Man-machine interaction-based motion control of a robotic walker

Abstract

BACKGROUND:

The aging population brings the problem of healthcare and dyskinesia. The lack of mobility extremely affects stroke patient’s activities of daily living (ADL) and decreases their quality of life. To assist these mobility-limited people, a robotic walker is designed to facilitate gait rehabilitation training.

OBJECTIVE:

The aim of this paper is to present the implementation of a novel motion control method to assist disabled people based on their motion intention.

METHODS:

The kinematic framework of the robotic walker is outlined. We propose an intention recognition algorithm based on the interactive force signal. A novel motion control method combined with T-S fuzzy controller and PD controller is proposed. The motion controller can recognize the intention of the user through the interactive force, which allows the user to move or turn around as usual, instead of using their hands to control the walker.

RESULTS:

Preliminary experiments with healthy individuals and simulated patients are carried out to verify the effectiveness of the algorithm. The results show that the proposed motion control approach can recognize the user’s intention, is easy to control and has a higher precision than the traditional proportional–integral–derivative controller.

CONCLUSION:

The results show that users could achieve the task with acceptable error, which indicates the potential of the proposed control method for gait training.

Keywords

Motion control intention recognition robotic walker lower rehabilitation robot stroke gait training kinematics disability mobility stroke patients activities of daily living quality of life

1. Introduction

Mobility is typically regarded as the “ability to move or be moved freely and easily” [1]. It is an essential skill that is used in almost all areas of life, such as walking and social interaction. People with impaired mobility usually have to rely on others to perform their activities of daily living (ADL), and it is inevitable that the lack of mobility will decrease their quality of life [2]. To provide mobility to those patients, walking sticks have been invented. However, the users must exert lots of force and keep balance carefully when using walking sticks. As a result, rollators are used to deal with the problem of balance. The wheels are equipped so that user can spend less force to move [3].

With the development of robotics, smart walkers have been proposed to facilitate the mobility of disabled people. Smart walkers can be divided into two categories: passive and active walker [4]. The motion of passive walkers completely depend on the user’s force, such as the Guide Cane [5] and RT-Walker [6], whereas active walkers are equipped with motors to drive the walker, such as Johnnie [4], Care-O-bot I & II [7, 8] and Carlos’s Smart Walker [9]. Some active smart walkers have included navigation to guide users based on the camera, sonar or laser sensors [10, 11]. Both kinds of smart walkers focus on providing support and safety, so that mobility is provided to the users. The active walker has a more complex system design because its wheels provide motion which rely on a control strategy. However, it is more convenient than the passive walker, since the user has to use less force. With the development of rehabilitation theory, it has become more and more difficult to execute the latest rehabilitation treatments in the passive walker.

The aim of walking rehabilitation is to return the freedom of motion to the patient, which is a complex process based on repeating tasks. The process relies on at least two therapists to help the patient achieve rehabilitation [12]. To relieve therapists from these intensive and repetitive tasks and offer patients task-oriented training, several active smart walkers have been proposed. For instance, the device proposed by Olensek et al. [13] is equipped with two motorized wheels and a helical spring housed in a steel cylinder on each side of the extended arms. An adjustment ring is attached to the spring. The rings bend the length of the springs to change the stiffness. This motorized device divided the output speed into three levels and then provided different levels of speed according to the quality of postural responses during walking. Though the device proposes an ingenious design to provide assistance in gait rehabilitation, its measure and control strategy does not produce the speed with high accuracy. Therefore, with the development of sensors, a new smart walker name HOIST [14] has been proposed. Furthermore, several robots, including the RAGT, the robotic walker and the Kinesis have been developed with passive devices to study pelvic robot intervention [15, 16, 17, 18, 19, 20]. However, with the development of rehabilitation theory, more attention should be paid to the pelvis during rehabilitation treatment. As a result, a new smart walker has been designed by Ji et al. [21], in which the pelvic manipulator has been added into the smart walker to ensure measurement of the interactive force. In terms of control strategy, it takes admittance control as its control method, but it does not correct the position of the pelvis.

In this paper a motion control method based on human intention is proposed. The walker has the following features: (1) The pelvis support mechanism allows the pelvic motions and provides a force field; (2) the intention recognition-based motion controller is based on pelvic motions and liberates the hands; and (3) the walker has an encoder to track the position of the pelvis during walking. This paper proposed a motion control method of a smart walker containing intention recognition. The paper is constructed as follows: in Section 2, a new smart walker is introduced including the electrical and drive system. The kinematic framework of the walker is outlined in Section 3. Then, in Section 4, the design of the intention recognition algorithm and motion control method are provided. The experimental results and a discussion of the results are presented in Sections 5 and 6.

2. System description

The purpose of the walker is to assist patients during natural walk. The walker mainly consists of two parts: a mobile platform (MP) and a body weight support mechanism (BWSM). The BWSM contains the pelvis support mechanism and the unloading force offer part, as illustrated in Fig. 1. During working, the robotic walker first recognizes the user’s motion intention by the interactive force signal, and then through the controller the walker can provide a modified walking speed to the user.

