# A Safe Admittance Boundary Algorithm for Rehabilitation Robot Based on Space Classification Model
## 1 Introduction  
The healthcare revolution in the second half of the 20 th century has dramatically prolonged people's life expectancies [1], although population aging has become a new social issue recently. Long-term healthcare services have to meet higher standards, given the prevalence of chronic disease in elderly people and the associated complications (e.g., cardiovascular disease and the resulting reduced muscle strength of the extremities, which leads to disabilities [2]). One major consequence is the sustainability risk faced by the healthcare system [3]. The significant shortage of rehabilitation nursing staff has already had some impact. Fortunately, rehabilitation robots have emerged as a new solution to this issue, along with the rapid progress in robot hardware and control technology. Rehabilitation robots offer assistance in patients' motor function recovery, guided by physical therapists [4, 5]. They are usually designed for the purposes of therapeutic exercise, which helps in relearning and reactivating residual motor functions. Rehabilitation robots can also help prevent secondary complications such as muscular atrophy [6]. Earlier rehabilitation robots were originally designed for passive training to help patients in the acute stage [7]. However, passive training is not appropriate for all patients. In the non-acute state, there is usually a greater need for the active training and recovery of motor flexibility and coordination of the limbs, which are highly important for muscle and nerve recovery [8, 9]. So far, several human-robot collaborative controllers have been developed to support the active participation of users in rehabilitation. Typical controllers include forcesensor-based impedance control [8; 10], admittance control [11], assist-as-needed (AAN) control [12], minimal intervention control [13], and electromyogram-based compensation control [14]. However, safety issues in HRI are still not addressed for controllers and robots for active training purposes. Rehabilitation robots usually have heavyweight, high-power actuators and stiff joints and cooperate closely with patients in a shared workspace (HRI space) [15]. Additionally, patients are given greater control in active training when working together with robots. This means that if a robot does not fit with a patient, or there is a misoperation, the robot may move beyond the patient's extremity range of motion, causing severe damage to the patient [16]. This problem has already been raised in earlier rehabilitation robot studies. During the development and optimization of the MIT-Manus wrist robot, [PERSON] et al. designed a sliding mechanism to prevent joint mismatch [17]. [PERSON] et al., inspired by the bio-reflection mechanism, designed a safe force sensor for faults to avoid a violation of space or collision in case the robot in the study went out of control [18]. [PERSON] et al. utilized ER fluid to add an ER brake and an ER actuator to the roboterapist in their study. These mechanisms could limit the robot's range of motion by generating passive damping if dangerous robot motion was accidentally triggered [19]. Similar mechanisms developed elsewhere include magnetorheological (MR) clutches [20] and torque limiters [21]. Several new solutions have emerged in recent years due to continuous technological advances. [PERSON] designed a driving mechanism with an electromagnetic sensor and an actuator to limit a robot's field angle of motion so as to adapt to the safe range of motion of the human wrist [22]. Various methods have been described in literature [23; 24] to limit the working ranges of robots by collecting physical (e.g., force and position) and psychophysiological (e.g., EMG and EEG) measurements to be integrated into their control strategies. Researchers in [25; 26; 27; 28] took advantage of the low stiffness and the extensibility of flexible materials during the design of rehabilitation robots with the purpose of imposing flexible constraints on a robot's range of motion.