Fuzzy-Logic-Based Terrain Identification with ... - IEEE Xplore

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IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 20, NO. 2, APRIL 2015

Fuzzy-Logic-Based Terrain Identification with Multisensor Fusion for Transtibial Amputees Kebin Yuan, Student Member, IEEE, Qining Wang, Member, IEEE, and Long Wang, Member, IEEE

Abstract—Terrain identification is essential for the control of robotic transtibial prostheses to realize smooth locomotion transitions. In this paper, we present a real-time fuzzy-logic-based terrain identification method with multisensor fusion. Five locomotion features, including the foot inclination angle at the first strike, the shank inclination angle at the first strike, foot strike sequence, the foot inclination angle at mid-stance, and the shank inclination angle at toe-off, are used to identify different terrains and terrain transitions. These features are measured by the fusion of two triaxis gyroscopes, two triaxis accelerometers, two force sensitive resistors, and a timer, which can be embedded into the prosthesis. Based on these features, a fuzzy-logic-based identification method is proposed to identify five terrains: level ground, stair ascent, stair descent, ramp ascent, and ramp descent. Moreover, a transition constraint function is developed to improve the identification performance. The execution time of the identification method is 0.79 ms ± 0.02 ms (mean ± standard error of mean) and continuous terrain identification results show that the method can be operated online in real time. The average identification accuracy of 98.74% ± 0.32% is obtained from experiments with six able-bodied and three amputee subjects during steady locomotion periods (no terrain transition). In locomotion transition periods, all the eight transitions we studied are correctly identified and the average identification delay is 9.06% ± 3.46% of one gait cycle. Index Terms—Fuzzy logic, locomotion transitions, multisensor fusion, terrain identification, transtibial prostheses.

I. INTRODUCTION RANSTIBIAL prostheses play an important role in the below-knee amputee’s locomotion. Most of the commercial prostheses are energetically passive, and these passive prostheses have deficiencies as they are associated with more metabolic energy consumption and asymmetrical gait patterns [1]. To deal with these deficiencies, increasing efforts have been made on active or powered transtibial prostheses during the last few decades [1]–[6]. Being able to provide positive work

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Manuscript received August 27, 2013; revised January 3, 2014; accepted February 22, 2014. Date of publication March 18, 2014; date of current version October 24, 2014. Recommended by Technical Editor N. G. Tsagarakis. This work was supported in part by the National Natural Science Foundation of China under Grant 61005082 and Grant 61020106005, in part by the Doctoral Fund of the Ministry of Education of China under Grant 20100001120005, and in part by the 985 Project of Peking University under Grant 3J0865600. (Corresponding author: Q. Wang.) The authors are with the Intelligent Control Laboratory, College of Engineering, Peking University, Beijing 100871, China, and also with the Beijing Engineering Research Center of Intelligent Rehabilitation Engineering, Beijing 100871, China (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMECH.2014.2309708

and mimic behaviors of the sound limb, powered prostheses can improve the amputee’s energy efficiency and make their gaits more natural. In addition, powered prostheses have the potential of terrain (e.g., level ground, stairs, ramps, etc.) adaptability and enable the amputees to handle different terrain transitions. But most existing powered prostheses are optimized only for level ground walking and manually switched locomotion mode transitions. As a result, the amputees may suffer balance impairment or even falling when walking on stairs and ramps. An active adaptation to terrains and locomotion transitions enhances safety for the amputees and brings about a more natural gait pattern. Thus, it is necessary to identify different terrains for the prosthesis control. Several kinds of terrain identification methods have been proposed based on different kinds of signals [7]–[11]. Au et al. [7] presented an approach to detect stair descent walking based on electromyography (EMG) signals measured from the amputee’s residual limb. The EMG signal has the advantage of appearing prior to motion, but it is not sufficient to be used independently for prosthesis control [8]. Wang et al. [9] proposed a method to identify different terrains based on the GRF measured by an insole with pressure sensors. Although GRF is easy to acquire, it is invalid during swing phase and on uneven ground surface where pressure sensors do not fully contact. Chen et al. [10] identified different locomotion modes without real-time gait transitions using wearable capacitive sensors. The inconvenience of the method was that the capacitive sensors had to be attached to the skin directly. In addition, Li et al. [11] used the IMU to identify level ground, stair ascent/descent, and ramp ascent/descent with a threshold method. This method had the advantage of requiring only a few sensors and low computation load, but the transition identification had a delay of one step. Multisensor fusion has the advantages such as improving system performance as well as improving robustness [17] and has been widely used in recent studies [18]–[21]. For lower-limb amputees, Varol et al. [12]–[14] used multiple mechanical sensors mounted on the powered prosthesis to detect stand, sit, stumble, walking at different speeds, and upslope walking, but they had not yet shown the ability to detect activities associated with stairs. Huang et al. [15], [16] combined EMG and GRF together and developed a neuromuscular–mechanical fusion algorithm to continuously recognize locomotion modes. But this method required installing seven or more electrodes on the residual limb as well as an insole with pressure sensors under the foot of the sound limb, which might aggravate the acceptance by amputees. In summary, a good terrain identification method should meet the following requirements.

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YUAN et al.: FUZZY-LOGIC-BASED TERRAIN IDENTIFICATION WITH MULTISENSOR FUSION FOR TRANSTIBIAL AMPUTEES

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TABLE I LOCOMOTION FEATURES

Fig. 1. Foot inclination angle at the first strike (θf f ) and foot strike sequence on different terrains of the able-bodied. (a) θf f of level ground is positive, so is the angle on ramp ascent. The heel strikes the ground prior to the toe. (b) θf f of stair ascent is around zero, and the heel and the toe strike the ground almost at the same time. (c) θf f of stair descent is negative and the toe strike the ground prior to the heel [22], [23].

