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Tong et al. Intell Robot 2024;4:125-45 I http://dx.doi.org/10.20517/ir.2024.08 Page 127

forces using external joint torque sensors or end-effector six-dimensional sensors to identify the motion in-
tent and subsequently conduct active rehabilitation training. Kim et al. used force sensors to obtain interac-
tion forces [20] , while Radke et al. employed a nonlinear disturbance observer based on a dynamic model to
estimate interaction forces [21] . The estimation of EMG signal-based motion intent involves establishing the
relationship between EMG signals and muscle forces using the Hill muscle model, combined with a skeletal
model, to calculate joint torques. Rosen et al. implemented this method’s control on a two-axis robot [22] .
Hashemi and Ison, on the other hand, directly established the mapping relationship between EMG signals and
joint torques using deep learning approaches [23,24] . The desired trajectory-based motion intent estimation
acquires the expected trajectory of a robot through interaction information and tracks it. Khan et al. used
neural networks to establish a mathematical model between interaction information and the desired trajec-
tory, achieving human-robot cooperative control [25] . In terms of active motion intent recognition, due to the
inconsistency and susceptibility of EMG signals to external factors such as electrode position, sweat, and hu-
midity, the desired trajectory method requires constructing a complex expected trajectory model. Therefore,
this paper adopts the interaction force-based motion intent estimation method, installing joint torque sensors
at the joints to detect human-robot interaction forces without additional devices.

Zero-force control is the foundation for implementing active training, and traditional zero-force control pri-
marily includes two methods: position control-based and torque control-based. In position control-based
zero-force control, the robot operates in position control mode, leveraging external sensors as feedback units
for force information. This method allows for precise detection of external force magnitude, providing higher
sensitivityandstability. Directteleoperationfunctionalityisachievedbytrackingpositioninformation, andex-
ternal force detection requires external sensors or conversion through joint current values. Precise calculation
of the dynamic model is needed, and the method demands high sensor accuracy but exhibits poor robust-
ness [26,27] . In torque control-based zero-force control, the robot operates in torque control mode, eliminating
external sensors and only requiring compensation for gravity and friction in the dynamic model [28,29] . How-
ever, challenges arise in overcoming inertial forces, motor internal reducer transmission losses, and other un-
certainties during motion. For patients with movement disorders, especially those with weak muscle strength,
overcoming the robot’s inertial forces and other impediments for rehabilitation training is challenging. There-
fore, this method falls short of meeting the requirements for active training. The precision of dynamic model
parameter identification is compromised due to uncertainties such as friction and internal motor reducer
transmission losses [30] .

In this paper, firstly, under the zero force control of the robot, a form based on the combination of outer-loop
PID feedback and feedforward control is proposed. The robot works in the torque control mode, calculates
the interaction force by computing the dynamics model using external torque sensors, and obtains the com-
pensation value of the feedforward torque by means of the outer-loop control, which not only provides the
compensation torque of the external force but also overcomes the inaccuracy of the dynamics model and im-
proves the robustness of the system. Meanwhile, an active rehabilitation training method based on outer-loop
fuzzy PID control is further proposed to address the shortcomings of ordinary PID control. The traditional
PID method has limitations in compensating torque with fixed parameters, which may not be suitable for all
patients, particularly those at different stages of rehabilitation treatment. Fuzzy PID control is more suitable
for the active rehabilitation training function compared to the normal PID control method [31] . First, it is more
robust to system nonlinearity and uncertainty and can better overcome the influence of uncertainty factors in
the dynamics model. Secondly, it is more responsive to the system and can respond faster to the motor inten-
tion of a patient [32] , which, in turn, enables the patient to provide less interaction force to complete the active
rehabilitation training and improves the rapidity and suppleness of the system.

This paper is organised as follows. Section 2 describes the rehabilitation robot device and modelling method.
Section 3 presents the active training method based on outer-loop PID and its fuzzy control improvement