# Hardware Development and Safety Control Strategy Design for a Mobile Rehabilitation Robot
###### Abstract
The design should be robust enough to overcome the uncertainties of human-centered limb rehabilitation robots. Generally, to guarantee control accuracy, the PID controller's gain is usually set to be significant; the high-gain PID control may result in a large overshoot. When the PID controller's gain is small, it exhibits a slow overdamped characteristic where a fast response cannot be ensured. On the other hand, large overshoots and oscillation may happen when the system encounters emergency events, e.g., sudden power outage, sensor faults, and accidental environmental contact. Therefore, in the conventional PID control method, it is challenging to simultaneously achieve both safety and work performance. Sliding mode control (SMC) can force the system state to be kept on the sliding-mode surface and converge to an equilibrium point in a finite time [22; 23]. However, the chattering phenomenon during the convergence process deteriorates the safety performance. To ensure both the tracking accuracy and security of the controlled system, a proxy-based sliding mode control (PSMC) was first introduced by [PERSON] et al. [24], which combines the features of SMC and PID to guarantee closed-loop dynamic behavior continuously. It is an improved version of PID control and has been applied in the nonlinear control field by many researchers due to the simplicity of the control architecture [3; 25; 26]. PSMC is widely applied in soft robotics because of its superiority in ensuring safety and precision in motion [27; 28]. It limits the control output strictly and combines overdamping to provide safe recovery from abnormal events with good tracking performance during regular operation [24; 25; 29; 30]. Even though the original PSMC has been well applied in various systems, it still needs significant improvements in the theoretical analysis of stability. The original PSMC is a model-free controller, and its stability can be verified by a conjecture (see [24]); however, its theoretical proof has not been well addressed. [PERSON]. [31] presented an extended PSMC strategy via the Lyapunov stability theorem to solve the problem of stability for the original PSMC. However, all system states and magnitudes of disturbances were assumed to be provided in the extended PSMC. However, in practical applications, it is impossible to obtain or measure all the states and disturbances of the system. Therefore, it is difficult to effectively apply extended PSMC to practical systems. To this end, this paper presents a novel safety control method that integrates linear extended state observer (LESO) combined with a proxy-based sliding mode control (ILESO-PSMC) for MRR. We used the new virtual coupling and LESO to design the ILESO-PSMC. LESO was used to estimate the system's states and total disturbance by involving the theoretical model. The stability of the ILESO-PSMC strategy was systematically proved by applying the Lyapunov theorem. This methodology simplifies the proof of the system's stability and makes the derivation simple. The experimental results show that the ILESO-PSMC enables the system to track the desired target in both overdamped and smooth mode. The rest of this paper is organized as follows. Section 2 introduces the design, hardware configuration, and functions of MRR. Section 3 describes the dynamic models of the AMBSS and LES. The controller design and stability analysis are described in detail in Section 4. Section 5 presents experiments demonstrating the effectiveness of the proposed control strategy and the verification of the feasibility of MRR. Finally, the conclusions of this study are drawn in Section 6.