2013 IEEE International Conference on Robotics and Automation (ICRA) Karlsruhe, Germany, May 6-10, 2013
A Fuzzy Logic Based Terrain Identification Approach to Prosthesis Control Using Multi-Sensor Fusion Kebin Yuan, Shiqi Sun, Zikang Wang, Qining Wang and Long Wang Abstract— This paper presents a fuzzy logic based terrain identification method using multi-sensor fusion for powered prosthesis control. Five locomotion features including rising time of ground reaction force, sequence of foot strike on ground, foot inclination angle during stance, shank inclination angle at toe-off and maximal shank inclination angle during swing are selected to identify different terrains. These features are measured by fusion of two gyroscopes, two accelerometers, two force sensitive resistors and a timer. Based on the features, a fuzzy logic identification method is developed to identify level-ground, stair ascent, stair descent, upslope and downslope online in real time. Average identification accuracy higher than 97.5% is obtained in experiments of five able-bodied subjects and a transtibial amputee. Continuous identification results show the prospect of using the proposed method to realize real-time terrain identification of powered prostheses.
I. INTRODUCTION Different from passive prostheses, powered prostheses can mimic the dynamic as well as kinematic behaviors of human limbs [1]. With powered prostheses, the amputee’s walking metabolic economy are improved and their gaits become more natural [2]. During the last few decades, increasing efforts have been made on different kinds of lower-limb powered prostheses, e.g. [2]–[5]. Although all these prostheses have the potential of terrain adaptability, most of them are optimized only on level ground. As a result, when an amputee walks on stairs or slopes, control strategy that is valid on level ground will not work and the amputee may suffer balance impairment or even falling. To solve this problem, a variety of terrain identification methods have been proposed, which can be classified into four categories according to the type of identification signals. The first category is based on electromyographic (EMG) signals. Au et al. [6] presented an approach to detect stair descent walking based on myoelectric signals measured from the amputee’s residual limb. Though the EMG signal have the advantage of appearing prior to motion, it is not sufficient to be used independently for prosthesis control [7]. The second category is based on ground reaction force (GRF). Wang et al. [10] proposed a locomotion mode recognition method with a wearable plantar pressure measurement system to identify locomotion modes such as sitting, standing, normal walking, stepping over obstacles, ascending stairs This work was supported by the National Natural Science Foundation of China (No. 61005082, 61020106005), Doctoral Fund of Ministry of Education of China (No. 20100001120005) and the 985 Project of Peking University (No. 3J0865600). The authors are with the Intelligent Control Laboratory, Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China.
[email protected]
978-1-4673-5643-5/13/$31.00 ©2013 IEEE
and descending stairs. Although GRF is easy to acquire, it presents only the interaction information between the prosthesis and the ground. Kinematic information of the prosthesis itself, such as foot inclination angle and joint angles, which are important for terrain identification, can not be acquired accurately. Huang et al. [8] combined EMG and GRF together and proposed a continuous locomotionmode identification method with support vector machine (SVM). However, this method needs to place seven or more electrodes on the residual limb, which may aggravate the acceptance of the method by the amputee. Additionally, the method is evaluated based on offline analysis of experimental data. The third category is based on inertial measurement units. Lawson et al. [11] proposed a method for slope identification with a three-axis accelerometer. This method of calculating inclination angle is accurate, however, only when the sensor measures no acceleration except the gravitational acceleration. Consequently, it is not valid during swing and at the moment of foot strikes. The fourth category is based on terrain modeling, as was performed by Bernhard et al. [12]. The authors combined a two-dimensional laser scanner and an inertial navigation unit to measure the distance to the structure in a two dimensional plain and to estimate the current three dimensional position and orientation of the prosthesis. This approach is supposed to have foresighted adaption to terrain variation, but there is no practical quantitative experiments except for a ramp slope match simulation. Besides, the algorithm’s high computational complexity and the sensor’s vulnerability to weather are also concerns to be solved. For a good terrain identification method, the identification accuracy rate should be as high as possible to send accurate command to powered prosthesis and ensure the amputee’s safety. In addition, it is better not to mount sensors on the sound-side leg. Moreover, the sensors should be able to embedded into the prosthesis to improve acceptance by the amputee. Furthermore, the method should identify current terrain as early as possible, thus sends control command to the prosthesis timely. Besides, the computational complexity of the method should not be very high and the method is able to be performed online in real time. This paper presents a fuzzy-logic based terrain identification method for prosthesis control using multi-sensor fusion to identify level ground, stair ascent, stair descent, upslope and downslope. All the sensors used can be embedded into the prosthesis. The terrain can be identified before swing phase when both the heel and toe are off the ground. Experiments with five able-bodied subjects and an amputee
