# Parameters Sensitivity Analysis of Position-Based Impedance Control for Bionic Legged Robots' [PERSON]
## 1 Introduction  
Bionic legged robots are better at adapting to unknown and unstructured environments. Their unique advantages, such as overcoming obstacles and executing tasks in the wild, have made them a major focus of research in the robotic domain [1; 2; 3; 4]. For the hydraulic drive robot, the highly integrated valve-controlled cylinder composes the drive component, which is called the hydraulic drive unit (HDU) [5; 6]. During the robotic motion process, the robotic feet interact with the ground frequently. This means that the demand for HDU not only includes characteristics of response ability and high control accuracy, but also dynamic compliance. Thus, the impact on the hydraulic system can be obviously reduced, which can protect the mechanical structure and components, and improve the moving stability of the robots. The selection of control methods directly affects the compliance of the HDU. As a commonly used control method for compliance, the impedance control method has been widely applied to motor-driving legged robots such as the Tekken [7], Scout [8] and MIT cheetah robot [9]. In recent years, as the hydraulic-driven legged robot became the focus of increased research, impedance control was also applied to this kind of robot, as exemplified by robots such as Bigdog [10], HyQ [11], and Scarl-1 [12]. Force-based and position-based impedance control methods are often used for dynamic compliance control. Their basic principle can be expressed as follows. Firstly, the hydraulic control system is taken as the control inner loop, and a dynamic control outer loop is attached to the system. When an external disturbance acts on the system, the input signal of the control innerloop can be changed through the control outer loop. Thus, the system is able to possess the desired dynamic compliance. In this paper, position-based impedance control is the focus of research. There are many parameters in hydraulic systems, such as structure parameters, working parameters, and control parameters. Considering the uncertainty of the parameter variation, the system cannot reach the ideal performance, which involves the effects of parameter variation on robot's overall compliance. So, in order to optimize the system more efficiently, it is necessary to know how greatly the parameters, particularly the main control parameters, influence the impedance control performance. The parameters that affect the system more should be compensated and optimized emphatically, while the ones that affect system less can be ignored. Thus, the effect of parameter variation on system dynamic characteristics can be quantificationally analyzed, and the analysis results can be used to optimize the robot's compliance performance. Sensitivity analysis is used to analyze the effect of parameter variation on system characteristics for both linear and nonlinear systems. By computing methods, sensitivity analysis methods can be classified into the trajectory sensitivity method, output sensitivity method, matrix sensitivity method, comparison sensitivity method, characteristic root sensitivity method, etc. By computing accuracy, sensitivity analysis methods can be classified into ties of first-order sensitivity method, second-order sensitivity method, or high-order sensitivity method. These methods have different characteristics in computing; they differ from each other in aspects such as computing accuracy, computing mode, and computing complexity. These differences give each method unique advantages and application ranges. In recent years, sensitivity analysis methods have been commonly used in many fields, but only a few have been applied to hydraulic systems. [PERSON] et al. [13] is the first scholar to apply first-order sensitivity analysis to hydraulic systems. For the position control system of valve-controlled cylinders, the sensitivity of 10 main parameters when they changed 1% in a single working condition is researched. [PERSON] et al.