1) High identification accuracy: The identification accuracy should be as high as possible to ensure correct prosthesis control as well as the amputee’s safety. 2) Minimal sensors: The method should not use too many sensors and attach sensors to the body and the sound-side leg, in case of interfering with the amputee’s motions. Additionally, the sensors should be able to be embedded into the prosthesis to improve convenience. 3) Short identification delay: During transitions, the method should identify the transition as early as possible, thus timely sending control commands to the prosthesis and bringing about smooth locomotion transitions. 4) Low computation load: High computation load leads to long computation time and high CPU power consumption. The computational load of the method should be as low as possible to enable real-time operation. In this paper, we present a fuzzy-logic-based method with multisensor fusion to identify terrains in real time. Five locomotion features measured by fusion of two force sensitive resistors (FSR), two triaxis gyroscopes, two triaxis accelerometers and a timer, are utilized to identify different terrains and transitions. Experiments are carried out with six able-bodied and three amputee subjects to verify the effectiveness of the proposed method. The rest of this paper is organized as follows. Section II introduces locomotion features for identification and how to measure these features with multisensor fusion. Section III describes the fuzzy-logic-based method in detail, followed by the description of the experimental protocol and performance evaluation methods in Section IV. Experimental results are presented in Section V. We discuss and conclude in Sections VI and VII, respectively. II. LOCOMOTION FEATURE MEASUREMENT WITH MULTI-SENSOR FUSION A. Locomotion Features on Different Terrains In addition to level ground, ramps and stairs are the most common terrains people come across in daily life. During locomotion on different terrains, the foot and the shank move in different ways and the different locomotion information can be used to identify terrains. In this paper, five features are selected, as shown in Table I. These features are selected for two reasons. First, these features vary a lot on different terrains and can be easily used to distinguish these terrains. Second, the selected

Fig. 2. Shank inclination angle at the first strike (θf s k ) on different terrains. θf s k of stair ascent is the minimum while that of the level ground is the maximum. θf s k of the ramp ascent/descent is similar to that of the stair ascent/descent, and it is not shown for conciseness. This feature is applicable to both the able-bodied and the amputee.

features are convenient to measure with just two IMUs and two foot pressure sensors. As for the transtibial amputees with passive prostheses, their locomotion features may be quite different from those of the able-bodied as their prostheses cannot behave like the sound limbs. Even for the robotic active prostheses, they may behave in an unnatural way before terrain of the next step is identified. Hence, such difference needs to be considered. 1) Foot Inclination Angle at the First Strike: Foot inclination angle refers to the relative angle between the foot and the horizontal plane. This angle is defined to be zero when the foot is placed on the level ground, positive when the foot rotates counterclockwise and negative when foot rotates clockwise. Foot strike refers to the moment when foot contacts the ground, and it includes heel strike and toe strike. For stair descent, the first strike is the moment when toe strikes the ground while for other terrains it is the heel strike, as shown in Fig. 1. 2) Shank Inclination Angle at the First Strike: Shank inclination angle refers to the shank angle relative to the vertical plane. We define that the angle is zero when the shank is perpendicular to the horizontal ground, positive if the knee joint extends to the forward direction and negative if the knee joint flexes to the backward direction. Shank inclination angles at this moment vary on different terrains, as shown in Fig. 2. 3) Foot Strike Sequence: For the able-bodied walking on level ground, the heel generally strikes the ground prior to the toe, which is the same case during walking on ramps. During stair ascent, however, the heel and the toe strike the ground almost at the same time, while the toe strikes the ground prior to the heel during stair descent [22]. Based on these differences, foot strike sequence can be used as a feature to distinguish stairs from the other terrains, as shown in Fig. 1. Note that there are also cases that the foot strikes the ground with the forefoot rather than the heel during stair ascent [24] and the foot strikes the ground with the heel rather than the forefoot

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Fig. 3. Foot strike sequence of the amputee on different terrains. (a) During ramp descent, the heel strikes the ground first and the toe may not strike the ground. (b) During ramp ascent, the toe strikes the ground first and the heel may not strike the ground. (c) During stair descent, the heel strikes the ground prior to the toe. The foot strike sequence during level ground and stair ascent is identical with that of the able-bodied.

can be measured by gyros, and the orientation angle can be calculated by integrating the gyro signals. In this paper, the direction cosine matrix (DCM) method was employed to calculate the inclination angle based on the gyro measurements. Detailed information can be found in [25]. Because of the gyro signal noise, the quantization error and the integration error, numerical integration introduces errors and causes the angle to drift. The two methods that are commonly used to correct the angle drift are extend Kalman filtering (EKF) and the complementary filter. Though EKF has been studied for many applications, it is computationally demanding and unsuitable for the small scale embedded processors in prostheses [26], [27]. In this paper, a nonlinear complementary filter (NCF) was designed based on the amplitude of the acceleration to correct the angle drift. According to [26], the drift error Err could be estimated by

Fig. 4. Foot inclination angle at mid-stance of the able-bodied. (a) During ramp descent, the angle is negative. (b) On level-ground, the angle is zero, so is this angle on stairs. (c) During ramp ascent, the angle is positive.

Err = Zs × as

Fig. 5. Shank inclination angle at toe-off (θt s k ) of different terrains. For all terrains, θt s k is negative, θt s k of the descent terrain (stair descent and ramp descent) is the minimum while the angle of the ascent terrain (stair ascent and ramp ascent) is the maximum. This feature is applicable to both the able-bodied and the amputee.

during stair descent because of different stair sizes and walking habits. As stair ambulation in these two cases is easy to identify, it is not taken into consideration in this paper. As for the amputees, their foot strike sequence during ramp/stair ambulation is quite different from that of the ablebodied for the prosthetic ankle is fixed, as shown in Fig. 3. 4) Foot Inclination Angle at Mid-stance: At mid-stance when both the heel and the toe are on the ground, the foot is parallel to the terrain surface and the foot inclination angle θfo ot is equal to the terrain surface inclination angle. These angles of level ground and stairs are quite different from those of ramps, as shown in Fig. 4. Note that when amputees walk on ramps with passive prostheses, the prosthetic feet may not be placed parallel to the ramp during stance phase as the ankle is fixed (see Fig. 3). This feature in this case will be invalid. 5) Shank Inclination Angle at Toe-Off: Shank inclination angle varies continuously during one gait cycle, and the variation ranges on different terrains are not the same. Toe-off refers to the end of the stance phase, when the shank inclination angle is close to the minimum. Such angles of different terrains are not the same, as shown in Fig. 5. B. Feature Measurement with Multi-sensor Fusion 1) Inclination Angle Measurement: The inclination angle can be described by the orientation relative to a reference direction. The change rate of the orientation, i.e., rotation rate,

(1)

where Zs refers to the third row of the rotating matrix R, and as refers to the accelerometer measurements. If as includes gravitational acceleration gs only, the estimated error is entirely accurate. However, as includes external acceleration besides gs during locomotion. As a result, the error calculated by (1) is not completely accurate. The accuracy degree of the estimated error is estimated by the norm ratio of as and gs . If as equals gs , the reference vector is regarded as accurate and its accuracy degree is the highest. If as deviates from gs , the reference vector becomes less accurate and the accuracy degree decreases. s Based on this relation between a gs and the accuracy degree, we designed the exponential nonlinear weighting function −

W =e

(

as −1 ) 2 gs c2

.

(2)

The parameter c determines the decay rate of the weight, and is selected by minimizing the tracking error between the estimated angle and the reference angle. Multiplying W , the filtered drift error Err F is Err F = W · Err.

