A type-2 fuzzy inference-based approach enables walking speed estimation that adapts to inter-individual gait patterns

Wearable hardware

In this paper, real-time extraction of gait features is achieved based on a single thigh-mounted IMU. The IMU (LPMS-BE2, ALUBI) has a sampling frequency of 100 Hz and communicates with the microcontroller (168 MHz, STM32F427, ST) using the SPI communication protocol. A force sensitive resistor (FSR) is used to detect the transition between the stance phase and the swing phase. Specifically, the switching of gait is realized by a two-state finite state machine. Prior to the experiment, we set the corresponding pressure threshold according to the individual’s physical condition to achieve the accurate switching of states. A low-power Bluetooth module is on-board the control board to achieve real-time communication with the host computer. The entire hardware module can be secured to the subject’s thigh by a band in order to acquire thigh motion features. In this case, the pitch axis of the IMU overlaps the coronal axis of the body to obtain the flexion and extension angles of the thigh in the sagittal plane (Figure 2).

Figure 2:

Wearable embedded hardware design. The two main sensors, IMU and FSR, are used to extract features of thigh movement (e.g. maximum thigh extension angle and thigh motion cadence) and gait event recognition (e.g. stance or swing), respectively.

Real-time detection of gait features

In order to realize the recognition of the user’s speed regulation intention, we extracted two features based on the kinematics of the thigh, which are the thigh motion cadence (Ω_thigh), and the maximum thigh extension angle (θ_MTE). The reason for using thigh kinematic features is that in the application of intelligent lower limb prostheses, above-knee amputees can control their residual thigh through the hip joint, thus enhancing their intuitive control experience. In addition, thigh kinematic data can be easily acquired by a thigh-mounted IMU for subsequent feature extraction [17], 18]. To obtain these features, we used different methods for each.

1. Ω_thigh=thigh motion cadence: When a person changes his cadence, the frequency of the thigh motion signal changes accordingly. Therefore, Ω_thigh can be used to characterize the user’s cadence intention. Adaptive frequency oscillator (AFO) is a dynamic system with oscillatory behavior, capable of quickly adapting to changes in rhythm and learning the characteristics of periodic input signals [19]. It is almost universally applicable to different individuals without the need for extensive parameter adjustments [20]. As gait is inherently periodic, we use AFO to real-time measurement of Ω_thigh, which can be obtained by inputting θ_thigh into AFO:

   (1)εt=θthight−θˆthight,

   (2)ω˙=−υωεtsinφthigh,

   (3)φ˙thigh=ω−υφεtsinφthigh,

   (4)α˙n=ηcosnφthighεtn=0,…,Nf,

   (5)β˙n=ηsinnφthighεtn=0,…,Nf,

   (6)θˆthigh=∑n=0Nfαncosnφthigh+βnsinnφthigh,

   where φ_thigh and ω are the phase and frequency of the oscillator synchronized with the thigh motion, here, we let Ω_thigh=λω, where λ is a scale coefficient, which was determined by the treadmill cadence walk performed prior to the experiment. Here, we set λ to 1.2; α_n and β_n are the Fourier coefficients used for estimating θˆthigh; εt is the error in this estimation. υ_φ and υ_ω are learning constants and η is a coupling factor that determine the dynamic response of the εt.

2. θ_MTE=maximum thigh extension angle: Although stride length is determined by a variety of factors, the thigh extension angle characterizes the user’s stride intent to some extent. General speaking, the more an individual extends his or her thigh backward during a stride, the greater the stride length is likely to be. In this paper, we use a peak search algorithm to achieve detection of θ_MTE. In order to achieve peak searches, we use a simple, and easily deployable, linear scanning algorithm to implement the comparison of values within a sliding window. In order to minimize the effect of walking speed on the accuracy of window-based peak search, we use the method in [21] to update the size of the window in real time. based on the Ω_thigh. The specific update formula is as follows:

   (7)W=122.44−1.31Ωthigh,

   where W is the optimal window size, which is linearly related to Ω_thigh.

Fuzzy-logic-based walking speed estimation

As mentioned above, we estimated individuals’ walking speeds by using SF and SL parameters obtained from real-time calculations. However, it is difficult to achieve robust inter-individual stride estimation because limb lengths vary between individuals. In addition, it is difficult to quantify inter-individual stride length, which is influenced by subjective factors. Fuzzy inference systems can process vague and uncertain input information and transform it into clear outputs, which can help us to realize the inference of stride intent.

