A command filter adaptive fuzzy backstepping control strategy is proposed for lowerlimb assisting exoskeleton. Firstly, the humanrobot model is established by taking the human body as a passive part, and a coupling torque is introduced to describe the interaction between the exoskeleton and human leg. Then, Vicon motion capture system is employed to obtain the reference trajectory. For the purpose of obviating the “explosion of complexity” in conventional backstepping, a secondorder command filter is introduced into the sliding mode control strategy. The fuzzy logic systems (FLSs) are also applied to handle with the chattering problem by estimating the uncertainties and disturbances. Furthermore, the stability of the closedloop system is proved based on the Lyapunov theory. Finally, simulation results are presented to illustrate the effectiveness of the control strategy.
Recently, the exoskeleton is increasingly used for powerassisting in industrial [
From the modeling point of view, it has been proved that some methods used now are effective such as NewtonEuler equations and Lagrange dynamics [
Nowadays, there have been several published papers on control strategies of humanrobot cooperative control [
However, most of the control methods mentioned have limitations. In modeling, taking the human effects as disturbance [
In this paper, a command filtered backstepping sliding model control equipped with FLSs is proposed based on a humanrobot model. Compared with the analogous literature, the main contributions are summarized as follows:
The proposed humanrobot model is established by taking the human leg as a passive part and the coupling torque between human and robot is introduced. Compared with the model built in [
For the purpose of testing the controller performance, an experiment is implanted to obtain the actual trajectory of the hipjoint. Compared with the sine curve, the upper bound increases rapidly after a few derivative operations, which may cause the system uncontrollable.
The command filter backstepping sliding model control is proposed. By using the command filter, the analytical derivate is unnecessary and the “explosion of complexity” in the controller design process is avoided [
The paper is organized as follows: in Section
As shown in Figure
1DOF lowerlimb exoskeleton.
In order to describe the system, an elementary model is used in this paper which consists of linearized onedegreeoffreedom (1DOF) models for the human leg and the exoskeleton. In the process of modeling the physical interaction between the human and exoskeleton, a coupling torque, expressed as combination of a linear spring and a damper, is introduced.
Then, the ideal dynamics of the humanrobot system are given as follows [
And the coupling torque is defined as follows:
The main way that the exoskeleton helps human complete the locomotion is tracking the human gait cycle. So a reasonable desired position trajectory is an essential factor for testing the model and controller. An experimenter (girl aged 25 years with mass of 52 kg and stature of 165 cm) volunteered to participate in the gait experiment with Vicon motion capture system, device provided by National Research Center for Rehabilitation Technical Aids (Figure
Vicon motion capture system.
Special trackers are fixed at the particular marks on the experimenter which can be captured by cameras distributed in reasonable location in experiment space. The information from different cameras are combined, and the actual hipjoint angle signals are obtained through data processing. From the considerable data obtained, the most reliable, representative, and authentic data is selected and reorganized. To ensure the smoothness of the trajectory, the Fourier series is introduced to describe the actual gait cycle. Note that the human locomotion satisfies the smooth characteristics.
Mathematical expression of the desired trajectory can be expressed as follows [
The parameters of the trajectory are obtained by the curve fit toolbox of MATLAB. In order to approximate the actual curve and simplify the calculation process, fundamental frequency to third harmonics, that is,
Parameter identification of the hip joint trajectory.
