3376
obtained an average accuracy rate higher than 97.5%. The rest of this paper is organized as follows. Section II introduces different locomotion features for terrain identification. Section III describes how to measure the features by multi-sensor fusion. Section IV introduces a fuzzy logic based identification method. Experimental results are shown in Section V. We conclude in Section VI. II. LOCOMOTION FEATURES ON DIFFERENT TERRAINS When walking on different terrains, both the interaction information between the foot and the ground and the motion states of our limbs differ, which can be used as features to identify terrains. In this paper, five features are selected for terrain identification. A. Rising Time of GRF at Heel GRF presents the interaction information between the foot and ground. When heel strikes ground, the GRF is applied at heel. As the body center of mass (COM) moves forward, the force will increase first and then decrease, which results in a maximal value. The time interval from the moment of heel strike to the moment when the GRF reaches its maximal value is defined as the rising time. As all the maximal values appear when the COM is just above the heel, then the rising time is determined by the initial COM position at the moment of heel strike, which is quite different between level-ground and stairs, as shown in Fig.1. COM axis
Fig. 1.
COM axis
COM axis
Different COM positions at the moment of heel strike.
COM is along the axis labeled in the figure. According to the figure, initial COM position of stair descent is the nearest to heel, thus the time interval from this heel strike moment to the maximal value moment of stair descent is the minimum when walking at the same speed and its GRF rising time is the maximum. Hence, rising time of GRF at heel can be used as a feature to identify different terrains. B. Sequence of Foot Strikes on Ground Foot strikes include heel strike and toe strike. When walking on level ground, heel generally strikes the ground prior to toe, which is the same case when walking on slopes. However, things are quite different when walking on stairs. During stair ascent, heel and toe strikes on the ground almost at the same time (less than 10% of the whole gait cycle), and toe strikes ground prior to heel during stair descent. Consequently, foot strike sequence can be used as a feature to distinguish level ground and stairs, as shown in Fig.2.
(b)
(a)
(c)
Fig. 2. Foot strike sequence on different terrains. (a) On level-ground, heel strike is prior to toe strike. (b) During stair ascent, heel strike and toe strike happen almost at the same time. (c) During stair descent, toe strike is prior to heel strike
C. Foot Inclination Angle during Stance Foot inclination angle refers to the relative angle between foot and the horizontal line in sagittal plane. During stance, foot is parallel to the terrain surface and foot inclination angle (θf oot ) equals the terrain surface inclination angle. It varies a lot between level ground and slopes and can be used to identify them, as shown in Fig.3. θ foot < 0
(a)
θ foot = 0
(b)
θ foot > 0
(c)
Fig. 3. Foot inclination angle. (a) During downslope walking, the foot inclination angle is negative. (b) On level-ground, the angle is zero. (c) During upslope walking, the angle is positive
D. Shank Inclination Angle at Toe-off Shank inclination angle refers to the shank angle relative to the vertical direction in sagittal plane. We define that the angle is positive if the knee joint extends to the forward direction and negative if the knee joint flexes to the backward direction. Toe-off refers to the very moment at the end of stance phase. For all the five terrains to be identified, shank inclination angles at toe off are negative, but their absolute values are different. The absolute shank inclination angle value of stair descent is the largest. Hence, shank inclination angle at toe-off can be used as a feature to distinguish stair descent from the other terrain types, as shown in Fig.4.
θtsk
θtsk
θtsk
Fig. 4. Shank inclination angle at toe-off (θtsk ) of different terrains. For all terrains, θtsk is negative, and the absolute θtsk of stair descent is the maximum.
E. Maximal Shank Inclination Angle during Swing Shank inclination angle varies continuously during walking. Swing ranges of the shank on different terrains differ, so does the maximal shank inclination angle. The angle of level ground is quite different from that on stairs, thus is selected as a feature to differentiate level ground and stairs, as shown in Fig.5.
3377
θ msk
θ msk
θ msk
Fig. 5. Maximal shank inclination angle during swing (θmsk ) of different terrains. θmsk appears just before heel strike and θmsk of level-ground is the maximal.