In this paper, an interval T2FIS is used to realize the inference of stride intention and based on this, the walking speed of individuals is estimated. The interval T2FIS uses intervals to represent fuzzy quantities, which reduces the error and uncertainty caused by subjective differences compared to the type-1 fuzzy logic system, and thus describes more accurately the fuzziness between the gait behaviors of different individuals. In the following, we first introduce the interval T2FIS; then, we build a fuzzy rule base based on gait features; and finally, the system is applied to the estimation of the walking speed.

1. Interval T2FIS: Assume that the inputs and outputs of a T2FIS at sample k are sk=s1ks2k…sNkT∈RN and ξk∈R, respectively. The fuzzy rules of the T2FIS that describes the relationship between input s and output ξ can be expressed in the form of “IF-THEN” as follows:

   (8)Rulel:IFskisC˜l,

   (9)THENξ˜lk=a˜0l+a˜1ls1k+a˜2ls2k+⋯+a˜NlsNk,

   where l=1, …, L, L is the number of fuzzy rules, C̃l is the type-2 fuzzy set, and sk is an interval denoted as:

   (10)μC˜lsk=μ̲Clsk,μ‾C˜lsk,

   where μ̲C˜lsk and μ‾C˜lsk are the lower and upper bounds, respectively, satisfying 0≤μ̲C˜lsk≤μ‾C˜lsk≤1. In the “THEN” part, the coefficients a˜il are also intervals, denoted as: a˜il=a̲il,a‾il,i=0,…,N, the output of the model, ξ˜lk=ξ̲lk,ξ‾lk, is derived by:

   (11)ξ̲lk=a̲0l+a̲1ls1k+a̲2ls2k+⋯+a̲NlsNk ξ‾lk=a˜0l+a˜1ls1k+a˜2ls2k+⋯+a˜NlsNk..

   By combining μC˜lsk and ξ˜lk of L fuzzy rules, the output of the T2FIS is obtained:

   (12)ξ(k)=∑l=1Lμ̲C˜l(s(k))⋅ξ̲l(k)2⋅∑l=1Lμ̲C˜l(s(k))+∑l=1Lμ‾C˜l(s(k))⋅ξ‾l(k)2⋅∑l=1Lμ‾C˜l(s(k)).

2. Fuzzy rule base and membership function: To design the fuzzy logic system, a standard Mamdani fuzzy inference system [22] is used. In this paper, the inputs of the fuzzy system are Ω_thigh and θMTE extracted from thigh motion, and the outputs are SF and SL. Based on the characteristics of the above features, the triangle function is chosen as the membership function (Figure 3). The interval T2FIS fuzzy the upper and lower boundaries of the membership function to reduce the effect of individual subjectivity. The range of Ω_thigh is set from 0 to 1 to cover the walking frequency at different walking speeds. We divide the Ω_thigh range into “small”, “middle” and “large”. As we move our thighs at a faster cadence, our stride frequency will undoubtedly be higher. The range of θMTE was set to 5–25° depending on individual walking characteristics. Just like when we walk, as we extend our thighs at a greater angle (in this case, closer to 25°), it means that the next step will be a greater stride (pathological gait is not considered in this paper). Based on the above experience, the fuzzy rules are set as shown in Table 1. The rule base contains nine fuzzy rules representing the corresponding typical FL combinations, such as large strides accompanied by slow cadence walking or small strides accompanied by fast cadence walking, and so on. Finally, a centroid-based method is used for defuzzification. After defuzzification the resulting SF and SL (both set between 0.4 and 1) were used for subsequent walking speed estimation. The closer the value of SF or SL is to 1, indicates that the individual has a stronger intention to walk at a fast cadence or large stride, and vice versa.

3. Estimation of walking speed: As described previously, our aim was to estimate walking speeds for each gait cycle from thigh kinematic features during the stance phase. When the switch from stance phase to swing phase is detected, we perform the estimation of the walking speed based on the output of the fuzzy inference system. The formula for calculating walking speed is as follows:

   (13)V=Γ×SF×SL,

   where Γ is a coefficient that needs to be set before the experiment. We determine the value of Γ based on the system’s feedback when walking at a constant speed on the treadmill, here we set it to 0.4. Once Γ has been set, it will not be modified from one individual to another because the individual’s walking speed is related to step frequency and stride length. From (13), it can be seen that the estimated walking speed is determined by SF and SL, which means that the method can be applied to individuals with different speed regulation strategies.