(3)

Based on the drift error Err F , a proportional-integral (PI) controller is used to calculate the drifting angular rate t ω drifting = KP · Err F + KI · Err F dt. (4) 0

By feeding this drifting angular rate back to the gyro outputs, the estimated angle will be forced to gradually track the reference angle and the drift is then canceled. The calculation is summarized in Fig. 6. The MPU-6050 motion measuring unit, which has an embedded triaxis gyroscope and a triaxis accelerometer, is used to measure rotation rate and acceleration signals. The gyroscope has a full-scale range of ± 2000◦ /s and a resolution of 0.06◦ /s while the accelerometer has a full-scale range of ± 16 g and a resolution of 0.5 mg. An active-based marker system (Codamotion, Charnwood Dynamics Ltd., Rothley U.K.) was used to evaluate the


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Fig. 6. Inclination angle measurement with drift correction. Zero offset of the original gyro signals was firstly removed before integration. Drift error calculated by the cross product of Z s and a s was fed back through the nonlinear complementary filter and the PI controller to cancel the drift.

Fig. 8. The feature set updates at different event moments of one gait cycle. The label ˆ means that the feature has been updated at this moment.

C. Feature Acquisition Fig. 7. Inclination angle measurement test. The test signal in red calculated by the proposed method can track the reference signal in blue measured by Codamotion with a RMS tracking error of 1.53◦ ± 0.11◦ .

effectiveness of the proposed method. The markers were placed at the side of the shank of an able-bodied subject, and the subject was required to walk along a track on level ground at his selfselected speed. The Codamotion camera was placed approximately 1 m at the side of the track which resulted in a marker tracking accuracy of 1 mm (based on factory testing). The Codamotion marker positions and the IMU data were recorded at 200 Hz. Two steps were recorded for each trial and ten trials were performed. The resulted angle data were shown in Fig. 7. The angle measurement method has a satisfactory accuracy (RMS (root mean square) tracking error of 1.53◦ ± 0.11◦ ) without drift and can be used to measure the foot and shank inclination angle accurately. 2) Foot Strike Measurement: The five features are related to four gait events, which are defined as heel strike, toe strike, midstance, and toe off. Foot strikes and toe-off are detected with the GRF measured by two FSRs (FlexiForce A401 produced by Tekscan). Each FSR has a circular sensing area of about 5 cm2 and a configurable measurement range from 0 – 1 to 0 – 7000 lb. The two FSRs are integrated into an insole. One is placed under calcaneus tuberosity to measure GRF applied at heel, and the other is placed near the first metatarsal bone to measure GRF applied at toe. Different measurement ranges are configured by different sensing circuits. Heel strike is determined if the GRF of the heel is continuously greater than a predefined threshold value for more than five sampling points. On the contrary, heel off is determined if the GRF of heel is continuously less than the threshold value for more than five sampling points. Toe strike and toe off can be determined in the same way.

Based on the measurements above, five features can be acquired. The measurement system records the locomotion information during the whole gait cycle and calculates the locomotion features at the first strike, the second strike, mid-stance, and toeoff, as shown in Fig. 8. The average gait cycle ratio of the four gait events are 0%, 8.8%, 27.6%, and 59.4%, respectively [22]. The feature set {F1 , F2 , F3 , F4 , F5 } is updated at every gait event moment. First, when the heel strikes the ground, F eature1 (foot inclination angle at the first strike) and F eature2 (shank inclination angle at the first strike) are acquired, as shown in Fig. 8(a). Second, at the moment of toe-strike, F eature3 (foot strike sequence) is acquired, which is normalized by the gait cycle period of the last step, as shown in Fig. 8(b). Third, at the moment when ωfo ot < ω0 and | afo ot −g| < a0 , F eature4 (foot inclination angle at mid-stance) is acquired. ωfo ot and afo ot refers to the angular rate and acceleration of the foot, respectively, and ω0 and a0 are the corresponding threshold values. This condition indicates that the foot is immobile at this moment, as shown in Fig. 8(c). Fourth, at the moment of toe-off, F eature5 (shank inclination angle at toe-off) is acquired, as shown in Fig. 8(d). During the swing phase, all the features have been acquired. The measurement system resets the feature set and gets ready for the next gait cycle, as shown in Fig. 8(e). III. FUZZY-LOGIC-BASED TERRAIN IDENTIFICATION Based on the locomotion features acquired, a simple way to identify terrains would be to apply different thresholds to the features. Such method may be effective when the number of identified objects is low and the variation of the feature values is distinct, such as the two-valued digital signal. Terrain identification we studied here, however, has five objects to identify, and the features used to identify terrains have varying values

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Fig. 9.


Base function: the modified Gaussian function with different c .

Fig. 10. Base function 2: the modified hyperbolic tangent function. x0 is the threshold value and s is the sensitivity coefficient, respectively.

during locomotion. As a result, it is inappropriate to process these signals with the threshold method. Thus, the fuzzy logic is used as the framework to make inferences of terrains. Fuzzy logic is a form of many-valued logic. It deals with reasoning that is approximate rather than fixed, and its identification rule is set based on the sound understanding of the problem [28], [29]. For terrain identification, identified objects are analyzed as a set of terrains, and the truth degree of that the current terrain is the target terrain determined by the fuzzy membership value. A. Membership Functions The membership function describes the truth degree of the identification that the current terrain is identified as the target terrain. It is designed according to the correlation of the feature value with the function value. Take the shank inclination angle at the first strike, for example, a larger feature value means that the current terrain is more likely to be level ground or descent terrains than ascent terrains. So the truth degree of level ground and descent terrains have a positive correlation with the feature value while that of ascent terrains has a negative correlation. Membership functions can then be designed accordingly. 1) Base Membership Functions: In general, each terrain has a unique membership function for a specific feature, and five terrains will result in 25 membership functions in total, which are troublesome to design. Note that truth degrees of some terrains have same correlation with specific features, and their membership functions of these features are the same. For example, truth degrees of level ground, stair ascent, and stair descent have the same correlation with F eature4. The more close the feature value is to 0◦ , the larger the truth degrees of these terrains are. Besides, for some other feature, correlation of different terrains is just symmetrical or has a simple mathematical relationship. Take ramp ascent and ramp descent, for example, their membership functions of F eature4 are symmetrical about θfo ot = 0. Hence, only two kinds of functions are selected as the base functions and the other membership functions can be derived from them. The first base function is a modified Gaussian function fb1 (x) = e−

( x −b ) 2 c2

(5)

where b is known as the expectation, and c is a constant proportional to the standard deviation. The graph of the base function is a bell curve, as shown in Fig. 9.