θa can be used to determine the initial orientation of the unit. It can also used as the reference signal to calibrate the inclination angle calculated by gyro (θg ). During swing, gyro rotation rate signals (ω) are first filtered to cancel the zero offset, and then used to calculate the inclination angle with rotation matrix. GRF measured by FSRs are used to detect swing and stance phase, as is shown in Fig.6. IV. F UZZY L OGIC I DENTIFICATION
III. M ULTI -S ENSOR F USION To acquire the five features, we need to measure three kinds of locomotion information including inclination angle, ground reaction force and time interval. The time interval can be measured easily by the timer embedded in STM32F103RBT6, which is a 32-bit microcontroller with a 72 MHz system clock produced by STMicroelectronics. To measure ground reaction force, two FlexiForce A401 FSRs produced by Tekscan are used. Each FSR has a circular sensing area of about 5 cm2 and a configurable measurement range from 0-1lb to 0-7000lb. The FSRs are integrated into an insole, one is placed under calcaneus tuberosity to measure GRF applied at heel, the other is placed near the first metatarsal bone to measure GRF applied at toe. Different measurement range are configured by different sensing circuit. The FSR at heel is with a relative large range to measure continuous GRF signals, while the FSR near toe is with a relative small range and is used as a foot switch. As for the inclination angle measurement, two kinds of sensors are used. One is the accelerometer, which can measure accelerations along the measurement axes. Inclination angle can be calculated by acceleration decomposition and trigonometry operation [13]. This method of calculating inclination angle is accurate, however, only when the sensor has no acceleration except the gravitational acceleration. Consequently, it is not valid during swing and at the moment of foot strikes. The other is the gyroscope, which can measure rotation rate signals along the measurement axes. Inclination angles can be calculated by integrating the rotation rate signals in the form of rotation matrix [14]. This method has a good dynamical performance, but the angle may drift during long time operation because of numerical integration errors and noise. The MPU-6050 Motion Processing Unit, which has an embedded 3-axis gyroscope and a 3-axis 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. One MPU-6050 is mounted at the forefoot while the other at the shank. Both x axes of MPU6050 are perpendicular to the sagittal plane, so the roll angles of the sensors are the inclination angles we need. To get an accurate measurement of the features, a fusion method is developed based on the multi-sensors. Inclination angle calculated by the accelerometer (θa ) is accurate during stance as the foot keeps stationary and the acceleromter on the foot measures only the gravitational acceleration. So
Based on the locomotion features acquired, a simple way to identify terrains would be to apply different thresholds to the features. This method is effective when the identified object numbers are low and the change of the feature signal is distinct, such as two-valued digital signal. Terrain identification in this paper, however, has 5 objects to be identified, and feature signals of each terrain change smoothly and continuously. As a result, it will be troublesome to process these signals with the threshold method. For this purpose, fuzzy logic based terrain identification method is developed. Fuzzy logic is a form of many-valued logic or probabilistic logic. It deals with reasoning that is approximate rather than exact and its identification rule is set based on the sound understanding of the problem. In the case of fuzzy logic, identification objects are analyzed as a set of terrains, where the probability of each terrain is determined by its fuzzy membership value (FMV). The larger the FMV of a terrain is, the higher the probability of the terrain is. A. Membership Function Design The membership function describes the probability of current identified terrain being the target terrain. It is designed according to the correlation of the feature value with the function value. Take the maximal shank inclination angle during swing for example Fig. 5. A larger feature value means a higher probability of level-ground, while a lower probability of stair descent. That is to say the feature has a positive correlation with the probability of level-ground and a negative correlation with the probability of stair descent. Corresponding membership functions can then be designed accordingly. In general, each feature has a unique membership function. As each terrain has five locomotion features, consequently there will be 25 membership functions in total and it is troublesome to design so many functions. Note that for some specific feature, correlation of the feature values with the membership value is identical for two or more terrains, so their membership functions are same. For example, levelground, stair ascent and stair descent have same membership functions of foot inclination angle during stance. Besides, for some other feature, membership functions of different terrains are just symmetrical or have a simple mathematical relationship. Take upslope and downslope for example, whose membership function of foot inclination angle during stance are symmetrical about θf oot = 0. Hence, we select only 3 kinds of functions as the base function. The other membership functions can be derived from the base function.
