**2. Gait characterization**

Generally, pathological gait shows a characteristic pattern with abnormal speed and range of joint movements, such as shortened stance phase, reduced gait cadence, limited extension/flexion, or inversion/eversion ankle movements. Professional physicians could easily recognize gait abnormalities and visually evaluate patients' progress during the physiotherapy treatments; however, quantitative measures allow a detailed description of these abnormalities, which would be desirable for diagnostic and therapeutic use. In this section, the system setup and ankle angles are first described, then the typical modes of dividing a gait cycle are discussed, and finally step lengths that can be provided by foot-mounted gyroscopes are discussed.

#### **2.1 Ankle angles**

In biomechanical analysis, kinematic information is a well-established set of gait parameters. To estimate spatiotemporal parameters, wearable gait analysis systems have been discussed in the literature, with two, three, four, or more gyroscopes attached to subject's lower limbs, such as the foot, shank, or thigh. Accurate orientation estimation using gyroscopes has been a major research interest in this field. For wearable systems, a reduction in the number of sensing units is highly desirable, as the system will be more portable, convenient, reliable, cost-effective, and easy-to-use, due to the reduction of total cost and weight, the power consumption and memory requirement, the time and operation needed for system setup, the hindrance to natural movement, etc.

For most types of pedal locomotion achieved by legged motion of human or animals, the intuitive experience is to implement gait analysis by attaching sensors to the feet. As the foot is the part of the lower limb distal to the leg, it functions as the interface between the lower limb and the ground and withstands high static and dynamic stresses that generate strong compression and shearing forces, making the periodic nature and disease symptoms of the foot more obvious than that of other parts of the lower limb. For example, diabetic foot is the distal ankle involvement induced by various causes, mainly because of the interaction of peripheral

**81**

*Applications of MEMS Gyroscope for Human Gait Analysis*

vasculopathy, neuropathy, and alterations in foot biodynamics [17]. Therefore, the

*Dual-sensor configuration for gait analysis and associated ankle angles. (a) Coordinate systems, (b) Foot* 

A dual-sensor configuration with one sensor on each foot is discussed in this chapter, as illustrated in **Figure 4(a)**, which is supposed to be a promising way for wearable gait analysis. As is seen, two coordinate frames are introduced for gait

• The body coordinate frame (*b*-frame for short) is parallel to the sensor's axes.

Such system can yield the angles of ankle movements, such as plantarflexion and dorsiflexion movements in the sagittal plane, as well as the inversion and eversion movements in the coronal plane, as shown in **Figure 4(b)** and **(c)**. These movements are described in terms of Euler angles to assess the ankle joint, as ankle rehabilitation includes range of motion training on eversion and inversion as well as

To analyze gait abnormalities, temporal gait parameters should be estimated first. Terminologically, gait is the movement pattern involved during locomotion, which exhibits periodic patterns termed as gait cycle. Each gait cycle is characterized by a sequence of ordered gait events that occur at specific temporal locations. These events can be detected by using the measurements of wearable MEMS gyroscope. Different researchers pay attention to different gait events according to their specific application requirements. Normally, there are four typical events in one gait cycle, i.e., heel-strike (HS), foot-flat (FF), heel-off (HO), and toe-off (TO), as shown in **Figure 5** identified relative to the right foot and defined in the

2.**FF event**: the toe touches the ground, and the foot becomes completely flat on

4.**TO event**: the toe leaves the ground, and the foot becomes totally in the air.

• The global coordinate frame (*g*-frame for short) is a local east-north-up (ENU)

foot is a preferred location of gyroscopes for gait data collection.

analysis purpose, which are defined as follows.

reference frame.

plantarflexion and dorsiflexion.

1.**HS event**: the heel strikes the ground.

3.**HO event**: the heel leaves the ground.

**2.2 Gait phases**

**Figure 4.**

following way:

the ground.

*DOI: http://dx.doi.org/10.5772/intechopen.86837*

*anatomical planes and (c) Ankle movements.*

*Applications of MEMS Gyroscope for Human Gait Analysis DOI: http://dx.doi.org/10.5772/intechopen.86837*

**Figure 4.**

*Gyroscopes - Principles and Applications*

**2. Gait characterization**

scopes are discussed.

hindrance to natural movement, etc.