This type of membership function describes the Gaussian correlation of the truth degree and the feature value that the more close the feature value x is to b, the larger the truth degree or membership value f (x) is. Truth degree distribution varies with different c. The second base function is the modified hyperbolic tangent function fb2 (x) =

1 [tanh(s · (x − x0 )) + 1] 2

(6)

where x0 is the threshold and s is the sensitivity coefficient related to the function slope, as shown in Fig. 10. The hyperbolic tangent function describes the correlation that when the feature value x is equal to the threshold value x0 , truth degree of this terrain is 0.5, neither large nor small. And this membership degree will increase or decrease at a speed determined by s if x deviates from x0 . Based on fb2(x) , another type of membership function can be derived, i.e., fd1 (x) = 1 − fb2 (x)

(7)

which describes a complementary correlation with fb2 (x). 2) Membership Function of Feature 1: During level ground walking, the knee joint at the first strike is extended while the ankle angle is close to 0◦ , consequently the foot inclination angle at this moment is greater than 0◦ . During stair ascent and ramp ascent, the knee is flexed and the ankle joint is in dorsiflexion, but the dorsiflexion degrees are different. During ramp ascent, the ankle dorsiflex to a relatively large angle to prevent the toe from striking the ramp, which makes the foot inclination angle at this moment greater than the ramp angle. During stair ascent, the ankle is in a small dorsiflexion degree and the foot inclination angle is around 0◦ [22]. During ramp descent and stair descent, the knee joint at the first strike is extended while the ankle at this moment is in plantarflexion. The plantarflexion degree of stair descent is quite large to make the toe strike the ground prior to heel and smoothly lower the body’s center of gravity. As a result, F eature1 of stair descent is less than 0◦ . While during ramp descent the ankle plantarflexion degree is relatively small, and the foot inclination angle is around 0◦ [23]. In summary, the membership values of level ground and ramp ascent have a positive correlation with the feature value while those of stair ascent and descent terrains have a negative correlation, as shown in Fig. 11. “LG” is short for level ground, “SA” for stair ascent,


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Fig. 11. Membership function of Feature 1 (the foot inclination angle at the first strike) on different terrains.

Fig. 13. Membership function of Feature 3, foot strike sequence on different terrains.

Fig. 12. Membership function of Feature 2, the shank inclination angle at the first strike on different terrains.

Fig. 14. Membership function of Feature 4, the foot inclination angle at midstance on different terrains.

“RA” for ramp ascent, “SD” for stair descent, and “RD” for ramp descent. The shorthand forms apply to the following figures. As for amputees with rigid prostheses, their ankle joints can neither dorsiflex nor plantarflex, and the foot inclination angle is determined by the shank extension/flexion degree. So this feature has similar differentiation degree to F eature2 and cannot provide more useful information to the identification. Hence, this feature is not used for the amputees. 3) Membership Function of Feature 2: Shank inclination angle at the first strike is determined by the extension range of the knee joint. When walking on ascent terrains, the knee joint is generally in the flexion state and the shank inclination angle is relatively small. On the contrary, when walking on level ground and descent terrains, the knee joint will extend to the maximal degree and the shank inclination angle is then relatively large, as shown in Fig. 2. The larger the F eature2 values are, the higher the truth degrees of level ground and descent terrains are, while the lower the truth degrees of the ascent terrains are, as shown in Fig. 12. As for terrains whose membership values have positive correlation with the feature value, there are some differences. For descent terrains, the extension range of the knee joint is limited by the stair length or the ramp inclination angle. This limitation causes the feature value of descent terrains smaller than that of the level ground. This difference is represented with different s, as shown in Fig. 12. Membership functions of this feature for the amputees are the same with those for the able-bodied. 4) Membership Function of Feature 3: For the able-bodied, the heel generally strikes the ground prior to the toe on terrains except for stair descent, where the toe strikes the ground prior

to the heel, as shown in Fig. 1. Foot strike sequence could be quantified by the time interval between two strikes. So the foot strike interval of stair descent is negative while those of the other terrains are positive, and the threshold value to differentiate these terrains is 0, as shown in Fig. 13. As for terrains which have positive feature values, there are still some differences. The strike interval of ascent terrains is usually smaller than that of the others for the foot inclination angle as the first strike is close to the terrain surface inclination angle. So if the feature value is smaller than the threshold value, the membership degree of ascent terrains should be greater than that of the others. On the contrary, if the feature value is greater than the threshold, the membership degree of ascent terrains should be smaller. This difference can be realized by changing the sensitivity coefficient s. Note that this feature of the amputees during stair and ramp ambulation is quite different from that of the able-bodied, as shown in Fig. 3, and the corresponding membership functions are also different. 5) Membership Function of Feature 4: Foot inclination angle at mid-stance equals the terrain surface inclination angle. It is obvious that this angle on level ground and stairs is 0◦ , while that of ramp ascent/descent is positive/negative (see Fig. 4). The threshold is set to be ± 5◦ , as shown in Fig. 14. Note that for amputees this feature is not valid during ramp ascent as the prosthetic foot cannot be placed parallel to the ramp, thus the membership function is not used. 6) Membership Function of Feature 5: Shank inclination angle at toe-off is determined by the flexion degree of the knee joint. As the flexion degree during stair/ramp descent is larger than that on the other terrains, the feature value on descent terrains is smaller than that on the other terrains. For the similar

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Fig. 15. Membership function of Feature 5, the shank inclination angle at toe-off on different terrains. TABLE II MEMBERSHIP FUNCTIONS ON DIFFERENT TERRAINS Fig. 16. Relative probability of different terrain transitions. The boldness of the transition line indicates the possibility scale.

reason, this feature value on level ground is smaller than that on ascent terrains, as shown in Fig. 15. The membership functions different terrains and features are listed in Table II, where “N” refers to that this feature of the corresponding terrain was not used for identification. B. Parameter Selection of Membership Functions All the membership functions of different terrains are derived from two kinds of base functions. For each base function, there are two parameters to be determined. As for the first base function shown in (5), b is selected as the mean feature value of the corresponding terrains, and c is selected to make the curve intersect with the other curves at target feature values, for example, ± 5◦ in Fig. 14. As for the second base function shown in (6), the selection of the parameters varies with different cases, and the cases are classified with different kinds of curve intersections. The first case is shown in Figs. 11 and 12, where the monotone increasing curve intersects with the monotone decreasing curve at x0 . Suppose that the terrains associated with the monotone increasing curve have the mean feature value μ1 and standard deviation σ1 , while the terrains associated with the monotone decreasing curve have the mean feature value μ2 (μ2 > μ1 ) and standard deviation σ2 , then the threshold value x0 is determined as (8) with a method similar to [11] σ1 x0 = μ1 + (μ2 − μ1 ) . (8) σ1 + σ2 The sensitivity parameter s is selected to ensure that the membership fb2 (μ1 ) = 0, and fb2 (μ2 ) = 1 exactly. The second case is shown in Fig. 13, where the monotone increasing curve intersect with the monotone decreasing curve at a predefined value