3378
ω FSRs
Gyros
Zero offset cancellation
GRF Accels
g
Acceleration Decomposition
θa
∆θ +
Yes
Stance ?
−
ωo Error Transformation
ωc
+ −
∆ω
Rotation Matrix
θ g or θ c
θ g or θ c Fig. 6. Sensor fusion structure. g refers to the gravitational acceleration, θa refers to the inclination angle calculated with accelerometer signals. Similarly, θg refers to the inclination angle calculated with gyro signals. While θc refers to the calibrated inclination angle. ω refers to the rotational rate signals.
fb1 (x) = a · e−
(x−b)2 c2
(1)
which is a kind of probability density function in probability theory. The parameter b is known as the expectation, c is the standard deviation and a is a scale factor satisfying a ≤ 1. Its graph is a bell curve. This kind of membership function describes the normal distribution correlation of membership value and feature value that the more close the feature value x is to b, the larger the membership value f (x) is. It can be used as membership functions of level-ground, stair ascent and stair descent to calculate the membership value by foot inclination angle during stance, which is around zero (b = 0) on these terrains. Another two kinds of membership functions can be derived from the base function, i.e. ½ 1 − fb1 x x ≤ b fd1 (x) = (2) 0 x>b ½ 0 x≤b fd2 (x) = (3) 1 − fb1 x x > b fd1 (x) can be used as the membership function of downslope for the feature θf oot . For if θf oot > 0, the current terrain is impossible to be downslope and the probability of downslope is zero. As θf oot decreases, the probability of downslope increases. When θf oot < −5◦ , probability of downslope will be the maximal among all terrains. The case of upslope is just opposite, whose membership function is fd2 (x). As shown in Fig.7.
The second base function is the modified hyperbolic tangent function, i.e. 1 (4) fb2 (x) = [tanh(s · (x − x0)) + 1] 2 where x0 is the threshold value and s is the sensitivity coefficient related to the slope of the function, respectively. The hyperbolic tangent function describes the correlation that when the feature value of some terrain x is equal to the threshold value b, membership or probability of this terrain is 0.5, neither large nor small, and this membership will increase or decrease at a speed determined by s if x deviates from x0 . This function can be used as the membership function of level-ground to calculate its membership by the feature maximal shank inclination angle during swing (θmsk ). For shank swings a larger range when walking on level-ground than stair ascent and stair descent, and there is a threshold θmsk to distinguish them. Based on fb2(x) , another kind of membership function can be derived, i.e. fd3 (x) = 1 − fb2 (x) (5) Similar to fb2 (x), fd3 (x) can be used as the membership function of stair ascent and stair descent to calculate their membership by θmsk , as shown in Fig.8. 1
0.6
0.4
0.2
1 Level−ground
0.8 Membership value
Level−ground Downslope Stair ascent Stair descent Upslope
0.8 Membership value
The first base function is a modified normal distribution function, i.e.
0 −5
Upslope Downslope
0.6
−5
Fig. 8. swing
5
0 5 10 15 20 25 Maximal shank inclination angle during swing (deg)
30
35
Membership function of maximal shank inclination angle during
0.4
The third kind of membership function is just a constant, i.e. fb3 (x) = c (6)
0.2
0 −15
Fig. 7.