Figure 1.

Prototype of the robotic walker.

2.1 Hardware

2.1.1 Mobile platform (MP)

The aim of the MP is to move the robotic walker freely. Depending on the left and right wheels’ speed, the MP can enable the walker to move. The MP relies on the difference between the wheels’ speed and can change the orientation of the walker.

The MP is equipped with a battery power supply, Programmable Logic Controller (PLC), two driven wheels and two castor wheels. The battery power in the control cabinet provides electricity for the table personal computer (PC), PLC and driven motors. It consists of two 48 V, 26 Ah lead-acid batteries that power the motor drivers, a 15 V switching power supply for the embedded computer and a separate 24 V switching power supply for PLC CX5130. PLC (CX5130; Beckhoff, Germany) controls all motors and collects the data from encoders. Two driven wheels provide necessary actuations to the robotic walker with an adjustable linear and angular velocity and each driven wheel has its own 170 W electric motor geared with a shaft encoder. Two castor wheels are planted on two sides of the front of the MP, respectively, which are made available when the robotic walker changes the orientation. The MP provides a space approximately 680 mm in the transverse direction and 960 mm in the longitudinal direction for the user to place their feet during walking.

2.1.2 Body weight support mechanism (BWSM)

The BWSM mainly consists of two parts: the pelvis support mechanism and the unloading force offer part. The pelvis support mechanism is used to keep the user’s balance, prevent falling and corrects the position of the user’s pelvis to collect the force signal from the user’s pelvis during walking. The unloading force offer part is used to offer unloading force to the user and adjusts the height to adapt to different users.

The pelvis support mechanism contains a four-bar mechanism and two extend arms (left and right side). The four-bar mechanism contains two springs and an encoder. The springs can produce a force field to correct the position of the user’s pelvis during walking and the encoder is used to determine the position of the user’s pelvis. On each side of the extend arm two independent pressure sensors (opposite each other) and two springs are installed. The spring connect the pressure sensor to a slider, which contains a buckle that could connect to the harness. Hence, when the user moves, the harness will pressure the spring and transfer the force to the pressure sensors.

The unloading force offer part consists of a motor, a screw and a slider. The motor at the bottom offers the driven torque and the screw and slider transfer the driven torque and change it to the force along the vertical axis. Besides, the slider is connected to the pelvis support mechanism. At the top of the unloading force offer part is a space for a table PC. For the safety of the user, two emergency stops are planted on both sides of the robotic walker, as shown in Fig. 1. The robotic walker will stop immediately when either of the emergency stops are pressed.

2.2 Sensors

As illustrated in Fig. 2, the walker is equipped with four independent pressure sensors, which range from 0 to 20 kg. Four springs are installed to connect four independent pressure sensors to sliders and each slider contains a buckle that can connect with the harness worn by the user. Thus, the sensors, springs and slider provide a simple method to measure the relative force between the user and walker. When the user tries to move, the relative position between the user and the walker will be changed and the harness moves when the user draws the slider, causing the slider press or draw of the springs. According to Hooke’s law, the elastic deformation of springs would produce a force which are collected by the pressure sensors.

Figure 2.

Intention recognition illustration.

The interactive force denoted by $F_{i}(i=1,2,3,4)$ can be used to recognize the user’s intention by the following equations:

$\displaystyle F_{s}=\sum F_{i}-F_{a}(i=1,2,3,4)$ (1) $\displaystyle M_{s}=\underbrace{(F_{3}-F_{4})}_{F_{R}}d_{L}-\underbrace{(F_{1}% -F_{2})}_{F_{L}}d_{R}$ (2)

where $F_{s}$ , $M_{s}$ are defined as composite force of all interactive forces and torques respectively, $F_{i}$ is the interactive force from the sensors, $F_{\rm a}$ is the setting assistant force, $F_{L}$ and $F_{R}$ are defined as the composite forces of the left side and right side respectively, $d_{L}$ is the arm of $F_{L}$ , and $d_{R}$ is the arm of $F_{R}$ .

Each driven wheel is driven by a servo motor and a rotational encoder is equipped at the end of each motor to measure the position of the wheel. Furthermore, for the purpose of focusing on the pelvis during walking, an encoder is installed on the four-bar mechanism to measure the rotation angle so that the position of the user’s pelvis can be determined.

3. Kinematic modeling

Since the main purpose of the walker is to provide assistance during natural walk, it is essential to build the kinematic model of the walker for the controller designer. The pelvis plays an important role during natural walk, so the position of the pelvis is also contained in the model. Thus, the kinematic model of the walker with the user’s pelvis is built as follows.