**2.1 Ankle angles**

MEMS sensors. The derived angle and position estimates are usually corrupted by varying sensor noises and biases, thereby resulting in the well-known continuously increasing error called drift, i.e., angular or positional deviations away from the ground truth. Many researchers addressed these issues and presented different methods to improve the system accuracy. It should be noted that the costs of MEMS accelerometers are decreasing while the accuracy is being improved, whereas the MEMS low-cost gyroscopes could not achieve the required accuracy for precise long-term positioning applications. Generally, MEMS gyroscopes have large bias drifts that can accumulate several degrees of orientation error during even 1 min. Such large error rates make it difficult to choose reasonably priced gyroscopes for inertial navigation applications, and hence the reliability and accuracy of gyroscopes are questionable [15, 16]. However, for gait analysis applications, gyroscope is the preferred device among the inertial sensors, due to the effects of human locomotion that rotational motion is more pronounced than translational motion. The systems using solely gyroscopes can provide both temporal and spatial gait parameters, whereas most other systems using accelerometers or foot switches are limited to temporal parameters merely. Therefore, the purpose of this chapter is to

demonstrate the applications of MEMS gyroscope for human gait analysis.

Generally, pathological gait shows a characteristic pattern with abnormal speed and range of joint movements, such as shortened stance phase, reduced gait cadence, limited extension/flexion, or inversion/eversion ankle movements. Professional physicians could easily recognize gait abnormalities and visually evaluate patients' progress during the physiotherapy treatments; however, quantitative measures allow a detailed description of these abnormalities, which would be desirable for diagnostic and therapeutic use. In this section, the system setup and ankle angles are first described, then the typical modes of dividing a gait cycle are discussed, and finally step lengths that can be provided by foot-mounted gyro-

In biomechanical analysis, kinematic information is a well-established set of gait parameters. To estimate spatiotemporal parameters, wearable gait analysis systems have been discussed in the literature, with two, three, four, or more gyroscopes attached to subject's lower limbs, such as the foot, shank, or thigh. Accurate orientation estimation using gyroscopes has been a major research interest in this field. For wearable systems, a reduction in the number of sensing units is highly desirable, as the system will be more portable, convenient, reliable, cost-effective, and easy-to-use, due to the reduction of total cost and weight, the power consumption and memory requirement, the time and operation needed for system setup, the

For most types of pedal locomotion achieved by legged motion of human or animals, the intuitive experience is to implement gait analysis by attaching sensors to the feet. As the foot is the part of the lower limb distal to the leg, it functions as the interface between the lower limb and the ground and withstands high static and dynamic stresses that generate strong compression and shearing forces, making the periodic nature and disease symptoms of the foot more obvious than that of other parts of the lower limb. For example, diabetic foot is the distal ankle involvement induced by various causes, mainly because of the interaction of peripheral

**80**

*Dual-sensor configuration for gait analysis and associated ankle angles. (a) Coordinate systems, (b) Foot anatomical planes and (c) Ankle movements.*

vasculopathy, neuropathy, and alterations in foot biodynamics [17]. Therefore, the foot is a preferred location of gyroscopes for gait data collection.

A dual-sensor configuration with one sensor on each foot is discussed in this chapter, as illustrated in **Figure 4(a)**, which is supposed to be a promising way for wearable gait analysis. As is seen, two coordinate frames are introduced for gait analysis purpose, which are defined as follows.


Such system can yield the angles of ankle movements, such as plantarflexion and dorsiflexion movements in the sagittal plane, as well as the inversion and eversion movements in the coronal plane, as shown in **Figure 4(b)** and **(c)**. These movements are described in terms of Euler angles to assess the ankle joint, as ankle rehabilitation includes range of motion training on eversion and inversion as well as plantarflexion and dorsiflexion.

#### **2.2 Gait phases**

To analyze gait abnormalities, temporal gait parameters should be estimated first. Terminologically, gait is the movement pattern involved during locomotion, which exhibits periodic patterns termed as gait cycle. Each gait cycle is characterized by a sequence of ordered gait events that occur at specific temporal locations. These events can be detected by using the measurements of wearable MEMS gyroscope. Different researchers pay attention to different gait events according to their specific application requirements. Normally, there are four typical events in one gait cycle, i.e., heel-strike (HS), foot-flat (FF), heel-off (HO), and toe-off (TO), as shown in **Figure 5** identified relative to the right foot and defined in the following way:


**Figure 5.**

*Typical events and phases in one gait cycle.*

Usually, HS event is specified as the beginning of a gait cycle, and a complete gait cycle is defined as the time interval between successive HS events of the same foot. The typical gait events can divide a gait cycle into two to four consecutive time intervals termed as gait phases. When considering more gait events, e.g., midstance and mid-swing, more gait phases will be delimited, which is not addressed in this chapter. As shown in **Figure 5**, there are three common modes of gait cycle division. The first mode (1) divides a gait cycle into two phases, i.e., stance and swing, where the stance phase lasts from HS to TO corresponding to about 60% of a gait cycle [18]. The second mode (2) divides a gait cycle into three phases, where the stance phase is delimited by HS and HO constituting about 40% of a gait cycle [19]. The third mode (3) divides a gait cycle into four phases, where the stance phase lasts from FF to HO comprising about 30% of a gait cycle [20].

