# PSO-SVM-Based Online Locomotion Mode Identification for Rehabilitation Robotic Exoskeletons

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data Collection and Processing

#### 2.1. Exoskeleton System Description

#### 2.2. Data Collection System

^{2}and has a measurement ranging from 0 kg to 100 kg. MEMS-based AHRS sensors (AHRS II, SkyLark, HongKong, China) are used to collect the movement information of the leg segment, especially when the leg is in the swing phase, during which the GRF has extremely small outputs. The AHRS includes gyroscopes, accelerometers and magnetometers and is capable of outputting three-axis (Roll, Pitch and Yaw) rotation posture, speed, and acceleration. The rotation angle can be obtained through the integration of angle speed. The accuracy of measurement can be improved by the compensation of the information fusion algorithm, e.g., extended Kalman filter. In this kind of used AHRS, the extended Kalman filter is used to deal with the problem of time drift and output accurate data in real time. The AHRS can output the measurement angles directly with a measurement range of (−180°, 180°), (−180°, 180°) and (−90°, 90°) in the Roll angle, the Yaw angle and the Pitch angle, respectively. The output of the AHRS can be transferred to the host computer through a standard RS-232 connector. The sampling frequency is 40 Hz and the baud rate is set as 115,200. The Roll angle is used for the measurement of the human limb gait trajectory. The AHRS, which are fixed on the middle of the shank and the side of the foot, are applied to measure the inclination angle of the shank and the foot.

#### 2.3. Feature Extraction and Dimension Reduction

#### 2.3.1. Feature Extraction

_{s}

_{1}, F

_{s}

_{2}and F

_{s}

_{1}are the three GRFs of the stance leg, θ

_{Ts}and θ

_{As}are the inclination angles of the thigh and the foot in the stance leg and θ

_{T}and θ

_{A}are the inclination angles of the other leg. Based on the phase identification, the features of the classifier are composed of GRF signals in the swing phase and the inclination angles of the leg segments. The simple amplitude of signals and its phase sequence are limited to identify locomotion modes. Feature extraction is the process of extracting useful information from the filtered signals. Features can be extracted from a time series of sensor signals. A time series is a series of observations of sensors shown as follows:

_{k}and g

_{k}are the quadrature mirror filters associated with the predefined scaling function and the mother wavelet function respectively. The double scaling equations are only necessary but insufficient conditions; therefore, more constraints should be added to determine h

_{k}and g

_{k}of different wavelets. Define the function set $\{{v}_{m}(t)|m\in N\}$ as follows:

_{i,j}denotes the energy of the decomposition coefficients C

_{i,j}. The feature vectors set can be constructed based on the energy. The feature set can be represented as follows:

_{mean}is the mean energy of those features and ${F}_{ea}^{\prime}$ is the new feature set. In this paper, three pressure sensors and four AHRSs are used for the locomotion mode identification. Then the extracted features using WPA for a time series of observations from one single sensor are shown as the following:

#### 2.3.2. Feature Set Composition

**F**∈R

^{n}is the feature vector of a time series

**x**

_{i}(t). Let

**Π**be the covariance matrix of

**F**, then:

**Ω**

**=**diag([λ

_{1}, …,λ

_{n}]), λ

_{1}≥ λ

_{2}≥…≥ λ

_{n}, are the eigenvalues of

**Π**,

**A**is a matrix whose columns are the orthonormal eigenvectors of

**Π**,

**AA**

^{T}=

**I**

_{n}. General detailed computation process of PCA can be shown in [37]. Let

**Φ**be a nonlinear mapping from the original space

**F**to the final feature space

**F**

_{s}, namely

**Φ**:

**F**→

**F**

_{s}. Assuming the kernel matrix

**K**is a symmetric and positive semi-definite matrix according to Mercer theorem, with the inner product of Φ(x

_{i}) and Φ(x

_{j}) in original space:

