## 1 Introduction
Aiming at this problem, the application of output constraint in exoskeletons [29; 30; 31] has attracted wide attention. Using the barrier Lyapunov function (BLF) is an effective method to constrain the output of an exoskeleton in joint space or task space. In [32], an output constraints controller is designed based on BLF, and it is ensured that there is no violation of the constraint rules. In [33], time-varying output constraints are considered. In [34], a pioneer output constraint controller is proposed for strictly feedback nonlinear systems. However, in the real world, due to factors such as measurement noise, it is impossible to obtain an accurate dynamic model of the exoskeleton. The uncertainty and complexity of the control system varies from patient to patient, so it is important to design a controller that meets the requirements of the unknown dynamics of the exoskeleton. Neural networks (NNs) are extensively applied to the control of uncertain, nonlinear, and complex systems due to their outstanding ability to approximate functions with high levels of accuracy [35; 36; 37; 38; 39]. Ref. [40] employed a neural network for disturbance estimation, significantly enhancing the robustness of the control approach. In [41], an adaptive NN is used to approximate the unknown nonlinearity of the hydraulic actuator of a hydraulic knee exoskeleton. Based on the above discussion, this paper attempts to solve the problem of exoskeleton impedance control affected by patients' subjective motor awareness in the later stage of lower limb rehabilitation. At the same time, the motion intention of the patient and the impedance learning of the exoskeleton were considered to improve the effect of rehabilitation training. An adaptive impedance control method combining neural networks and output constraints is proposed for dealing with the problem of human-robot interaction. The main contributions of this paper are as follows:1. Compared with the existing impedance control methods in [12; 15], which use a predefined trajectory for the exoskeleton, this paper proposes a novel neural network-based motion intention estimation method for human-robot interaction, where the exoskeleton is able to actively interact with the patient. 2. The impedance control of the exoskeleton in [16; 17; 18] cannot deal with the problem of output constraint. This paper incorporated the barrier Lyapunov function to construct the controller, where the output constraint is well addressed. 3. In this paper, an RBFNN is used to compensate for the uncertainties in the exoskeleton dynamics, further improving the accuracy of the system. Additionally, strict stability analysis is carried out to ensure the effectiveness of the rehabilitation training. The structure of this paper is as follows. In Section 2, the dynamics of a lower limb rehabilitation exoskeleton is constructed and analyzed, and impedance control objectives are introduced. The algorithms of human motion intention estimation and impedance learning are designed and analyzed in Section 3. Under the output constraints, a NN-based adaptive impedance controller is designed, and the stability of the system is analyzed. In Section 4, the feasibility and effectiveness of the parameter learning and control algorithm are verified by numerical simulation. In Section 5, the conclusion is given.