Obviously, out-of-sequence events are not permitted in normal gait, and hence a breakdown in gait rhythm and bilateral coordination plays a significant role in identifying pathologic gait, e.g., freezing of gait in Parkinson's disease. Besides, for the patients with gait abnormalities, the affected lower limb fails to support the body weight well, which makes the corresponding stance phase short-lasting and results in a highly unstable situation. Monitoring gait cycle distribution in temporal domain has been applied to detect the onset of neurodegenerative diseases and injuries [21].

In this chapter, for demonstration purpose, the mentioned four typical gait events are modeled and identified, and hence a normalized gait cycle is divided into four phases as that in the first division mode (1). In this division, the stance phase is the time interval when the foot is entirely on the ground, the swing phase is the time interval when the foot is entirely in the air, and the two remaining phases are the transition states between stance and swing. Furthermore, as the motions of subject's two feet are strongly coupled with each other, detecting gait events using the measurements of both feet is supposed to obtain more accurate results than just using that of the ipsilateral limb. When the concerned gait events of each foot are correctly detected, the gait cycles will be divided, the gait phases will be delimited, and therefore the temporal gait parameters will be derived accordingly.

#### **2.3 Step lengths**

When the gait phases are delimited, the spatial gait parameters can be derived accordingly. The distance-related gait parameters involve step length, step width, and step height, corresponding to the maximum covered distance in the forward, lateral, and vertical directions, respectively, over a step, as shown in **Figure 6**. Among these

**83**

*Applications of MEMS Gyroscope for Human Gait Analysis*

which is about 0.79 m for males and 0.66 m for females.

between different step length estimators are presented in [27].

contralateral rear foot that supports the forward motion of the swing leg.

adopted to estimate the step length by

Therefore, a mathematical model from indirect gyroscope measurements can be

*SL* = *L* ⋅ [sin(θ1) + sin(θ2)] (1)

three parameters, the step length in the sagittal plane needs to be calculated separately for each step of each individual, as it varies considerably due to inter- and intraindividual gait variability. Actually, several factors can account for the phenomenon of gait variability, such as leg length, walking speed, and gait pattern. Step length has different values among the literature data. As reported in [22], the average step length is around 0.75 m for healthy adults walking at their self-selected normal speed of about 1.4 m/s, while, as reported in [23], the average step length varies with gender,

As shown in **Figure 6**, a stride consists of two consecutive steps. Both stride length and step length are meaningful gait parameters to assess gait performance. Gait slowness with reduced step length is a manifestation of diseases affecting walking ability, such as spinal cord injury, stroke, Parkinson's disease, and osteoarticular disorders. Many methods for estimating step length and gait speed have been proposed in the literature, e.g., using a mathematical model. Prior studies have employed a single inverted pendulum model to estimate the step length [24], by using a uniaxial gyroscope. A more sophisticated method presented in [25] employs a double pendulum model comprised of an inverted double pendulum pivoting about the ground during stance and a double pendulum pivoting about the hip during swing. A four-sensor configuration is proposed to deal with the non-pendulum nature of double limb support [26]. Typically, a gait model can be driven by various combinations of direct or indirect gyroscope measurements, with the sensors attached to the subject's shank, thigh, or lower lumbar spine near the body's center of mass (COM), etc. Comparisons

Based on different gait models, necessary relations between the step length and various measurable or computable gait variables can be formulated. For the dualsensor configuration shown in **Figure 4(a)**, a modified gait model was presented in our previous study [28], which is driven by the measurements from foot-mounted gyroscopes solely. In this model, human gait is represented by a single inverted pendulum model of a kneeless biped, taking the anthropometric data specific to each subject's biomechanics into consideration, as shown in **Figure 7**. This model functions as a self-contained step length estimator, which does not simply resort to other ranging technologies based on infrared, RF, or ultrasonic devices that usually use some type of beacon or active badge [29, 30] nor directly double integrate the gravitycompensated translational acceleration over time. The step length *SL* can be estimated as the forward distance traversed by the body's COM, during the stance phase of the