   

   Figure 3:

   Membership functions. (A) Membership functions of the Ω_thigh. (B) Membership functions θ_MTE. (C) Membership functions SF. (D) Membership functions SL. The interval type-2 membership function is represented by an upper membership function (red line) and a lower membership function (blue line). The region enclosed by these membership functions is the footprint of uncertainty (FOU).

Performance of speed estimation

This article introduces a speed estimation technique inspired by human walking behaviors. We first extracted the corresponding features of two variables (e.g. SF and SL) that are closely related to individual speed regulation. Figure 4(A and B) demonstrates the extraction results of thigh kinematic features during a gait cycle. The feature extraction method used is capable of efficiently extracting features independent of the user’s gait pattern. A supportable observation is that during transitional gaits, where the recorder asks the subject to change their gait pattern (e.g. from PG to FC), T2FIS is able to adjust the output accordingly within 2–3 steps. This is similar to the individual’s speed regulation habits [23].

In this paper, we use fuzzy inference system to implement the inference and quantification of an individual’s intention to regulate speed. Generally, membership functions and fuzzy rules are set with strong subjective experience, which is not conducive to achieving good generalization. For example, the similarity of the large stride of subject 1 relative to the stride of the preferred gait of subject 3 makes it difficult to define a threshold setting for the membership function. In order to minimize the error associated with such subjectively set rules, the use of an interval T2FIS is an effective solution. This is evidenced by the fact that the variation in the RMSE of walking speed estimates for both Subject 1 and Subject 3 in different gait patterns was no more than 0.0232 (Figure 5(B)).

The focus of this paper is to develop and validate a speed estimation method that can accommodate different gait patterns among individuals. The method was tested on five subjects, in which the subjects walked in three gait patterns, PG, FC, and LS, at each speed. The overall RMSE was 0.070 ± 0.0087 indicating that our method is able to accurately estimate the walking speeds of different individuals while accommodating different gait patterns. As shown in Figure 5(C), we note that the proposed method shows better performance when walking in PG pattern (RMSE=0.065 ± 0.011) and worst in FC pattern (0.074 ± 0.005). This may be related to the difficulty of individuals adapting to a fast-paced walking style at the fixed treadmill speed, which directly contributes to the poor quality of the extracted thigh features and affects the subsequent fuzzy inference results.

This article, although validated for only three speeds (0.6, 0.8, and 1.0 m/s), the proposed method holds promise for a wider range of walking speed estimation performance. This was rooted in the mechanism by which our method could adapt to the changing speeds of different individuals. When an individual wants to change speed, such as decelerating from 0.8 to 0.4 m/s or accelerating from 0.8 to 1.2 m/s, the individual needs to change his/her gait pattern, i.e., change the SF or SL or a combination of both. Therefore, accurate recognition of the two parameters, SF and SL, of an individual will facilitate robust speed estimation. This article extracts thigh motion features based on an adaptive frequency oscillator, which is capable of capturing minor variations in an individual’s gait pattern, which helps the T2FIS to achieve robust gait pattern inference. Therefore, the proposed method can achieve accurate estimation performance at other walking speeds as well.

Advantages of our method

As shown in Table 2, our method has several advantages over other methods in previous studies. The first advantage is that the proposed T2FIS-based walking speed estimation method has a more targeted adaptive capability, i.e., it can be adapted to different speed control strategies for different users. Using this approach, wearable lower limb robots can achieve speed adaptation based on the user’s preferred gait pattern (or FL combination). The second advantage is that even without an accurate speed model, our method achieves the same performance (RMSE: 0.0704 m/s) as the machine-learning model-based methods in [11] (RMSE: 0.070 m/s) and [24] (RMSE: 0.12 m/s) with fewer sensors. The third advantage is that our method is more interpretable compared to other methods. Our method performs speed estimation based on thigh motion features, and the user can intuitively adjust the SL and SF parameters through the thigh. In the field of lower limb prosthetics, the proposed method allows the user to control the prosthesis more intuitively, considering that transfemoral amputees have an intact hip to control the residual thigh.

Limitations and future work

This article proposes a speed estimation method that can be adapted to different speed regulation strategies, and treadmill experiments with five able-bodied individuals are preliminary validation of the feasibility of the method. However, future deployment and validation of the algorithm in control systems for intelligent prostheses is needed. In addition to this, considering the differences between treadmills and real walking environments, future tests in non-laboratory environments are still needed to validate the proposed method.