(0 in Fig. 13) instead of x0 . In this case, x0 of each curve is selected as the mean feature value of the associated terrains, and s is selected to make that the curves intersect at the predefined feature value and the membership degree of this value approximates 0. The third case is shown in Figs. 12 and 13, where the two monotone increasing curves intersect at x0 . In this case, the two intersected curves have the same x0 selected as the mean feature value. s of one curve is determined with the methods mentioned above, and s of the other curve is increased by 50%. The last case is shown in Figs. 14 and 15, where the monotone hyperbolic tangent function intersects with the nonmonotone Gaussian function, x0 is also selected as the mean feature value, c of the Gaussian function is selected to make the function intersect with the hyperbolic function at x0 , and s is selected to make that the membership degree of the hyperbolic function decreases to 0 at feature value b of the Gaussian function. C. Membership Function Composition A single feature is not precise enough to identify all the terrains, so memberships of five features are combined together to get the total membership of a specific terrain μ(Ti ) = μ1 i + μ2 i + μ3 i + μ4 i + μ5 i

(9)

where μ(Ti ) is the membership degree of terrain Ti and μ1 i , μ2 i , μ3 i , μ4 i , and μ5 i are the corresponding membership values of different features. D. Transition Constraint Modulation Human daily activities encounter different terrains and perform various transitions. However, it may be simplified with constraints from the view of prosthesis control and transition possibility differences. For example, if current terrain is stair ascent, the terrain of the next step will most possibly be stair ascent or level ground. Although the next step may also be stair descent or ramp ascent/descent, the probability is relatively small, which can be described by Fig. 16. Based on the transition probability difference, membership degree of specific terrains are modulated with a modulation


constant cm d , μm d (Ti ) = μ(Ti ) + cm d

(10)

where μm d refers to the modulated membership degree, cm d ranges from 0 to 1 and is determined experimentally, Ti refers to the last identified terrain or level ground. Modulated by (10), the membership degrees of level ground and the last identified terrain are increased by cm d for every identification. Based on the calculation and modulation, the target terrain Tm is selected as the one with the maximum μm d Tm = arg max(μm d (Ti )). Ti

(11)

The fuzzy-logic-based identification method with multisensor fusion can be summarized as Fig. 17. IV. EXPERIMENT PROTOCOL AND PERFORMANCE EVALUATION A. Subjects and Experiment Protocol Nine subjects, including six able-bodied and three transtibial amputees participated in the experiments and were provided with informed consent. Able-bodied subjects (four male and two female) have an average height of 1.70 ± 0.03 m, an average weight of 59.8 ± 4.58 kg, and an average age of 21.8 ± 1.01 years old. Amputee subjects (three male) have an average height of 1.72 ± 0.03 m, an average weight of 62.7 ± 4.26 kg, and an average age of 33.67 ± 5.70 years old. All the amputee subjects have used prostheses for more than 7 years and are experienced at prosthesis ambulation. They wore their daily used prostheses in the experiment. Subjects were firstly instrumented with the multisensor system and then conducted the required experiments. The experiment consisted of two sections. The first section included ten experiment trials for training and determining parameters such as the threshold values of GRF and shank inclination angle. The second section included 20 experiment trials for test. In each trial, the subjects were required to walk on different terrains at their self-selected speeds and all the terrains and locomotion transitions were included. The subjects stood still at the beginning, and then performed level-ground walking, stair ascent, level-ground walking, ramp descent, level-ground walking, standing, turning back, level-ground walking, ramp ascent, level-ground walking, stair descent, level-ground walking, and ended with standing again, as shown in Fig. 18. The stair is 75 cm in width, 40 cm in depth, and 14 cm in height while the ramp inclination angle is 16.5◦ . Terrain identification was performed online in real time by the STM32 MCU. The measured locomotion features and the identified terrain were sent to the computer by the wireless transmitter (NRF24L01).

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For the later, we concerned whether and how early could locomotion transitions be detected, and they were evaluated separately. Moreover, algorithm execution time was measured to evaluate the computation load of the proposed identification method. 1) Steady Locomotion Period: The first performance index is the average identification accuracy (IA) defined as IA =

Ncorrect × 100% Ntotal

(12)

where Ncorrect is the number of correct identification while Ntotal is the total number of test events in the experiment. The second performance index is the confusion matrix which describes the error distribution between terrains ⎞ ⎛ c11 c12 · · · c15 ⎟ ⎜ ⎜ c21 c22 · · · c25 ⎟ ⎟ (13) CM = ⎜ ⎜··· ··· ··· ··· ⎟. ⎠ ⎝ c51

c52

···

c55

The element of the confusion matrix is defined as nij cij = n × 100% j =1 nij

(14)

where nij is the number of events that terrain i is identified as terrain j. The denominator is the number of total events of terrain i. Note that the diagonal elements are the identification accuracy and the off-diagonal elements refer to the errors. 2) Locomotion Transition Period: To evaluate whether the transition can be identified in time, the critical moment when the transition takes place is defined. For most terrains, gaits of the able-bodied and the amputees are similar and the critical moment is defined as foot-flat when the second foot strike happens. During ramp ascent of the amputee, however, there is no foot-flat and the critical moment is defined as 20% after the first strike. Identification delay is calculated by DI =

ti − tc × 100% G

(15)

where ti is the moment when the locomotion transition is identified and tc is the defined critical moment. The prediction delay is normalized by the gait cycle G. 3) Algorithm Execution Time: Computation load is vital for onboard operation and real-time identification. The resulted algorithm execution time is defined as the time period from the moment when the feature acquisition starts to the moment when the target terrain is acquired, as shown in Fig. 17. V. EXPERIMENTAL RESULTS

B. Performance Evaluation

A. Identification Accuracy of the Steady Locomotion Period

To make a detailed evaluation of the identification performance, the locomotion period was divided into steady locomotion period (i.e., no locomotion transitions) and locomotion transition period. For the former, the emphasis of identification was to discriminate the targeted terrain from the others.