As shown in Fig. 3, XOY is the global coordinate, $X_{\Omega}O_{\Omega}Y_{\Omega}$ is the user’s pelvic coordinate, and $X_{L}{O}_{L}{Y}_{L}$ and $X_{R}{O}_{R}{Y}_{R}$ are coordinates of the left and right wheel, respectively. $\dot{\theta}_{L}$ and $\dot{\theta}_{R}$ are the rotation speeds of the left wheel and right wheel respectively. Denote $\theta_{F}$ as the rotation angle of four-bar mechanism, $l_{F}$ as the length of four-bar mechanism, $c$ as the wheel tread and $\varphi$ as the original angle of the robotic walker.

Figure 3.

Kinematic framework of the robotic walker.

Let $\bm{\theta}_{W}=[\theta_{L}∼{}∼{}\theta_{R}]^{\rm T}$ be a set of positions from the encoders in the left and right wheels respectively and then ${\dot{\bm{\theta}}}_{W}=[\dot{\theta}_{L}∼{}∼{}\dot{\theta}_{R}]^{\rm T}$ is a set of rotation speeds of the left and right wheel. Furthermore, define the linear velocity of the wheels $v$ and the angle velocity of the wheels $\omega$ ,

$\displaystyle\left[\begin{array}[]{c}v_{L}\\ {\omega}_{L}\end{array}\right]=\left[\begin{array}[]{cc}\frac{d}{2}&0\\ -\frac{d}{4c}&\frac{d}{4c}\end{array}\right]\left[\begin{array}[]{c}\dot{% \theta}_{L}\\ \dot{\theta}_{R}\end{array}\right]$ (3) $\displaystyle\left[\begin{array}[]{c}v_{R}\\ {\omega}_{R}\end{array}\right]=\left[\begin{array}[]{cc}0&\frac{d}{2}\\ -\frac{d}{4c}&\frac{d}{4c}\end{array}\right]\left[\begin{array}[]{c}\dot{% \theta}_{L}\\ \dot{\theta}_{R}\end{array}\right]$ (4)

where $d$ is the diameter of the drive wheels, $c$ is the wheel tread, $\theta_{F}$ is the rotation angle of the four-bar mechanism and $l_{F}$ is the length of the four-bar mechanism. The coordinate system $\Omega(X_{\Omega}{O}_{\Omega}{Y}_{\Omega})$ is defined as follows: the origin is at the center of the PSM which is also the center of the user’s pelvis, the $X$ axis $(X_{\Omega})$ is perpendicular to the left extend arm and points to the left wheel, and $Y$ axis $({Y}_{\Omega})$ is along the orientation of the walker, as is illustrated in Fig. 3. Since the change of the four-bar mechanism along $Y_{\Omega}$ is small, it is ignored to simplify the computation. Thus, the velocity of the walker in coordinate $\Omega[{v}_{X,\Omega}∼{}∼{}{v}_{Y,\Omega}∼{}∼{}{\omega}_{\Omega}]^{\rm T}$ is as follows:

$\displaystyle\left[\begin{array}[]{c}v_{X,\Omega}\\ v_{Y,\Omega}\\ {\omega}_{\Omega}\end{array}\right]=\left[\begin{array}[]{ccccc}0&0&0&0&\sin% \theta_{F}\\ \frac{1}{2}&l_{F}\sin\theta_{F}&\frac{1}{2}&0&0\\ 0&0&0&1&0\end{array}\right]\left[\begin{array}[]{c}v_{L}\\ {\omega}_{L}\\ v_{R}\\ {\omega}_{R}\\ \dot{\theta}_{F}\end{array}\right]$ (5)

Project it to the global coordinate system $[{v}_{X}∼{}∼{}{v}_{Y}∼{}∼{}\dot{\phi}]$ :

$\displaystyle\left[\begin{array}[]{c}v_{X}\\ v_{Y}\\ \dot{\varphi}\end{array}\right]=\left[\begin{array}[]{ccc}\cos\varphi&\sin% \varphi&0\\ -\sin\varphi&\cos\varphi&0\\ 0&0&1\end{array}\right]{\dot{q}}_{\Omega}$ (6)

As a result, let $\dot{\bm{\theta}}={[\dot{\theta}_{L}∼{}∼{}\dot{\theta}_{R}∼{}∼{}\dot{\theta}_{% F}]}^{\rm T}$ , the following kinematic constraint is valid:

$\displaystyle\left[\begin{array}[]{c}v_{X}\\ v_{Y}\\ \dot{\varphi}\end{array}\right]=J\dot{\theta}$ (7)

Where the Jacobian matrix can be expressed as:

$\displaystyle J=\left[\begin{array}[]{ccc}\frac{{\rm d}\sin\varphi}{4}-\frac{{% \rm d}l_{F}{\sin\theta}_{F}\sin\varphi}{4c}&\frac{{\rm d}\sin\varphi}{4}+\frac% {{\rm d}l_{F}{\sin\theta}_{F}\sin\varphi}{4c}&{\sin\theta}_{F}\cos\varphi\\ \frac{{\rm d}\cos\varphi}{4}-\frac{{\rm d}l_{F}\sin\theta_{F}\cos\varphi}{4c}&% \frac{{\rm d}\cos\varphi}{4}+\frac{{\rm d}l_{F}{\sin\theta}_{F}\cos\varphi}{4c% }&{-\sin\theta}_{F}\sin\varphi\\ {-d}/{4c}&{d}/{4c}&0\end{array}\right]$ (8)

Figure 4.

