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Figure 2. 2-DOF lower limb exoskeleton dynamic simulator block diagram. The exoskeleton controllers are implemented in MATLAB
interfacing with the human and exoskeleton models defined in Opensim. 2-DOF: two-degree-of-freedom.

4. SIMULATION
To verify the effectiveness of the AFOFTSM control algorithm proposed in this paper on the suppression of ex-
ternal disturbances, we used OpenSim and Matlab software to develop a lower limb exoskeleton co-simulation
control system to simulate the motion state of the human body wearing lower limb exoskeleton rehabilitation
robot, which is depicted in Figure 2. OpenSim is open-source software for modeling, simulating, controlling,
and analyzing the human neuromusculoskeletal system, developed by the National Institutes of Health (NIH)
Center for Biomedical Computing at Stanford University [28,29] . OpenSim is a developable platform. Using the
template and experimental data provided by OpenSim, we built a human musculoskeletal model with a height
of 1814mm and a weight of 72.6kg and wore the lower extremity exoskeleton on the model [30] . At the same
time, the controller algorithm was written in Matlab to calculate the input torque of each exoskeleton joint and
control the lower limb exoskeleton to drive the human body to move together.

In the following simulation, the established simulation system was run in Matlab software, the simulation time
was 3s, the simulation step size was 0.001s, and the standard hip and knee joints of a healthy subject when
walking horizontally were used as the reference track.

At the same time, the discrete CSMC algorithm [26] and the discrete FTSMC algorithm [27] are respectively
applied to the dynamics model of the lower limb exoskeleton robot for comparison. The design methods of
CSMC and FTSMC are as follows:

1) CSMC

For simplicity, the CSMC [26] control input is given directly:

−1 (49)
= [ ( )] [ ( + 1) − ( ) − (1 − ) ( ) + ( ( ))] .

In the formula (49), ( ) is the sliding mode variable, which is defined as follows:

( ) = ( ) + ¤ ( ) (50)