The identification accuracy of nine subjects on different terrains is shown in Table III. The identification accuracy of the able-bodied ranges from 96.88% to 100% while the amputee’s accuracy rate is a little bit worse, ranging from 94.37% to 100%. Among the five terrains,

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Fig. 17. Block diagram of the identification method. Accelerometers, gyroscopes, and FSRs were used to measure locomotion information and detect gait events. At every event moment, the feature set was updated and the identification was performed to calculate possibilities of different terrains. After that, the calculated possibilities of terrains were modulated by the transition constraint function. Target terrain was determined as the one with the largest possibility.

Fig. 18. The proposed multisensor system and the snapshots of the experimental videos. Two IMUs were mounted at the forefoot and shank while two FSRs were mounted near heel and toe in the insole, respectively. The MCU was also attached to the shank. The subjects stood still at the beginning, and then performed levelground walking, stair ascent, level-ground walking, ramp descent, level-ground walking, standing, turning back, level-ground walking, ramp ascent, level-ground walking, stair descent, level-ground walking and ended with standing again. TABLE III IDENTIFICATION ACCURACY OF DIFFERENT TERRAINS

ramp descent and ramp ascent have the best identification accuracy because their foot inclination angles at mid-stance are quite different from that of the other terrains, while the accuracy of level ground is the worst. The average identification accuracies of five terrains are higher than 97.82%, which is satisfactory for practical use. B. Confusion Matrix of the Steady Locomotion Period The confusion matrices of the able-bodied and the amputee are shown in Fig. 19, where most confusions appear between level ground and other terrains. As for the able-bodied, most confusions occur between level ground and stair ascent, which is because the features of stair ascent are quite similar to that of level ground in some cases, and vice versa. For example, if the instrumented leg leads the transition from level ground to stair ascent and the step length is relatively large, then the resulted values of F eature1 and F eature2 will be quite large and are similar to that of level ground. In this case, stair ascent will be misidentified as level ground. Similar reasons caused the confusion between level ground and ramp as-

Fig. 19. Confusion matrices (mean ± standard error of mean) on different terrains. (a) is the matrix of the able-bodied while (b) is the matrix of amputees.

cent before F eature4, foot inclination angle at mid-stance was acquired. The confusions between level ground and stair descent resulted from similar values of F eature1 and F eature5. For example, if the last step is level ground, and the instrumented leg leads the transition from level ground to stair descent at this step, stair descent may be misidentified as level ground before a new distinctive feature is updated, because most features of the feature set at this moment belong to that of level ground.


TABLE IV IDENTIFICATION DELAY OF LOCOMOTION TRANSITIONS

Similar reasons caused the confusion between level ground and ramp descent. As for the amputee, the confusions between level ground and the other terrains are resulted from the similar reasons to that of the able-bodied. What seems puzzling is that 0.42% identifications of ramp ascent are misidentified as stair ascent as features of these two terrains are very different, especially for the foot inclination angle at mid-stance. This is because prosthetic feet of the amputees cannot be placed parallel to the ramp when ascending ramps as their ankle cannot dorsiflex, and the foot inclination angle at mid-stance is not available. C. Identification Delay of Locomotion Transition Period Eight transitions between five terrains are studied. During the experiments, all the transitions can be correctly detected and the average identification delay of the able-bodied and the amputee is listed in Table IV. The main differences between level ground and stair ascent are F eature1 and F eature2. So generally the transition LG → SA and SA → LG can be identified at the first strike prior to the critical moment. If the instrumented leg leads the transition LG → SA and the step length is large as mentioned above, stair ascent will be misidentified as level ground and the transition delay will increase. As for level ground and ramp descent, the main difference is F eature4. The identification delay of LG → RD and RD → LG is mainly caused by the time interval between the second foot strike and mid-stance, so is the delay of transitions between level ground and ramp ascent. As for the transition LG → RA of the amputee, the toe strikes the ground first and the transition can be detected at the critical moment, so the identification delay is 0. For the able-bodied, the toe strikes ground prior to the heel during the transition LG → SD and the transition can be identified at foot-flat when F eature3 is acquired. As for that of the amputee, the heel strikes the ground prior to the toe, which is the same as that on level ground, and generally the transition cannot be identified until F eature5 is acquired, so is the transition SD → LG, and the resulted identification delay is as large as 37.44% of one gait cycle. As for the transition SD → LG of the able-bodied, there is a distinct variation of the foot strike interval, so the transition can be identified as soon as foot-flat when Feature 3, foot strike sequence is acquired and the identification delay is 0.

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D. Algorithm Execution Time At each gait event moment, the feature set {F1 , F2 , F3 , F4 , F5 } updates and the identification are performed. Take the ablebodied as an example of the identification process: first, membership functions listed in Table II calculate the corresponding membership based on the feature set, and 25 membership values are obtained; second, the membership values belonging to the same terrain are added together and five membership degrees corresponding to five terrains are acquired; third, membership degrees of specific terrains are modulated according to the terrain transition constraint; finally, the terrain with the maximal membership degree is selected as the identified terrain. For each identification, the calculation includes addition, multiplication, exponentiation, and trigonometric operations. Identification algorithm execution time is tested with the STM32 MCU, which is a popular low-cost microcontroller with a 72MHz system clock. Average execution time of 20 tests is 0.79 ms ± 0.02 ms, which is satisfactory for online identification in real time. Real-time consecutive terrain identification results are shown in Fig. 20. E. Influence of the Transition Constraint Modulation As is described in Section III-D, the transition constraint aims to modulate membership degrees of some specific terrains based on transition possibility differences, and bring influences on the identification performances. To evaluate the influence quantitatively, identification accuracy and identification delay of the nine subjects are recalculated by removing the transition constraint. 1) Influence on the Identification Accuracy: As shown in Fig. 16, it is equally possible to transit from level ground to other terrains, so the modulation (10) has no influence on level ground. For the other terrains, the transition constraint works differently, and the accuracy variations are shown in Table V. Without transition constraint modulation, the average identification accuracy has a decrease of 2.30 %. 2) Influence on the Identification Delay: As is mentioned above, transition from level ground to any other terrain has equal possibilities, so the identification delay is not influenced. As for transition from other terrains to level ground, membership degrees of the current terrain and level ground are increased equally by (10), so the transition delay is not influenced either. F. Influence of Stair Height and Ramp Inclination Angle During the experiments, parameters of the platform are constant, and the proposed method is able to work well on the constant platform. When applied to prosthesis control in the amputee’s daily life, stair height and ramp inclination angle may be different from the experimental ones, and the validity of the proposed method on a varied platform needs to be evaluated. So we changed the stair height from 14 to 12 cm and 16 cm, the ramp inclination angle from 16.5◦ to 12.5◦ and 8.5◦ , respectively, and repeated the experiment with an amputee subject using the previously trained model. To evaluate the influence of stair height and ramp inclination angle exclusively, step length