Flowchart of the motion control.

4. Walking assistance control

The flowchart of the motion control of the robotic walker is shown in Fig. 4. The input of the motion control is interactive force $F_{i}(i=1,2,3,4)$ and through a Kalman filter it will reduce the interference from noise first. The reference force is the assistance force providing user force to walk forward during walking. Then, the signal process part contains intention recognition and the dead zone will deal with the signal and deliver the result to the motion controller, which is the major part for calculating the rotation speed of the wheels. The execution part, i.e. the wheels, will execute the command after receiving the rotation speed from the controller and then, based on the kinematic model mentioned in Section 3, the robotic walker will move. When changing the robotic walker and the users’ position, the interactive force between them will be collected by the pressure sensors again and will be the input of the motion control in the next moment.

In order to get a better performance, the controller is achieved by ‘blending’ the fuzzy and D controllers. The major part of the controller is the fuzzy control part while the D control part is used to quicken the response. This paper mainly presents the fuzzy control.

4.1 Kalman filter

The pressure sensors may collect both force and noise signals that will interfere with the control of the system. In order to separate the force signals from the noise signals, it is necessary to place a filter in the force signals. A Kalman filter was used since it shows a great ability of handling signals with noise. The following states are selected for the state vector $x_{k}$ :

$\displaystyle x_{k}={[F_{1,k}∼{}∼{}F_{2,k}∼{}∼{}F_{3,k}∼{}∼{}F_{4,k}]}^{\rm T}$ (9)

where $F_{L,k},F_{R,k}$ are the values collected from the left and right pressure sensors at the moment $k$ . So, the state equation and observation equation in Kalman filter are:

$\displaystyle X_{k}=Ax_{k-1}+W_{k}$ (10) $\displaystyle Z_{k}=HX_{k}+V_{k}$ (11)

where ${X}_{k}$ is the real state of the system at moment $k$ , $W_{K}$ is processing noise and ${Z}_{k}$ is the observation value of the system at moment $k$ , and $V_{k}$ is the observation noise. They are independent and in accordance with Gaussian distribution. The implementation of the algorithm is given in the appendix.

Figure 5.

Flowchart of the motion control.

4.2 Intention recognition

The motion direction of the user could be categorized into: (1) step forward straightly, (2) turn left, (3) turn right, (4) step back straightly, (5) stand still, (6) rotate left, (7) rotate right, (8) step back and turn left, and (9) step back and turn right. To guarantee the safety, motions (8) and (9) are not allowed in this smart walker.

The user’s intention is recognized in terms of the force sensors and Eq. (1) and Eq. (2). It is obvious that the difference of $F_{L}$ and $F_{R}$ produces a torque $M_{s}$ and the torque $M_{s}$ leads to the change of orientation while the sum of $F_{L}$ and $F_{R}$ lead to an intention of acceleration. Thus, the composite force of interactive force $F_{s}$ and torque $M_{s}$ are used for the intention recognition system. The flowchart of the intention recognition is illustrated in Fig. 5.

The composite force $F_{s}$ and the torque $M_{s}$ directly indicate the intention of the user for motion. This is justified by the following assumptions:

1.
The user’s intention to walk can be classified into three major orientations: forward, backward and stand still. Every major orientation can be subdivided into three intentions: turn left, turn right and straight. In other words, wherever the user wants to move, his/her intention is one situation of these nine intentions (step forward straightly, turn left forward, turn right forward, step back straightly, turn left backward, turn right backward, stand still, rotate left, and rotate right).
2.
When the user intends to step forward, the user will start a move in the forward direction, causing its relative position with regards to the walker to move forward and the composite force $F_{s}$ will immediately have a positive value. On the other hand, when the user intends to move backward, the user will start a backward move, leading to a relative position to the walker and $F_{s}$ will have a negative value.
3.
When the user intends to speed up or slow down, the user’s speed will increase or decrease, respectively. This directly results in relative position of the user with regards to the walker to change to a more forward (user is speeding up) or more backwards (user is slowing down) position.
4.
When the user intends to turn, the user will rotate his/her pelvis. When the user would like to turn left, he/she will rotate his/her pelvis to the left, causing the relative position at both sides of the pelvis to change: the left side of the pelvis is backward while the right side of the pelvis is forward. So $F_{1}$ has a negative value and $F_{2}$ has a positive value causing $F_{L}$ a negative value while $F_{3}$ has a positive value and $F_{4}$ has a negative value causing $F_{R}$ a positive value. According to Eq. (2), the torque $M_{s}$ will have a positive value. On the other hand, when the user would like to turn right, he/she will rotate his/her pelvis to the right, causing the relative position at both sides of the pelvis to change: the left side of the pelvis is forward while the right side of the pelvis is backward, so $F_{L}$ will have a positive value and $F_{R}$ will have a negative value. According to Eq. (2), the torque $M_{s}$ will have a negative value.