−10
−5 0 5 Foot inclination angle during stance
10
15
Membership function of foot inclination angle during stance
where c ∈ (0, 1] and usually has a value of 0.5. This function means that the terrain is not relevant to this feature, such as θmsk of upslope, as shown in Fig.8. 3379
The membership functions of different terrains for different features are listed in Table I. TABLE I M EMBERSHIP FUNCTIONS OF DIFFERENT TERRAINS Features Feature A Feature B Feature C Feature D Feature E
Level ground fb2 (x) fd3 (x) fb1 (x) fb2 (x) fb2 (x)
Stair ascent fb2 (x) fb1 (x) fb1 (x) fb2 (x) fd3 (x)
Stair descent fd3 (x) fb2 (x) fb1 (x) fd3 (x) fd3 (x)
Up slope fb3 (x) fd3 (x) fd2 (x) fb2 (x) fb3 (x)
Down slope fb3 (x) fd3 (x) fd1 (x) fb2 (x) fb2 (x)
B. Membership Functions Composition To calculate the probability of some terrain by membership values of 5 features, the Larsen product implication method [15] is used, P (Ti ) = µAi · µBi · µCi · µDi · µEi
(7)
where P (Ti ) is the probability of terrain Ti and µAi , µBi , µCi , µDi and µEi are the corresponding membership values of different features. The target terrain Tm is selected as the one with the largest probability (8) Tm = arg max(P (Ti ))
The subjects were firstly required to walk on different terrains at their self-selected speeds for a few steps to determine the parameters including maximal shank inclination angle during swing, shank inclination angle at toe-off and GRF rising time. The stair is 75 cm in width, 40 cm in depth and 15 cm in height while the slope inclination angle is 20 degrees. After parameters predefinition, two kinds of experiments were conducted. The first one is the repetitive terrain identification without transitions to test the accuracy rate of the method. Subjects were required to walk on a specific terrain repeatedly. The first step on each terrain was requested to start with the normal limb, which is the same case of amputees, especially when they walk on stairs and slopes. Each subject walked at least 150 steps on each terrain. Step counting and terrain identification were performed online by the MCU in real time, and the results were stored in an onboard memory (AT24C64). The second one is the real-time consecutive terrain identification including different transitions. Subjects stood still first, and then walked on terrains in the following sequence: levelground Õ stair ascent Õ level-ground Õ downslope Õ levelground Õ upslope Õ level-ground Õ stair descent Õ levelground. This experiment was designed to test the ability of the identification method to be performed online in real time.
Ti
.
Level−ground
98.45
0.47
0.39
0.00
0.70
Stair ascent
0.41
97.67
0.96
0.41
0.55
Stair descent
0.73
0.44
98.84
0.00
0.00
Upslope
0.00
0.10
0.73
99.16
0.00
Downslope
0.11
0.00
0.11
0.00
99.79
V. E XPERIMENTAL R ESULTS A. Subjects and Experimental Protocol
D
ps
ns pe lo
e
p lo
ow
U
nt ce es
rd ai St
Fig. 10.
t en sc ra ai St
nd
ou
gr l− ve Le
Six subjects, including five able-bodied subjects and one transtibial amputee participated in the experiment. Ablebodied subjects have an average height of 1.71 (± 0.12) m and an average weight of 62.1 (± 8.3) kg. The amputee subject is 1.70m in height, 71 kg in weight and is experienced at prosthesis ambulation. He wore his own prosthesis (a 25cm Otto Bock 1S90 foot) during the experiment.
Confusion matrix of the terrain identification results (%)
B. Results
Fig. 9.
Multi-sensor system
Subjects were instrumented with the multi-sensor system. Two MPU6050 nnits were mounted at the forefoot and shank while two FSRs were mounted near heel and toe in the insole, respectively. The STM32 MCU with embedded timers were also mounted at shank. Both the sensors and the MCU are small enough to be embedded into the prosthesis, as shown in Fig.9.
The identification accuracy (the number of successfully classified testing data divided by the total number of testing data) of six subjects on different kinds of terrain types is shown in table II. The accuracy rate of the able-bodied ranges from 95.33% to 100% while the amputee’s accuracy rate ranges from 95.56% to 100%. The confusion matrix is shown in Fig. 10. The confusion between level-ground and slopes may be caused by the measurement errors of foot inclination angle during stance. Similarly, the measurement errors of shank inclination angle may result in the confusion between level-ground and stairs. However, as the confusion percent is smaller than 3%, it is satisfactory for practical use. Real time consecutive terrain identification results are shown in Fig. 11. The figure shows that the identification
3380
Foot inclination angle (deg)
5
10
15
20
25
30
35
40
45
50
Shank inclination angle (deg)
20 0 −20 −40 −60 0
5
10
15
20
25
30
35
40
45
50
5
10
15
20
25
30
35
40
45
50
5
10
15
20
25
30
35
40
45
50
Ground reaction force
40 20 0 −20 −40 −60 0
4000 2000 0 0
Downslope Upslope Level−ground Stair descent Stair ascent Standing 0
Time(s)
Fig. 11. Real time consecutive terrain identification for 50-s long trial. As for the figure of GRF, the bold line represents the GRF at heel while the thin line represents the GRF at toe. Ordinate represents the relative force value. TABLE II ACCURACY RATE OF TERRAIN IDENTIFICATION Subject Able-bodied Able-bodied Able-bodied Able-bodied Able-bodied Amputee Average
1 2 3 4 5
Level ground 99.30% 98.54% 99.35% 98.22% 98.90% 96.92% 98.54%
Stair ascent 97.33% 99.13% 95.33% 98.48% 99.17% 95.59% 97.51%
Stair descent 98.59% 99.15% 100% 98.43% 99.16% 96.43% 98.63%
Up slope 99.22% 99.50% 100% 99.33% 98.67% 95.56% 98.71%
[2]
Down slope 99.59% 100% 100% 100% 99.33% 100% 99.82%
[3] [4] [5]
[6]
method can be performed online in real time and all the terrains can be identified accurately before swing phase when the foot is off the ground.