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Fig. 20. Real-time consecutive identification of the able-bodied subject for 38-s long trial. The identification did not take the turning back into consideration and this period was depicted with dash line. The bottom subfigure indicates the identification delay between the real terrain and the identified terrain. TABLE V ACCURACY VARIATION WITHOUT TRANSITION CONSTRAINT

TABLE VII IDENTIFICATION DELAY ON DIFFERENT STAIRS AND RAMPS

TABLE VI IDENTIFICATION ACCURACY ON DIFFERENT STAIRS AND RAMPS

on changed platform remained the same with that on previous platform. 1) Influence on Identification Accuracy: As shown in Table VI, the identification performances on lower stairs decreased, while that on higher stairs vary little. This was mainly resulted from that higher stairs brought smaller F eature2 and F eature5, while lower stairs had greater feature values. According to Figs. 12 and 15, lower feature values increase the membership degree of stair ascent and stair descent, respectively, and help to distinguish these terrains from the others better, while greater feature values decrease the membership degree and may lead to misidentifications. As for ramp ascent, the amputee’s toe strikes the ground first and the heel does not strike the ground during the whole gait cycle. This character exists on the all tested ramps and can easily distinguish ramp ascent from the other terrains. So the accuracy rate of ramp ascent on different terrains does not change much. As for ramp descent, smaller ramp inclination angle caused F eature5 (Shank inclination angle at toe-off) to increase and decreased the membership degree of ramp descent. In addition,

the distinction degree of F eature4 also decreases as the ramp inclination angle approximates the threshold value (− 5 ◦ ). As a result, identification accuracy decreases with smaller inclination angles. 2) Influence on Identification Delay: The resulted identification delay on different terrains is shown in Table VII. For transitions from level ground to the other terrains, larger stair height and ramp inclination angle tend to decrease the identification delay as the membership degrees calculated by associated features increase. As for transitions from the other terrains to level ground, the identification delay does not vary significantly except for transition LG → RD on the ramp of 8.5◦ , where two transitions were not identified at the first step and the average delay was increased by these two misidentifications. VI. DISCUSSION A fuzzy-logic-based terrain identification method with multisensor fusion was proposed to identify terrains online in real time. Experimental results validated that the proposed method is applicable for prosthesis control for the following reasons. First, the proposed method has studied most common terrains in daily life and the achieved accuracy of 98.74% ± 0.32% are comparable with previous studies [10], [11], [15]. Second, the


proposed method needs only two IMUs and two FSRs, and there is no need to attach sensors to the sound limb as well as other body parts, which makes it more convenient than methods with EMG [15] or capacitive signals [10]. Third, the features and membership functions selected for the terrain identification are based on the sound understanding of the subject’s locomotion characteristics, which represent the subject’s specific walking habits and rarely change along time. This character makes the method appropriate for long-term use, while EMG signals are prone to muscle fatigue. Fourth, the proposed method uses five features and two base membership functions only. All the calculation and identification can be fulfilled in less than 1 ms, which enables the method to perform online in real time while most of previous work are based on offline analysis [9], [10], [15]. Fifth, the proposed method can correctly identify all the studied eight transitions between five terrains and the average identification delay is 9.06% ± 3.46% of one gait cycle, which is far less than one step. Moreover, for some transitions such as SA → LG, the proposed method can identify it in advance. Note that previous methods that can identify transitions in advance need much more sensors and attaching sensors to the sound limb [10], [15], [16] while methods that use similar sensors to our study have an considerable identification delay of one step [11]. Despite the above advantages, the method suffers from several limitations. The first is that the identification delay of the amputee’s transitions between level ground and stair descent is relatively long, which may result in lagging adjustment of the prosthesis control. The second limitation is that the modulation constant of the terrain transition constraint was determined experimentally without statistical results. Last, the proposed method does not consider the speed variation, which may lead to changes to human walking patterns. VII. CONCLUSION In this paper, we have presented a fuzzy logic approach to identify terrains in real time based on multisensor fusion. Five locomotion features are utilized to identify level ground, stair ascent, stair descent, ramp ascent, ramp descent as well as the transitions between them. Average identification accuracy of six able-bodied and three amputee subjects during steady locomotion periods is 98.74% ± 0.32%. During locomotion transition periods, all the studied transitions are correctly identified and the average identification delay is 9.06% ± 3.46% of one gait cycle. The execution time of the proposed method is 0.79 ms ± 0.02 ms and the continuous terrain identification results show that the proposed method can be operated online in real time. Future studies include the extension of the identification to more locomotion modes such as pivot steering, obstacle overcome, and walking with speed variations and combination of the proposed method with a powered transitibial prosthesis for real-time operations. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their valuable suggestions that made possible the improvement of this paper.