**F**must be centered. This centering can be conducted as the following:

## 3. Locomotion Mode Identification Using SVM Optimized by PSO

#### 3.1. SVM for Classifier

_{i}〉 denotes the dot product, (x

_{i}, y

_{i}) is the pair for input and output, ${\xi}_{i},\text{}{\xi}_{i}^{*}$ are slack variables, and Φ is the kernel function, which has multiple forms such as linear kernel, Gaussian RBF kernel, multi-layer perceptron kernel and spline kernel. We can solve Equation (17) by using KKT optimality conditions namely the dual Lagrange method [39]:

_{i}is Lagrange multiplier, and N is the number of input features. Let

**a*** be the minimization of this dual problem and suppose the hyper-plane of SVM as H(w*,b*). Define [40]

#### 3.2. PSO-Based SVM

_{best}. Another best value called l

_{best}which is tracked by the particle swarm optimizer, is obtained so far by any particle in the neighbors of the particle. In PSO, the process of velocity updating is shown as follows [26]:

_{1}and c

_{2}are the constants which describe the searching ability for local and global optimization separately, ${x}_{id}^{k}$ represents the k-th particle, $\text{}{p}_{id}^{k}$ and ${p}_{gd}^{k}$ are best values currently and among all particle in the population respectively, α and β are random values between 0 and 1. Based on the updated velocities, each particle changes its position according to the following equation:

_{1}= c

_{2}= 2, and the parameters to be optimized are located in the intervals [0.1, 250] and [0.1, 1200].

#### 3.3. Post-Processing Using Majority Voting Algorithm (MVA)

_{1},l

_{2},…,ln), where l

_{i}is a label representing a locomotion mode. The object of the algorithm is to find the majority number defined as the number that appears most times. The majority voting algorithm is widely used in classification problems to make sure that the classification labels keep consistent during a sequence of fixed size to improve the accuracy of classifier. In this paper, five locomotion modes, i.e., level ground walking, stair ascent, stair descent, ramp ascent and ramp descent, need to be identified, which are labeled as 1, 2, 3, 4, and 5, respectively. The sensor data measured by the sensor in real time can be applied in the online algorithm. The predictive label can be obtained online to illustrate the real locomotion mode. The MVA is applied to improve the identification accuracy of the predictive labels.

## 4. Experiment Protocol and Results Analysis

#### 4.1. Experiment Protocol

#### 4.2. Performance Evaluation

_{correct}is the number of correct identification while N

_{total}is the total number of test events. The usage of the confusion matrix is helpful to quantify the error distribution of the identification, which is defined as the following:

_{ij}is the number of events in the i-th locomotion mode that is classified as j-th locomotion mode and ${\overline{m}}_{i}$ is the total numberof events in the i-th locomotion mode. It is notable that the diagonal elements of the confusion matrix C are the identification accuracy and the off-diagonal elements denote the errors. To evaluate whether the transition can be identified in time, the critical moment is defined as the moment when one foot is located in stance phase and the other foot strikes the floor. The ID is defined as:

_{i}is the moment when the locomotion mode transition is identified correctly for the first time, T

_{c}is the critical moment and T

_{gait}is the total time in the walking gait cycle.

#### 4.3. Results Analysis

_{i}, T

_{c}and T

_{gait}. As Table 5 shows, the negative ID shows the T

_{i}is smaller than the T

_{c}, while the positive ID shows the T

_{i}is larger than the T

_{c}. The transition of W to D-S or D-S to W has the largest ID, while the transition of W to U-R, U-R to W has the smallest ID. If the ID is large, the corresponding transition is easy to be misidentified.