[7]
VI. CONCLUSION In this paper, we have proposed a fuzzy logic approach to identify terrains in real time based on multi-sensor fusion. Two force sensitive resistors (FSR), two gyroscopes, two accelerometers and a timer are combined to measure five locomotion features. These locomotion features are utilized to identify level ground, stair ascent, stair descent, upslope and downslope. The terrains can be identified before swing when both the heel and toe are off the ground. Experiments with five able-bodied subjects and an amputee achieved an average accuracy rate higher than 97.5%. Future study includes the improvement of the multi-sensor approach to get more accurate measurement of locomotion features and the extension of the proposed approach to more motion cases.
[8]
[9] [10]
[11] [12] [13]
R EFERENCES
[14]
[1] Q. Wang, J. Zhu, Y. Huang, K. Yuan, and L. Wang, ”Segmented foot with compliant actuators and its applications to lower-limb prostheses and exoskeletons,” Smart actuation and sensing systems - Recent
[15]
3381
advances and future challenges, edited by G. Berselli, R. Vertechy, G. Vassura, I-Tech Education and Publishing, 2012. S. K. Au, J. Weber, and H. Herr. ”Powered ankle-foot prosthesis improves walking metabolic economy,” IEEE Trans. Robotics, vol. 25, no. 1, pp. 51-66, 2009. G. K. Klute, J. Czerniecki, and B. Hannaford. ”Development of powered prosthetic lower limb,” The 1st National Meeting of Veterans Affairs Rehabil, 1998. F. Sup, A. Bohara, and M. Goldfarb, ”Design and control of a powered transfemoral prosthesis,” Int. J. Robot. Res., vol. 27, no. 2, pp. 263273, 2008. J. Zhu, Q. Wang, and L. Wang. ”PANTOE 1: Biomechanical design of powered ankle-foot prosthesis with compliant joints and segmented foot,” Proc. of the IEEE/ASME Int. Conf. Advanced Intelligent Mechatronics, pp. 31-36, 2010. S. K. Au, M. Berniker, and H. Herr. ”Powered ankle-foot prosthesis to assist level-ground and stair-descent gaits,” Neural Networks. vol. 21, pp. 654-666, 2008. H. Huang, T. A. Kuiken, and R. D. Lipschutz. ”A strategy for identifying locomotion modes using surface electromyography,” IEEE Trans. Biomedical Engineering, vol. 56, no. 1, pp. 65-72, 2009. 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. Biomedical Engineering, vol. 58, no. 10, pp. 2867-2875, 2011. D. H. Gates. ”Characterizing ankle function during stair ascent, descent, and level walking for ankle prosthesis and orthosis design,” Masters thesis, Dept. Biomed. Eng., Boston Univ., Boston, MA, 2004. 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,” Proc. of the 12th Int. Conf. Intelligent Autonomous Systems, 2012. B. E. Lawson, H. A. Varol, and M. Goldfarb. ”Ground adaptive standing controller for a powered transfemoral prosthesis,” Proc. of the IEEE Int. Conf. Rehabilitation Robotics, 2011. K. Bernhard and C. Denis. ”Foresighted control of active foot prostheses,” SENSORS and TEST Conferences 2011 - SENSOR Proceedings, pp. 669-672, 2011. W. Svensson and U. Holmberg, ”Foot and ground measurement using portable sensors,” Proc. of Int. Conf. Rehabilitation Robotics, 2005, pp. 448-451. R. Mahony, C. Sung-Han, and T. Hamel. ”A coupled estimation and control analysis for attitude stabilisation of mini aerial vehicles,” Australasian Conf. Robotics and Automation, 2006. P. M. Larsen, ”Industrial applications of fuzzy logic control,” Int. J. Man-Machine Studies, vol. 12, no. 1, pp. 3-10, 1980.