Based on these assumptions, the values of $F_{s}$ and $M_{s}$ can be used directly as an estimation of user intention for acceleration and turning.

Because a user’s center of gravity is always changing whenever he/she stands or walks [22], a dead zone was added to solve the problem of measurement (noise) in the vicinity of the user’s neutral position and allow the user to keep the robotic walker stationary when needed.

The following experiment is done to ensure the value of threshold. Eight subjects (Table 2) are allowed to try to move in seven directions (mentioned above) and each direction is repeated several times. The data of the interactive force $F_{i}(i=1,2,3,4)$ , the composite force of the left side $F_{L}$ and the composite force of the right side $F_{R}$ were collected and recorded. According to Eq. (2), the torque $M_{s}$ can be computed. Thus, $F_{i}$ and $M_{s}$ in each direction were averaged since they were repeated ten times. Then, the largest of these averaged $F_{i}$ and $M_{s}$ in each direction among eight subjects were chosen as the thresholds of the motion direction to ensure that the intention recognition part would not be too sensitive to recognize the users’ intentions correctly. Some of the experiment data is illustrated in Fig. 6.

Figure 6.
Data from the intention recognition experiment. (a) and (b) are the $F_{s}$ and $M_{s}$ in subject one’s forward position, respectively, (c) and (b) are the $F_{s}$ and $M_{s}$ in subject two’s stand still, respectively, and (e) and (f) are the $F_{s}$ and $M_{s}$ in subject three’s turn right, respectively. The $x$ -label is the sequence of data and the $y$ -label is the value of force and moment, respectively.

Hence, each motion direction has a pair of thresholds: ${D}^{1}_{\rm Fs},{D}^{1}_{\rm Ms};{D}^{2}_{\rm Fs},{D}^{2}_{\rm Ms};\ldots{D}^% {7}_{\rm Fs},{D}^{7}_{\rm Ms}$ . The resulting equation can be written as:

$\displaystyle F_{c}=\left\{\begin{array}[]{cc}0&F_{s}<D^{N}_{\rm Fs}\\ F_{s}-D^{N}_{\rm Fs}&F_{s}\geqslant D^{N}_{\rm Fs}\end{array}\right.$ (12) $\displaystyle M_{c}=\left\{\begin{array}[]{cc}0&|M_{s}|<D^{N}_{\rm Ms}\\ M_{s}-D^{N}_{M}&|M_{s}|\geqslant D^{N}_{\rm Ms}\end{array}\right.$ (13)

${F}_{s}$ and $M_{s}$ are the composite forces of all interactive forces and torques respectively, the ${D}^{N}_{\rm Fs}$ , ${D}^{N}_{\rm Ms}(N=1,2,3,\ldots,7)$ are the pairs of thresholds of $F_{s}$ and $M_{s}$ in different actions respectively, and $F_{c}$ , $M_{c}$ are the input of the controller. The algorithm is simplified and given in the appendix.
4.3 Fuzzy controller

The relationship between the interactive force and velocity of the walker is nonlinear and it is difficult to build a mathematical equation. Inspired by [23], a fuzzy controller is used in the walker since the fuzzy controller is good at nonlinear and uncertain system.

The input of the fuzzy control system are $F_{c}$ and $M_{c}$ given by Eqs (12) and (13), and the output is the velocity of the left and right wheels. Hence, the T-S fuzzy controller is a two input and two output system. The fuzzy control rules are as follows:

$\displaystyle\text{Rule }m:\text{IF }F_{c}isA^{m}_{1}\text{THEN }y_{m}=k^{y}_{% m};\text{IF }M_{c}isA^{m}_{2}\text{THEN }z_{m}=k^{z}_{m}$

where $m=1,2,\ldots,n$ , and $n$ is the number of inference rules. $A^{m}_{1}$ denotes the $m$ th fuzzy inference rule for the first $F_{c}$ and $A^{m}_{2}$ denotes the $m$ th fuzzy inference rule for the second input $M_{c}$ , $y_{m}$ and $z_{m}$ are the $m$ th output from the inference rules which determine the final output of the fuzzy controller $U$ , $k^{y}_{m},k^{z}_{m}$ are the output of $y_{m}$ and $z_{m}$ respectively defined in the reference rules. The final output of the fuzzy controller $U_{y}$ and $U_{z}$ is inferred as follows:

$\displaystyle{U}_{y}=\frac{\sum^{n}_{m=1}{w^{y}_{m}y_{m}}}{\sum^{n}_{m=1}w^{y}% _{m}}=\frac{w^{y}_{1}y_{1}+w^{y}_{2}y_{2}+\ldots+w^{y}_{n}y_{n}}{w^{y}_{1}+w^{% y}_{2}+\ldots+w^{y}_{n}}$ (14) $\displaystyle{U}_{z}=\frac{\sum^{n}_{i=1}{w^{z}_{m}y_{m}}}{\sum^{n}_{m=1}w^{z}% _{m}}=\frac{w^{z}_{m}y_{m}+w^{z}_{m}y_{m}+\ldots+w^{z}_{n}y_{n}}{w^{z}_{m}+w^{% z}_{m}+\ldots+w^{z}_{n}}$ (15)

where

$\displaystyle w^{y}_{m}=A^{m}_{1}(F_{c})$ (16) $\displaystyle w^{z}_{m}=A^{m}_{2}(M_{c})$ (17)