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REFERENCES [1] S. K. Au, J. Weber, and H. Herr, “Powered ankle-foot prosthesis improves walking metabolic economy,” IEEE Trans. Robot., vol. 25, no. 1, pp. 51– 66, Feb. 2009. [2] G. K. Klute, J. Czerniecki, and B. Hannaford, “Development of powered prosthetic lower limb,” presented at the First Natl. Meeting, Veterans Affairs Rehabil. R and D Service, Washington, DC, USA, 1998. [3] R. Versluys, A. Desomer, G. Lenaerts, O. Pareit, B. Vanderborght, G. Perre, L. Peeraer, and D. Lefeber, “A biomechatronical transtibial prosthesis powered by pleated pneumatic artificial muscles,” Int. J. Modell. Identif. Control, vol. 4, pp. 394–405, 2008. [4] J. Hitt, T. Sugar, M. Holgate, R. Bellman, and K. Hollander, “Robotic transtibial prosthesis with biomechanical energy regeneration,” Ind. Robot, vol. 36, no. 5, pp. 441–447, 2009. [5] J. Zhu, Q. Wang, and L. Wang, “On the design of a powered transtibial prosthesis with stiffness adaptable ankle and toe joints,” IEEE Trans. Ind. Electron., to be published. [6] A. Grabowski and S. D’Andrea, “Effects of a powered ankle-foot prosthesis on kinetic loading of the unaffected leg during level-ground walking,” J. NeuroEng. Rehabil., vol. 10, no. 49, pp. 1–11, Jun. 2013. [7] S. K. Au, M. Berniker, and H. Herr, “Powered ankle-foot prosthesis to assist level-ground and stair-descent gaits,” Neural Netw., vol. 21, pp. 654– 666, May. 2008. [8] H. Huang, T. A. Kuiken, and R. D. Lipschutz, “A strategy for identifying locomotion modes using surface electromyography,” IEEE Trans. Biomed. Eng., vol. 56, no. 1, pp. 65–72, Jan. 2009. [9] X. Wang, Q. Wang, E. Zheng, K. Wei, and L. Wang, “A wearable plantar pressure measurement system: Design specifications and first experiments with an amputee,” in Proc. 12th Int. Conf. Intell. Autonomous Syst., 2012, pp. 273–281. [10] B. Chen, E. Zheng, X. Fan, T. Liang, Q. Wang, K. Wei, and L. Wang, “Locomotion mode classification using a wearable capacitive sensing system,” IEEE Trans. Neural Syst. Rehabil. Eng., vol. 21, no. 5, pp. 744–755, Sep. 2013. [11] Y. Li and E. Hsiao-Wecksler, “Gait mode recognition and control for a portable-powered ankle-foot orthosis,” in Proc. IEEE Int. Conf. Rehabil. Robot., 2013, pp. 1–8. [12] H. Varol, F. Sup, and M. Goldfarb, “Multiclass real-time intent recognition of a powered lower limb prosthesis,” IEEE Trans. Biomed. Eng., vol. 57, no. 3, pp. 542–551, Mar. 2010. [13] F. Sup, H. Varol, and M. Goldfarb, “Upslope walking with a powered knee and ankle prosthesis: Initial results with an amputee subject,” IEEE Trans. Neural Syst. Rehabil. Eng., vol. 19, no. 1, pp. 71–78, Feb. 2011. [14] F. Sup, H. A. Varol, J. Mitchell, T. J. Withrow, and M. Goldfarb, “Preliminary evaluations of a self-contained anthropomorphic transfemoral prosthesis,” IEEE/ASME Trans. Mechatronics, vol. 14, no. 6, pp. 667– 676, Dec. 2009. [15] H. Huang, L. J. Hargrove, Z. Dou, D. R. Rogers, and K. B. Englehart, “Continuous locomotion-mode identification for prosthetic legs based on neuromuscular-mechanical fusion,” IEEE Trans. Biomed. Eng., vol. 58, no. 10, pp. 2867–2875, Oct. 2011. [16] F. Zhang, Z. Fang, M. Liu, and H. Huang, “Preliminary design of a terrain recognition system,” in Proc. Ann. Int. Conf. IEEE EMBS, 2011, pp. 5452– 5455. [17] D. Hall and J. Llinas, “An introduction to multisensor data fusion,” Proc. IEEE, vol. 85, no. 1, pp. 6–23, Jan. 1997. [18] H. Ren and P. Kazanzides, “Investigation of attitude tracking using an integrated inertial and magnetic navigation system for hand-held surgical instruments,” IEEE/ASME Trans. Mechatronics, vol. 17, no. 2, pp. 210– 217, Apr. 2012. [19] S. Foong, K.-M. Lee, and K. Bai, “Harnessing embedded magnetic fields for angular sensing with nanodegree accuracy,” IEEE/ASME Trans. Mechatronics, vol. 17, no. 4, pp. 687–696, Aug. 2012. [20] F. Aghili and A. Salerno, “Driftless 3-D attitude determination and positioning of mobile robots by integration of IMU with two RTK GPSs,” IEEE/ASME Trans. Mechatronics, vol. 18, no. 1, pp. 21–31, Feb. 2013. [21] R. C. Luo and O. Chen, “Wireless and pyroelectric sensory fusion system for indoor human/robot localization and monitoring,” IEEE/ASME Trans. Mechatronics, vol. 18, no. 3, pp. 845–853, Jun. 2013. [22] R. Riener, M. Rabuffetti, and C. Frigo, “Stair ascent and descent at different inclinations,” Gait Posture, vol. 15, pp. 32–44, 2002. [23] A. S. McIntosh, K. T. Beatty, L. N. Dwan, and D. R. Vickers, “Gait dynamics on an inclined walkway,” J. Biomech., vol. 39, pp. 2491–2502, 2006.

630


[24] D. H. Gates, “Characterizing ankle function during stair ascent, descent, and level walking for ankle prosthesis and orthosis design,” Master’s thesis, Dept. Biomed. Eng., Boston Univ., Boston, MA, USA, 2004. [25] S. B. Niku, Introduction to Robotics: Analysis, Control, Applications. Hoboken, NJ, USA: Wiley, 2010. [26] M. Euston, P. Coote, R. Mahony, J. Kin, and T. Hamel, “A complementary filter for attitude estimation of a fixed-wing UAV,” in Proc. IEEE Int. Conf. Intell. Robots. Syst., 2008, pp. 340–345. [27] T. S. Yoo, S. K. Hong, H. M. Yoon, and S. Park, “Gain-scheduled complementary filter design for a MEMS based attitude and heading reference system,” Sensors, vol. 11, pp. 3816–3830, 2011. [28] J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications. Upper Saddle River, NJ, USA: Prentice-Hall, 1995. [29] J. Maiers and Y. Sherif, “Applications of fuzzy set theory,” IEEE Trans. Syst. Man Cybern., vol. SMC-15, pp. 175–189, Jan./Feb. 1985.

Kebin Yuan (SM’13) received the Bachelor’s degree in automation from Chongqing University, Chongqing, China, in 2010. He is currently working toward the Ph.D. degree in the Intelligent Control Laboratory, College of Engineering, Peking University, Beijing, China. His research interests include pattern recognition and control of robotic rehabilitation devices.

Qining Wang (SM’06–M’09) received the Bachelor’s degree in computer science and technology from China University of Geosciences, Beijing, China, in 2004, and the Ph.D. degree in dynamics and control from Peking University, Beijing, China, in 2009. He was an Assistant Professor in the Center for Systems and Control, College of Engineering, Peking University, from July 2009 to July 2012. He is currently an Associate Professor in the College of Engineering, Peking University, and the Director of the Beijing Engineering Research Center of Intelligent Rehabilitation Engineering. He is the Project Leader of the robotic prosthesis R&D group, Peking University. His research interests include the fields of bioinspired robots and rehabilitation robotics.

Long Wang (M’99) was born in Xi’an, China, on February 13, 1964. He received the Bachelor’s and Master’s degrees in dynamics and control from Tsinghua University, Beijing, China, in 1986 and 1989, respectively, and the Doctorate degree in dynamics and control from Peking University, Beijing, China, in 1992. He has held research positions at the University of Toronto and the University of Alberta, Canada, and the German Aerospace Center, Munich, Germany. He is currently Cheung Kong Chair Professor of Dynamics and Control and the Director of the Center for Systems and Control at Peking University. He is also a Guest Professor at Wuhan University and Beihang University. His research interests include the fields of complex networked systems, collective intelligence, and biomimetic robotics.