## 5. Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Mechanical structure of the exoskeleton.

**A**: battery power source;

**B**: control system enclosure;

**C**: carried load;

**D**: springs connecting the backpack with the waist part;

**E**: waist part;

**F**: thigh segment;

**G**: shank segment;

**H**: wearable shoes which have pressure sensors;

**I**: optical encoder on the hip joint;

**J**: actuation system consisting of DC motor, gear ratio and screw;

**K**: connection cuff interacting with human limbs;

**L**: optical encoder on knee joint;

**M**: ankle joint;

**N**: signal transfer for foot pressure.

**Figure 2.**Mechanical structure of the robot used in this study.

**A**and

**H**: wearable shoes where three pressure sensors are placed in each;

**B**and

**G**: AHRS sensors which collect the inclination angles of foot for double legs;

**C**and

**F**: AHRS sensors which are attached to the leg segments to collect the inclination angles of shanks;

**D**and

**E**are motors with screws for the system;

**I**: the central control system which collects data and produces control signals.

**Figure 3.**The placement of GRF sensors in the wearable shoe. Two GRF sensors are arranged on the forefoot and one sensor is placed on the heel. The labels

**1**,

**2**and

**3**represent the three sensors.

**Figure 4.**The signal collection structure. The measuring range of pressure sensors is 0~100 kg while that of AHRS sensors is −180°~180° in the sagittal plane.

**Figure 5.**The GRF sensor and the AHRS sensor of the system, which are small and thin to be embedded in the mechanical structure.

**Figure 6.**Signal curves comparison between pre-filter and post-filter. Signals through filter are smoother. (

**a**) GRF curves from the sensor placed on the heel; (

**b**) Inclination angle curves from the AHRS on the foot.

**Figure 7.**Windowing and feature extraction for a time series of observations. W(T) is the window of the T interval and F(T) is the corresponding output features. In the case of half overlap, there is a feature set output at each half window, F(T,2) is the features produced due to overlap.

**Figure 8.**Three layers wavelet packet analysis. A(i,j) represents the j-th approximation coefficient in the i-th layer. D(i,j) is the j-th detail coefficient in the i-th layer.

**Figure 9.**Coefficients of a time series of GRF measured from the heel. The x-axis denotes the number of the length of data while the y-axis denotes the amplitude of those coefficients.

**Figure 10.**A two-class classification problem by SVM. Data shown by “cross” and “circle” represent binary class +1 and −1, respectively. w and b are parameters of the hyper-plane.

**Figure 12.**Experiments for locomotion mode identification. (

**a**) Stair descent; (

**b**) Stair ascent; (

**c**) Ramp descent; (

**d**) Ramp ascent; (

**e**) Level-ground walking.

**Figure 13.**Block diagram of the proposed method. GRF signals and AHRS signals are used to obtain the elements of the time series. The GRFs signals in the swing phase are ignored since it does not change. The trained SVM is obtained offline in MATLAB and the online testing is conducted in Visual Studio.

**Figure 14.**The online identification accuracy comparisons for several locomotion modes: (

**a**) comparison between pre-MVA and post-MVA under PSO; (

**b**) Comparison between without-PSO and with-PSO under MVA.

**Figure 15.**The classification result using PSO-SVM with MVA. Those five instances along the sample axis are those five locomotion modes. Misidentification happens when the actual instances (the circle point) misalign with the prediction instances (the star point).