$A^{m}_{1}(F_{c})$ is the grade of membership of input $F_{c}$ and $A^{m}_{2}(M_{c})$ is the grade of membership of input $M_{c}$ . Then, the output is coupled as follows:

$\displaystyle v_{L}=U_{y}-U_{z}$ (18) $\displaystyle v_{R}=U_{y}+U_{z}$ (19)

To raise the degree of accuracy, we divided the membership function into 13 fields. In order to locate the field of the input quickly, we used the variable comparison and FOR-EXIT loop structure. The details are given in the appendix.

The robotic walker must have a quick response to ensure the comfort of the user, so it is necessary to add a D controller to raise the sensitivity of the system. Hence, the fuzzy and D controllers are blended to a P-D controller. The extra coefficients, $k_{v,L}$ and $k_{v,R}$ , are added to the output of the fuzzy controller.

$\displaystyle\dot{\theta}_{L}=k_{v,L}v_{L}+k_{d}\frac{{\rm d}F_{L}}{{\rm d}t}$ (20) $\displaystyle\dot{\theta}_{R}=k_{v,R}v_{R}+k_{d}\frac{{\rm d}F_{R}}{{\rm d}t}$ (21)

Although parameters in the controller greatly rely on the walking ability of the user, a series of generic values for the parameters has been chosen at first and then the parameters have been further determined in experimental runs. By using these parameters, test subjects were able to control the robotic walker in a precise and smooth manner.

Table 1

Experiment settings

	Experiment 1	Experiment 2	Experiment 3
New motion controller	$\sqrt{}$		$\sqrt{}$
PID controller		$\sqrt{}$
Simulated patients			$\sqrt{}$

Figure 7.

The robotic walker was tested in experiment 3 (simulated patients).

5. Walking assistance control

The proposed walker and control approach were tested in an experimental study in a laboratory environment. Mainly the motion control of the walker was tested, and the experimental results are presented below.

5.1 Experimental design

The experiment was carried out in an 8 m $\times$ 5 m space with a wooden floor (Fig. 7). The experiment was limited to eight healthy subjects (seven males and one female). They provided informed consent prior to the study for the three different experiments: the proposed motion control, the traditional proportional-integral-derivative (PID) control, and simulated patients (Table 1). Detailed information of the subjects is listed in Table 2. Subjects were allowed to spend five minutes familiarizing themselves with the robotic walker prior to the experiments. All subjects signed an informed consent form before using the robot.

To test the performance of the control system including the intention recognition part and the fuzzy D controller, a pattern, $\infty$ , was used to test the motion control in the experiment since this pattern contains various radii of curvature. As shown in Fig. 7, some points are marked to depict the path of eight and it is ensured that the next marked point could been seen by subjects during walking. The subjects were told to stand still at the start point and had to face the path for several seconds and then follow the path until they returned to the start point.

The three experiments were executed in the following order:

1.
In the first experiment, the proposed motion control system is used and the subjects were instructed to walk along the path in order to test the system.
2.
In the second experiment, the traditional PID control method [24] was used instead of the proposed motion control approach in order to compare the two controls.
3.
In the third experiment, the subjects wore a splint to limit their knees’ available angle, in order to test the performance of the proposed motion control system in the clinical rehabilitation process.

The rotation speed of the wheels and the time the subjects spent in each run were recorded to evaluate the tracking quality including the execution precision of the reference trajectory shape and the error of the walker’s directional angle.

Table 2
The subjects’ information

Subjects Gender Age Height (cm) Weight (kg) Dominant side

S1 Male 26 165 75 Right

S2 Female 23 166 54 Right

S3 Male 25 170 65 Right

S4 Male 25 172 66 Right

S5 Male 23 178 68 Right

S6 Male 23 175 75 Right

S7 Male 24 171 66 Right

S8 Male 30 178 65 Right

The data of the wheels’ rotation speed was imported into MATLAB to evaluate the tracking quality by comparing the user’s trajectory with the reference pattern. Since the rotation speed of the left wheel ( $\dot{\theta}_{L}$ ) and right wheel and ( $\dot{\theta}_{R}$ ) and the cycle of the system ( $T{}_{s}$ ) are known, the distance that the users go forward in one cycle is given as follows:

$\displaystyle\Delta d=[{{\rm d}T_{s}}/{2}∼{}∼{}{{\rm d}T_{s}}/{2}]\begin{% bmatrix}\dot{\theta}_{L}\\ \dot{\theta}_{R}\end{bmatrix}$ (22)

The change of the walker’s directional angle in one cycle is given by the following equation:

