## 1 Introduction  
Stroke and spinal cord injury (SCI) are the main causes of human lower limb motor dysfunction [1; 2; 3]. Motion disability not only causes difficulties with physical control, but also serious psychological problems to the patient, which greatly reduce the quality of life of the patient. Rehabilitation training can effectively help patients with lower limb motor dysfunction improve muscle strength, restore walking ability, and reduce complications [4]. In terms of the rehabilitation process, the training mode of the robot can be divided into passive training and active training. Passive training requires the robot to drive the patient into predetermined trajectory movement, and the robot usually adopts the control method of trajectory tracking. In this article, aiming at the challenge of low tracking accuracy in trajectory tracking control, research on control methods was carried out to improve the performance of trajectory tracking control. In the early stage of rehabilitation training, the patient's lower limbs are almost completely paralyzed (bed-ridden) and rely on external assistance to complete the training action. Traditional rehabilitation gait therapy requires multiple therapists to manually drive the patient's legs, which increases labor costs [5], or uses auxiliary equipment connected to the hospital bed to achieve rehabilitation training [6; 7]. In the early stage of treatment, these approaches are effective, but when the patient leaves the bed for overground gait training, they cannot guarantee better results. With the emergence of lower limb rehabilitation exoskeleton robots including LOKOMAT [8] in 2005, HAL [9] in 2008, ReWalk [10] in 2010, and ExoMotus [11] in 2018, a large number of clinical applications have shown that lower limb rehabilitation exoskeleton robots can play good auxiliary roles for patients with different degrees of injury [12; 13]. Trajectory tracking control, which is one of the main control strategies in the control method of lower limb rehabilitation exoskeleton robots, is the basis and key to realizing different training modes. The lower limb rehabilitation exoskeleton robot is a multiple-degree-of-freedom open-chain mechanism composed of irregular links that have complex nonlinearity and strong coupling characteristics [12; 13]. These robots are vulnerable to disturbances from the patient and the ground during the control process. Therefore, it is difficult to establish a complete and accurate mathematical model of the robot, which leads to difficulties in robot motion control and poor trajectory tracking accuracy. Traditional control methods including proportional-integral-derivative (PID) control [14], computed torque method [15], adaptive control [16], and robust control [17] have difficulty in meeting the actual needs of patients using lower limb rehabilitation exoskeleton robots because their trajectory tracking abilities are limited. The sliding mode control does not depend on a mathematical model of the controlled object and has strong anti-interference ability and good robustness [18; 19], consequently, sliding mode controls are widely used in robot control systems [20]. A sliding mode control divides the motion process of the robot system state into two stages. The first stage is from the initial state to the sliding surface, and the second stage gradually converges to an equilibrium point in the sliding surface [21]. However, after the system state reaches the sliding surface, it is difficult to strictly slide along the sliding surface to the equilibrium point. Instead, the system state moves back and forth across the sliding surface to approach the equilibrium point, which results in buffeting [22]. Many researchers have designed reaching laws to change the reaching speed and weaken the chattering of sliding mode controls. [PERSON] et al. [23] and [PERSON] et al. [24] proposed a sliding mode control based on the constant velocity reaching law for a lower limb rehabilitation exoskeleton robot. [PERSON] et al.