## 1 Introduction  
Robot gait training systems which help the patient regain their gait function of the lower limb via repetitive movement in training sessions have received great attention in the last decade. Most of the commercial rehabilitation systems are driven by electric motors [1; 2; 3; 4; 5; 6; 7; 8] due to the fact that advanced control techniques can easily be applied to achieve the best performance. One typical example is the LOKOMAT system from Hocoma AG, Volketswill, Switzerland [1]. This system has not only been available on the market but also extensively studied in many rehabilitation centers. This system consists of a bodyweight support, a treadmill and a powered leg orthosis. It is capable of providing various training strategies such as trajectory tracking control and patient cooperative or assist-as-needed (AAN) [2; 3; 4]. The hip and knee joints are actuated by a direct current (DC) motor with helical gears. Similar systems such as ReoAmbulator (Motorika Ltd., Mount Larel, NJ, USA) [5], lower extremity powered exoskeleton (LOPES) [6; 7], or active leg exoskeleton (ALEX) [8; 9; 10] with linear actuator are also available with AAN rehabilitation strategy. However, these motorized systems are fairly expensive due to the high cost of the servo system including the driver, motor, sensors and gear. Besides, low power/weight ratio is also a major concern. Recently, lower-limb rehabilitation systems based on pneumatic artificial muscles (PAMs) have attracted much attention from researchers due to the similarity between PAMs and human muscle. The PAM is shortened in the longitudinal direction and enlarged in the radial direction during the contraction stage when it is being inflated, and vice versa. PAMs are light weight and exhibit a higher power/weight ratios in comparison with the motorized actuator. In addition, PAMs have a nature compliance attribute which a suitable for the human-robotics system. Thus, the applications of PAM in rehabilitation robotics field are growing despite the inherent drawbacks such as hysteresis, compressibility and time variance which yield extreme difficulties in constructing an accurate mathematical model. Various prototype systems have been developed in research centers [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22]. To handle the nonlinear behavior of the PAM, a three-element model [23] based on the sliding mode control (SMC) has been considered as a good choice for tracking control of both single PAM [24] and robots powered by PAMs [14; 15; 18; 19; 20]. Besides, AAN strategy which provides interactive human-robot gait training is also indispensable in these systems [20; 21; 22]. The AAN strategy can be achieved by compliance control in which the nominal pressure of the PAM is adjusted [17; 19; 20; 21; 22]. In our previous studies [25; 26; 27; 28; 29], a high compliant gait training system actuated by PAMs based on the treadmill and body weight support (BWS) name AIRGAIT has been developed. In comparison with the existing robotic orthosis actuated by two mono-articular actuators for hip and knee joints [11; 12; 13; 14; 15; 16; 17; 18], our developed system is based on the human musculoskeletal configuration with an additional bi-articular muscle connecting between the hip and knee joints. The existence of an antagonistic pair of bi-articular muscles can positively contribute to the compliant property of the multi-articular extremities. Furthermore, this additional actuator also provides more power for position and force control of the endpoint of the extremities, which may result in smooth, fine and precise movements [30]. Several strategies have been used for trajectory tracking control of the developed system such as co-contraction model, modified feedforward-feedback. However, the system only shows good performance without the participation of the subject at low walking speed [25; 26; 27]. Although the tracking performance has been improved at higher walking speed, the AAN strategy has not been integrated yet [28; 29].