$\displaystyle\Delta\varphi=[{{\rm d}T_{s}}/{2c}∼{}∼{}-{{\rm d}T_{s}}/{2c}]% \begin{bmatrix}\dot{\theta}_{L}\\ \dot{\theta}_{R}\end{bmatrix}$ (23)

So, the position ( ${x}_{k}$ and $y_{k}$ ) and the angle ( $\varphi_{k}$ ) of the user’s pelvis in the global coordinate system at moment $k$ is:

$\displaystyle\left[\begin{array}[]{c}x_{k}\\ y_{k}\\ {\varphi}_{k}\end{array}\right]=\left[\begin{array}[]{c}x_{k-1}\\ y_{k-1}\\ \varphi_{k-1}\end{array}\right]+\left[\begin{array}[]{cc}\sin\varphi_{k-1}&0\\ \cos\varphi_{k-1}&0\\ 0&1\end{array}\right]\left[\begin{array}[]{c}\Delta d\\ \Delta\varphi\end{array}\right]+\left[\begin{array}[]{c}l_{F}\sin\Delta\theta_% {F}\cos\varphi_{k-1}\\ {-l}_{F}\sin\Delta\theta_{F}\sin\varphi_{k-1}\\ 0\end{array}\right]$ (24)

where $\Delta\theta_{F}$ is changing the walker’s pelvis’s directional angle collected by the encoder in the four-bar mechanism. The mathematical model of the reference $\infty$ pattern is as follows:

$\displaystyle x_{e}=\frac{k_{x}\times\cos(2\pi n_{d})}{\sin^{2}(2\pi n_{d})+1}$ (25) $\displaystyle y_{e}=\frac{k_{y}\times{\cos(2\pi n_{d})}\times\sin(2\pi n_{d})}% {\sin^{2}(2\pi n_{d})+1}$ (26)

where $n_{d}$ is the number of points of the data sequences collected from the encoder. The data sequences were processed by interpolation so that the point of the user’s trajectory corresponds to the point in the reference $\infty$ pattern.
5.2 Results and data processing

Subjects	Gender	Age	Height (cm)	Weight (kg)	Dominant side
S1	Male	26	165	75	Right
S2	Female	23	166	54	Right
S3	Male	25	170	65	Right
S4	Male	25	172	66	Right
S5	Male	23	178	68	Right
S6	Male	23	175	75	Right
S7	Male	24	171	66	Right
S8	Male	30	178	65	Right

Figure 8.

Results of the experiments. The eight lines present the results of the eight subjects and the three rows stand for the three experiments: E1, E2 and E3 respectively. In E1, the new control method is used whereas in E2 a traditional PID control method is used. In E3 a splint is used.

Figure 8.

continued.

In order to show the execution precision of the reference trajectory shape, the normalized integral square error (ISE) cost function $J_{c}$ of the post error is defined as a difference between the user’s trajectory and reference pattern samples in $x,y,\varphi$ in a global coordinate system. The cost function consists of position ( ${J}_{p}$ ) and orientation ( ${J}_{o}$ ).

$\displaystyle{J}_{c}=\underbrace{\frac{1}{L}\sum^{n_{d}}_{i=1}{({(x_{i}-x_{e,i% })}^{2}+{(y_{i}-y_{e,i})}^{2})}}_{{J}_{p}}+\underbrace{\frac{1}{L}\sum^{N}_{i=% 1}{{({\varphi}_{i}-\varphi_{e,i})}^{2}}}_{{J}_{o}}$ (27)

The normalization value $L$ is the total length of the reference path. Values of cost functions for all experiments are gathered in Table 3.

Table 3

Cost function contains the position $J_{p}$ and orientation $J_{o}$ for all runs in the experiment. The average values and variance values are calculated in the last two rows

Cost function	E1		E2		E3
	$\bm{J}_{p}$	$\bm{J}_{o}$	$\bm{J}_{p}$	$\bm{J}_{o}$	$\bm{J}_{p}$	$\bm{J}_{o}$
S1	0.06	3.54	0.12	3.98	0.26	3.85
S2	0.08	2.25	0.70	3.61	0.18	2.01
S3	0.08	2.43	0.34	4.27	0.26	1.81
S4	0.08	2.75	0.45	2.84	0.29	4.41
S5	0.07	3.41	0.41	3.91	0.28	3.04
S6	0.04	2.57	0.28	5.39	0.36	3.62
S7	0.06	2.87	0.39	2.94	0.16	2.60
S8	0.06	2.28	0.27	3.64	0.19	3.39
Avg	0.07	2.76	0.37	3.82	0.25	3.09
Var	0.0002	0.24	0.0284	0.64	0.0045	0.82

5.3 Discussion

As shown in Fig. 8, all subjects’ trajectory in E1 are close to the reference path and the results of Table 3 also show a small value both in $J_{p}$ and $J_{o}$ , which proves that the trajectories in E1 have a good execution precision.