*DOI: http://dx.doi.org/10.5772/intechopen.86837*

**Figure 6.**

*Distance-related spatial gait parameters.*

*Applications of MEMS Gyroscope for Human Gait Analysis DOI: http://dx.doi.org/10.5772/intechopen.86837*

**Figure 6.** *Distance-related spatial gait parameters.*

*Gyroscopes - Principles and Applications*

*Typical events and phases in one gait cycle.*

**Figure 5.**

Usually, HS event is specified as the beginning of a gait cycle, and a complete gait cycle is defined as the time interval between successive HS events of the same foot. The typical gait events can divide a gait cycle into two to four consecutive time intervals termed as gait phases. When considering more gait events, e.g., midstance and mid-swing, more gait phases will be delimited, which is not addressed in this chapter. As shown in **Figure 5**, there are three common modes of gait cycle division. The first mode (1) divides a gait cycle into two phases, i.e., stance and swing, where the stance phase lasts from HS to TO corresponding to about 60% of a gait cycle [18]. The second mode (2) divides a gait cycle into three phases, where the stance phase is delimited by HS and HO constituting about 40% of a gait cycle [19]. The third mode (3) divides a gait cycle into four phases, where the stance phase lasts

Obviously, out-of-sequence events are not permitted in normal gait, and hence a breakdown in gait rhythm and bilateral coordination plays a significant role in identifying pathologic gait, e.g., freezing of gait in Parkinson's disease. Besides, for the patients with gait abnormalities, the affected lower limb fails to support the body weight well, which makes the corresponding stance phase short-lasting and results in a highly unstable situation. Monitoring gait cycle distribution in temporal domain has been applied to detect the onset of neurodegenerative diseases and injuries [21]. In this chapter, for demonstration purpose, the mentioned four typical gait events are modeled and identified, and hence a normalized gait cycle is divided into four phases as that in the first division mode (1). In this division, the stance phase is the time interval when the foot is entirely on the ground, the swing phase is the time interval when the foot is entirely in the air, and the two remaining phases are the transition states between stance and swing. Furthermore, as the motions of subject's two feet are strongly coupled with each other, detecting gait events using the measurements of both feet is supposed to obtain more accurate results than just using that of the ipsilateral limb. When the concerned gait events of each foot are correctly detected, the gait cycles will be divided, the gait phases will be delimited,

and therefore the temporal gait parameters will be derived accordingly.

When the gait phases are delimited, the spatial gait parameters can be derived accordingly. The distance-related gait parameters involve step length, step width, and step height, corresponding to the maximum covered distance in the forward, lateral, and vertical directions, respectively, over a step, as shown in **Figure 6**. Among these

from FF to HO comprising about 30% of a gait cycle [20].

**82**

**2.3 Step lengths**

three parameters, the step length in the sagittal plane needs to be calculated separately for each step of each individual, as it varies considerably due to inter- and intraindividual gait variability. Actually, several factors can account for the phenomenon of gait variability, such as leg length, walking speed, and gait pattern. Step length has different values among the literature data. As reported in [22], the average step length is around 0.75 m for healthy adults walking at their self-selected normal speed of about 1.4 m/s, while, as reported in [23], the average step length varies with gender, which is about 0.79 m for males and 0.66 m for females.

As shown in **Figure 6**, a stride consists of two consecutive steps. Both stride length and step length are meaningful gait parameters to assess gait performance. Gait slowness with reduced step length is a manifestation of diseases affecting walking ability, such as spinal cord injury, stroke, Parkinson's disease, and osteoarticular disorders. Many methods for estimating step length and gait speed have been proposed in the literature, e.g., using a mathematical model. Prior studies have employed a single inverted pendulum model to estimate the step length [24], by using a uniaxial gyroscope. A more sophisticated method presented in [25] employs a double pendulum model comprised of an inverted double pendulum pivoting about the ground during stance and a double pendulum pivoting about the hip during swing. A four-sensor configuration is proposed to deal with the non-pendulum nature of double limb support [26]. Typically, a gait model can be driven by various combinations of direct or indirect gyroscope measurements, with the sensors attached to the subject's shank, thigh, or lower lumbar spine near the body's center of mass (COM), etc. Comparisons between different step length estimators are presented in [27].

