# The Energy Consumption and Robust Case Torque Control of a Rehabilitation Hip Exoskeleton
## 1 Introduction
For a safe hip rehabilitation exoskeleton, a series elastic actuator (SEA) is chosen for this research, as it presents a compliant interface, accurate and stable torque control over time, low impedance and shock tolerance (elasticity), all of which afford highly confident force control and comfortable wearability and it extends the operational life time of the joint [8; 16; 28; 29; 30; 31; 32; 33; 34]. An SEA was used at the hip joint to replicate the hip torque signals of a healthy joint as desired movements in the controller. However, the functions of the controller depend on the mathematical representation and modelling of the system. This can be a challenge because it is an approximation to a real system, which can also be affected by parametric uncertainties, variations or short-term and long-term stochastic noise disturbances (ageing) [27; 35]. To the best of our knowledge, no research has validated the LQR for robustness and energy consumption. Therefore, the goal of this study is to validate the LQR controller of a rehabilitation hip exoskeleton for such variations and uncertainties and to establish the foundation of safe human-robot interactions for future research. Hence, the basic design for the exoskeleton and the SEA was introduced in [8; 28; 36]. Estimating the states of the system was essential for the controller; therefore, the Luenberger observer (LO) was used. The implementation and design of the LO are elaborated in [8]. Not only did the controllers attract the attention of researchers and innovators, but also the weight of such devices, as rehabilitation exoskeletons are usually attached to deficit limbs. Therefore, the energy consumption is worth studying to avoid the extra weight of additional batteries, especially when the powered hip rehabilitation exoskeleton is used outdoors and at home. The contributions of this paper are threefold: an examination of the robustness of four LQR controller cases, validation of the performance of such controllers and investigation of the energy consumption of our rehabilitation hip exoskeleton performing STS and walking movements at each control case and at various speeds. The experiments were conducted in a simulated environment as it provided insight into how an exoskeletal system behaved in a virtual environment that mimicked a real one. They assessed the performance of the model by testing various parameters that were difficult, expensive and time-consuming to reproduce using the physical model [37]. This was especially true of safety, which is a critical factor in experimental designs for human-robot interactions. This paper is organised as follows: Section 2 presents the importance of the STS and walking activities trained by the rehabilitation hip exoskeleton, LQR strategy, concepts of robustness, performance of the controller in tracking a trajectory signal measured by root mean square errors (RMSEs), energy consumption and STS and walking power calculations. In Section 3, the methods used to test the robustness of four optimal control cases, the RMSE and a simulation energy consumption of a proposed rechargeable battery during the STS and walking movements are analysed. Finally, the results and conclusion are provided in Sections 4 and 5, respectively.