When comparing the results between E1 and E2 of all subjects, two conclusions can be drawn. First, during the first quarter of the journey, the path is a curve to the right. Most subjects ‘rushed out’ the reference path in E2, which did not happen in E1, which indicates that the motion control system performs better than the traditional PID system in terms of turning right. Second, during the second quarter of the journey, the path is a curve to the left. The trajectories in E2 are further from the reference path than in E1, which reveals that the motion control system performs better than the traditional PID system in terms of changing orientation. The third and fourth quarter of the journey give similar results and confirm that the motion control system performs better than the traditional PID system in terms of turning left and changing orientation.

From Tables 3 and 4, three conclusions can be drawn. First, the $J_{p}$ and $J_{o}$ had a smaller value in E1 than in E2, which shows that the performance of the new motion controller is better than the traditional PID controller. Second, the variance of $J_{p}$ and $J_{o}$ in E1 is smaller than in E2, which shows that the new motion system is more stable than the traditional PID system. Third, the time subjects spent in E1 is lower than in E2, which shows that the new motion system is smoother and easier to control than the traditional PID system.

As shown in Fig. 8, the trajectories in E3 are close to the reference pattern in the left side but smaller than the reference $\infty$ pattern in the right side. This may be caused by the differences among the power of subjects’ right legs, which leads to the different effects of splint. The splint was applied to completely limit the subjects’ leg power, but when a subject with a comparatively strong leg tries to walk with a splint, the splint can only limit a part of his/her power, causing the change in his/her walking. So, when a subject with a comparatively strong leg tries to step out his/her limited leg, he/she will find that his/her power is limited, so he/she will then try to use more power in stepping out his/her limited leg, which subjects with a weak leg cannot do. However, this manner of walking differs from what the subjects usually do, so they cannot control their power well and usually will use a much bigger force than needed. As a result, in the right side, most of the trajectories were smaller than the reference pattern, which means that the subjects used a much bigger force in their right leg. Besides, the reference path in the right side is the curve to the right and the right leg plays a leading role, so the trajectories show a much smaller patterns than the reference $\infty$ pattern.

As shown in Table 3, even though $J_{o}$ in E3 shows a higher value compared to the averaged E1, sometimes the subjects had a smaller value in $J_{o}$ in E3 than in E1, such as S2, S3, S5 and S7. Although the subjects might use more power than needed during walking, it is no doubt that subjects’ walking speed was slowed down. As can be seen from Table 4, the task took longer in E3. It is well-known that an object with a higher velocity has more difficult to turn left or right. Therefore, it is easier for subjects to turn in E3. In addition, the reason of a high variance value is because of differences among the subjects’ power of their right legs, as mentioned above.

Table 4
The time spent in each run of the experiments. The average values in time are listed in the last row

Time (s)	E1	E2	E3
S1	33.02	45.32	55.22
S2	41.59	46.22	59.10
S3	40.07	53.59	57.15
S4	36.59	44.67	57.12
S5	35.02	45.25	45.62
S6	33.52	51.10	49.15
S7	43.09	47.17	45.10
S8	41.65	44.75	60.60
Avg	38.07	47.27	53.63

To sum up, interestingly, for subjects in E3 is was easier to turn right and left, but it was more difficult to keep a high execution precision. However, the sum of average $J_{p}$ and $J_{o}$ in E3 is still a small value, which shows that it is possible that the robotic walker could be used for clinical rehabilitation of real patients.

Some huge breaks at the start points were found, which can be seen in Fig. 8f, h, i, n, o, s, t and v, which were caused by sliding. When the rotation speed of the left or right wheel has a large value but a small value in another, the subject overpowers the machine, which causes a sliding on the low rotation speed wheel which in turns leads to a loosening of the correct odometry data.

6. Conclusion

The robotic walker with the proposed control system has been tested in the experimental study, and the results show that users could achieve the task with acceptable error. The following conclusions can be drawn. First, the proposed motion control approach can recognize the user’s intention. Second, the proposed motion control approach is easy to manipulate by the users. Third, the novel controller has a higher precision than the traditional PID controller. The robotic walker can assist patients in rehabilitation sessions, and can potentially enhance human mobility and expedite the rehabilitation process.

Footnotes

Acknowledgments

This work was supported by the National Key Research and Development Program of China (Grant No. 2018YFC2001600) and the Shanghai Science and Technology Commission Project (Grant No. 17441907600).

Conflict of interest

None to report.

Appendix

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Man-machine interaction-based motion control of a robotic walker

Abstract

BACKGROUND:

OBJECTIVE:

METHODS:

RESULTS:

CONCLUSION:

Keywords

1. Introduction

2. System description

2.1.1 Mobile platform (MP)

2.1.2 Body weight support mechanism (BWSM)

2.2 Sensors

4.1 Kalman filter

5.1 Experimental design

Table 4 The time spent in each run of the experiments. The average values in time are listed in the last row

Footnotes

Acknowledgments

Conflict of interest

Appendix

References

Table 4
The time spent in each run of the experiments. The average values in time are listed in the last row