According to (
The actual hipjoint trajectory obtained by experiment.
The control objectives for the humanrobot system are illustrated as follows:
An adaptive controller for highorder humanrobot system is designed, such that the position of human leg
The prescribed output tracking error
For the exoskeleton, the human leg is a passive part and fulfills the locomotion with the interaction torque between the human and robot. For the dynamics shown in (
Note that all the states and the torques are timevarying variables and time flags are omitted for convenience.
Taking the lump uncertainties, parametric/unmodeled uncertainties as well as the external disturbances, into account, (
Note that the specific parameters of human leg are hard to be measured and the actuator of the exoskeleton includes mechanical errors which cannot be described precisely. Hence, the uncertainties of the system existed and are inevitable.
Considering that the system has highorder features, a backstepping sliding model method is introduced to solve the complex problem with a recursive form [
In order to handle the system chattering problem caused by the uncertainties and disturbances, fuzzy logic systems (FLSs) are equipped to estimate the upper bounds of the lump uncertainties. FLSs provide realtime compensations for the humanrobot system to reduce the switching items of the sliding model control.
Being equipped with secondorder command filter and FLSs, a backstepping sliding mode control strategy for the humanrobot system with uncertainties and disturbances is proposed in this paper.
Some reasonable and useful assumptions are given at first which ensure the stability of the system.
There exist constants
For
The design of the FLS consists of two steps. First, the fuzzy rule base should be made up as follows:
if
then
where
The second step is defuzzification. Center average defuzzification operator is applied in this paper which can be expressed as
Define the fuzzy basis vector as
Denote
The optimal parameter
For
Consider the characteristics of the humanrobot system, a backstepping sliding model control with secondorder command filter is proposed in this paper. The controller design process is shown in this section.
The output tracking errors and compensated tracking errors of the subsystems are defined, respectively, as
The
Equation (
For the purpose of eliminating the “explosion of complexity,” a secondorder nonlinear command filter is designed to calculate
The filter initial conditions are
In order to find the optimal parameters of the FLSs, the adaptive laws are chosen for
Considering the compensating errors and the closedloop dynamics, the virtual law can be defined as follows:
The
For the system illustrated in (
The tracking error
Due to the fact that
Note the fact that the command
Then, define the control Lyapunov function for the closedloop system as
Then the time derivative of the Lyapunov function (
Substitute
The simplification can be written as
Replace
Let
That is
According to Barbalat Lemma proposed in [
The block diagram of controller design is shown in Figure
Block diagram of the controller design. (CF represents the command filter defined by (
In this section, a simulation of an 1DOF lowerlimb exoskeleton is established. All the parameters of the 1DOF exoskeleton are illustrated in Table
Parameters of the humanrobot system.
PARM  Value 

















The PARM is short for parameter, and the notation is omitted for convenience through the paper as long as special notation is not required.
All the parameters are cited in [
The lump uncertainties are chosen as follows:
To ensure the stability of the system, the specific parameters of the controller are tuned in a trialanderror procedure and shown in Table
The parameters of the controller.
PARM  Value 





















The simulation results are given in Figures
Position tracking of humanrobot system.
Tracking errors of humanrobot system.
Control inputs of every subsystem.
Control input of the humanrobot system.
Compensated tracking error.
The estimate of the uncertainties and disturbances with the FLSs.
Figures
Figures
Figure
All the signals remain bounded in a reasonable range during the process. Obviously, the proposed control strategy with command filters and FLSs can be a suitable method for lowerlimb exoskeleton.
A humanrobot cooperative control strategy based on a convincing highorder model is proposed for a lowerlimb assisting exoskeleton. A secondorder command filter backstepping method is employed to determine the time derivatives of virtual control signals without differential operations. The FLSs are used to approximate the uncertainties and disturbances and compensate the system timely. In addition, the stability of the system is proved based on the Lyapunov theory. Finally, simulation results are presented to verify the effectiveness of the proposed command filter adaptive fuzzy control strategy.
Future work will focus on the performance of the control strategy in actual experiment and the filtering errors should be proved to converge rigorously. Besides, further research on the state constrain control for highorder nonlinear systems [
The authors declare that they have no conflicts of interest.
This work is supported by National Natural Science Foundation (NNSF) of China under Grants 61703134, 61503118, and 61703135, the Natural Science Foundation of Hebei Province (nos. F2015202150; F2017202119; F2016202327), the Natural Science Foundation of Tianjin (no. 17JCQNJC04400), and Foundation of Hebei Educational Committee (nos. QN2015068; ZD2016071).