Property-Part | Thigh | Shank |
---|---|---|

Mass (kg) | 0.82 | 0.6 |

Length (mm) | 431 | 390 |

Range of DoF (°) | −37~70 | 0~75 |

D-S | U-S | D-R | U-R | W | |
---|---|---|---|---|---|

D-S | 86.4% ± 1.2% | 4.73% ± 0.6% | 0.15% ± 0.04% | 1.5% ± 0.13% | 7.22% ± 1.1% |

U-S | 25.3% ± 0.85% | 72.1% ± 1.56% | 0.0% ± 0.0% | 0.0% ± 0.0% | 2.62% ± 0.2% |

D-R | 10.98% ± 1.1% | 3.28% ± 0.2% | 75.9% ± 1.24% | 4.34% ± 0.03% | 5.5% ± 0.23% |

U-R | 17.72% ± 1.05% | 5.54% ± 0.04% | 0.94% ± 0.25% | 63.97% ± 2.56% | 11.84% ± 0.42% |

W | 7.3% ± 0.25% | 2.07% ± 0.13% | 0.07% ± 0.01% | 1.61% ± 0.13% | 88.96% ± 2.1% |

D-S | U-S | D-R | U-R | W | |
---|---|---|---|---|---|

D-S | 97.6% ± 0.85% | 1.05% ± 0.05% | 0.15% ± 0.03% | 0.06% ± 0.0% | 0.06% ± 0.01% |

U-S | 2.45% ± 0.1% | 97.4% ± 0.56% | 0.0% ± 0.0% | 0.0% ± 0.0% | 0.18% ± 0.06% |

D-R | 1.64% ± 0.22% | 0.67% ± 0.1% | 95.4% ± 1.14% | 0.39% ± 0.01% | 1.93% ± 0.15% |

U-R | 1.87% ± 0.03% | 0.6% ± 0.0% | 0.26% ± 0.02% | 93.8% ± 0.25% | 3.5% ± 0.24% |

W | 1.94% ± 0.11% | 0.6% ± 0.02% | 0% ± 0.0% | 0.54% ± 0.02% | 96.9% ± 0.86% |

D-S | U-S | D-R | U-R | W | |
---|---|---|---|---|---|

D-S | 99.5% ± 0.05% | 0.0% ± 0.0% | 0.0% ± 0.0% | 0.05% ± 0.05% | 0.0% ± 0.0% |

U-S | 0.34% ± 0.01% | 98.3% ± 0.62% | 0.0% ± 0.0% | 0.85% ± 0.05% | 0.51% ± 0.02% |

D-R | 0.01% ± 0.01% | 0.58% ± 0.08% | 97.3% ± 0.45% | 0.0% ± 0.0% | 2.02% ± 0.05% |

U-R | 0.77% ± 0.1% | 0.0% ± 0.0% | 0.51% ± 0.12% | 97.36% ± 0.66% | 2.13% ± 0.13% |

W | 0% ± 0% | 0.0% ± 0.0% | 0.0% ± 0.0% | 0.47% ± 0.11% | 98.66% ± 0.24% |

Transition | ID |
---|---|

W to D-S | 48% ± 2.8% |

D-S to W | 46.8% ± 4.5% |

W to U-S | −10.4% ± 1.2% |

U-S to W | −6.4% ± 0.8% |

W to D-R | 31.5% ± 2.45% |

D-R to W | 40.5% ± 5.2% |

W to U-R | 2.5% ± 0.8% |

U-R to W | 4.5% ± 1.8% |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Long, Y.; Du, Z.-J.; Wang, W.-D.; Zhao, G.-Y.; Xu, G.-Q.; He, L.; Mao, X.-W.; Dong, W.
PSO-SVM-Based Online Locomotion Mode Identification for Rehabilitation Robotic Exoskeletons. *Sensors* **2016**, *16*, 1408.
https://doi.org/10.3390/s16091408

**AMA Style**

Long Y, Du Z-J, Wang W-D, Zhao G-Y, Xu G-Q, He L, Mao X-W, Dong W.
PSO-SVM-Based Online Locomotion Mode Identification for Rehabilitation Robotic Exoskeletons. *Sensors*. 2016; 16(9):1408.
https://doi.org/10.3390/s16091408

**Chicago/Turabian Style**

Long, Yi, Zhi-Jiang Du, Wei-Dong Wang, Guang-Yu Zhao, Guo-Qiang Xu, Long He, Xi-Wang Mao, and Wei Dong.
2016. "PSO-SVM-Based Online Locomotion Mode Identification for Rehabilitation Robotic Exoskeletons" *Sensors* 16, no. 9: 1408.
https://doi.org/10.3390/s16091408