Based on different gait models, necessary relations between the step length and various measurable or computable gait variables can be formulated. For the dualsensor configuration shown in **Figure 4(a)**, a modified gait model was presented in our previous study [28], which is driven by the measurements from foot-mounted gyroscopes solely. In this model, human gait is represented by a single inverted pendulum model of a kneeless biped, taking the anthropometric data specific to each subject's biomechanics into consideration, as shown in **Figure 7**. This model functions as a self-contained step length estimator, which does not simply resort to other ranging technologies based on infrared, RF, or ultrasonic devices that usually use some type of beacon or active badge [29, 30] nor directly double integrate the gravitycompensated translational acceleration over time. The step length *SL* can be estimated as the forward distance traversed by the body's COM, during the stance phase of the contralateral rear foot that supports the forward motion of the swing leg.

Therefore, a mathematical model from indirect gyroscope measurements can be adopted to estimate the step length by

$$S\_L = L \cdot \left[ \sin \left( \Theta\_1 \right) + \sin \left( \Theta\_2 \right) \right] \tag{1}$$

**Figure 7.** *Kneeless inverted pendulum model of walking gait.*

where *L* denotes the pendulum length related to the subject's height and leg length and θ1 and θ2 denote the amplitudes that the pendulum swings away from vertical, which are approximated by the maximum positive and negative rotation angles of foot pitch motion, respectively, and related to the plantarflexion and dorsiflexion angles on the sagittal plane.

### **3. Gait data acquisition**

Gait analysis can be achieved by examining the patterns of sensed data from the measuring instruments. There are two sources of gait data in our study, i.e., inertial data and optoelectronic data. The optoelectronic data are measured by using the Vicon® optical motion capture system from Oxford Metrics Ltd., UK [10], which is used as reference data to provide ground truth for gait analysis algorithms. As illustrated in **Figure 8(a)**, the MEMS inertial sensors and Vicon retroreflective markers are attached to the subject's lower limbs. However, for demonstration purpose, only the measurements from foot-mounted devices are considered in this chapter, as shown in the partial enlarged drawing in **Figure 8(b)**. Two types of inertial

#### **Figure 8.**

*System setup for gait data acquisition. (a) Sensor placement on lower limbs and (b) Foot-mounted sensors and markers.*

**85**

**Table 1.**

**Figure 9.**

*MEMSense nIMU used for gait data collection.*

*Key specifications of gyroscope in MEMSense nIMU.*

*Applications of MEMS Gyroscope for Human Gait Analysis*

sensors are used for gait data collection in our study, i.e., Nano IMU (nIMU) from MEMSense Inc., USA [31], and ADIS16448 *i*Sensor® device from Analog Devices

The first type of inertial sensors used in our study is the MEMSense nIMU [13, 33], which is a small-size and low-weight MEMS unit and costs about \$1300, as shown in **Figure 9** that illustrates the data acquisition process under normal conditions. Since nIMU is a wired sensor node, when communicating with it, one needs to connect it to a USB interface board first and then connect the USB interface board to a computer for further processing. The software used for acquiring and storing sensed data is the MEMSense IMU Data Console (IDC), which is a console-based, menu-driven application and allows basic display and collection using a specified

The nIMU is compensated for temperature sensitivities to bias and scale factor and provides serial outputs including 3D acceleration, 3D angular rate, and 3D magnetic field intensity, with a sampling rate of 150 Hz. The key manufacturer

A segment of raw measurements is shown in **Figure 10**. As the IMUs are placed on the subject's feet, the gyroscope measurements feature periodic and repetitive patterns according to the transitions of gait phases. These patterns are helpful for gait analysis, by facilitating the detection of the key gait events and the concerned gait phases correspondingly. Since the feet are exposed to quite extreme dynamics at HS events, it is found that the bandwidth and dynamic ranges of the gyroscope in nIMU are insufficient for optimal gait characterization, as seen in **Figure 10**. These insufficiencies would induce systematic measurement and modeling errors to the system. When testing the sensor for running gait, the achieved tracking results are reasonable but would improve considerably if the gyroscope has sufficient dynamic range, so as to accurately monitor the impact of foot on the ground. According to research in [34], the maximum angular velocity experienced by toe-mounted gyroscopes can

specifications of the gyroscope in nIMU are listed in **Table 1**.

Mass (g) 20 Size (mm) 45 × 23 × 13 Operating temperature (°C) 0 to +70 Gyroscope Range (°/s) ±600

> Nonlinearity (% of FS) ±0.1 Noise (°/s) 0.56 (0.95) Bandwidth (Hz) 50

*DOI: http://dx.doi.org/10.5772/intechopen.86837*

Inc., USA [32], as described below.

**3.1 MEMSense IMU**

RS422 protocol.

sensors are used for gait data collection in our study, i.e., Nano IMU (nIMU) from MEMSense Inc., USA [31], and ADIS16448 *i*Sensor® device from Analog Devices Inc., USA [32], as described below.
