**θ**= (β, α, γ) needs to be calculated through the process explained below.

_{f}, y

_{f}has to be determined. The IMU was fixed to the foot to assure that the IMU sensor axis x

_{s}lies in the sagittal plane of the foot, and then we proceeded to determine the x

_{f}, y

_{f}axis as follows: at the foot flat position, the IMU accelerometer readings a(t) are integrated over time, and the resulting vector is normalized to the unit magnitude z

_{ff}, applying the Euclidian norm:

_{ff}is nearly vertical. Then, y

_{f}is calculated as follows:

_{f}is calculated as follows:

**ω**is started that produces the rotation matrix R

_{ff}(t). By transforming x

_{f}to the reference frame, we calculate the pitch angle α:

**θ**of the IMU local coordinate system. The first is through the three-axis accelerometer signals

**g**= (gx, gy, gz), which measure the vector of the acceleration of gravity, and trigonometric relations are used to calculate one estimation for the angular position

**θ**. The second is through the three-axis gyroscope, which measures the angular velocity

**ω**, whose numerical integral with respect to time gives an approximation of the angular rotation since the beginning of the integration, and is used to compute a second estimation for the angular position

**θ**. These means that in the first source, information is highly noisy due to the accelerations caused by vibrations that can occur in rehabilitation procedures. This makes it unreliable in short periods, but this same source is reliable on average over a longer period of time. The second source of information is very reliable in short periods, but accumulates offset errors as time progresses. For this reason, the MPU-6050 incorporates a digital motion processor (DMP), which is an internal processor that executes MotionFusion algorithms to combine the accelerometer and gyroscope data together to minimize the effects of the errors that are inherent in each sensor, avoiding having to compute the filters by an external processor. The DMP computes the results in terms of quaternions; it can also convert the results to Euler angles, and perform other filtering computations with the data as well [36].

## 3. Foot Attitude Biofeedback Device

#### 3.1. MPU-6050

#### 3.2. Libraries for the MPU-6050

#### 3.3. Calibration

#### 3.4. Connections

#### 3.5. Communication between Arduino and Unity

#### 3.6. SQLite

## 4. Experimental Results and Discussion

#### 4.1. Motion Range Evaluation

#### 4.2. Therapist Evaluation

#### 4.3. Evaluation with Application

#### 4.4. Results

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Foot anatomical reference frame, and the six basic movements: abduction, adduction, plantarflexion, dorsiflexion, inversion, and eversion. Sign of the rotation is specified according to the mathematical definition of the counterclockwise (positive) or clockwise (negative) rotation.

**Figure 2.**Correct placement of the IMU device MPU-6050, considering the approximate foot anatomical reference frame.

Pin AD0 | Address 12C |
---|---|

AD0 = HIGH (5 V) | 0 × 69 |

AD0 = LOW (GND or NC) | 0 × 68 |

MPU-6050 | Teensy 2.0 |
---|---|

VCC | 3.3 V |

GND | GND |

SCL | D0 |

SDA | D1 |

Bluetooth HC-05 | Teensy 2.0 |
---|---|

VCC | 5 V |

GND | GND |

RXD | B1 |

TXD | D2 |

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## Share and Cite

**MDPI and ACS Style**

Gómez-Espinosa, A.; Espinosa-Castillo, N.; Valdés-Aguirre, B.
Foot-Mounted Inertial Measurement Units-Based Device for Ankle Rehabilitation. *Appl. Sci.* **2018**, *8*, 2032.
https://doi.org/10.3390/app8112032

**AMA Style**

Gómez-Espinosa A, Espinosa-Castillo N, Valdés-Aguirre B.
Foot-Mounted Inertial Measurement Units-Based Device for Ankle Rehabilitation. *Applied Sciences*. 2018; 8(11):2032.
https://doi.org/10.3390/app8112032

**Chicago/Turabian Style**

Gómez-Espinosa, Alfonso, Nancy Espinosa-Castillo, and Benjamín Valdés-Aguirre.
2018. "Foot-Mounted Inertial Measurement Units-Based Device for Ankle Rehabilitation" *Applied Sciences* 8, no. 11: 2032.
https://doi.org/10.3390/app8112032