## 1 Introduction  
Legged robots are receiving increased attention as the most prominent mobile robot technology for almost all terrain adaptations [1; 2]. With the development of driving and sensing technology and the application of novel stabilization-control algorithms, stabilized locomotion and anti-disturbance capability become even more prominent, such as Bigdog [3; 4] walking on ice and the back flips of Atlas [5]. However, compared to humans and animals, the energy efficiency of these robots remains relatively low [6]. The more general methods for improving the energy efficiency of legged robots can be divided into three classes: employment of structures or actuators with elastic or flexible components, passive locomotion, and motion optimization. For the first strategies, elastic or flexible elements, such as mechanical springs and rubber bands, are always connected to the limb structure to form passive joints, such as in HYQ designed by [PERSON] et al. [7], and Cheetah, designed by [PERSON] et al. [8]. Thus, the gravitational potential energy of the robot can be converted to elastic potential energy and released as the body moves forward. Elastic components can also be connected in series between the output of the actuator and the load to form a series elastic actuator [9; 10] or a variable stiffness actuator [11; 12]. These kinds of actuators not only can obtain the precise output force by controlling the deformation of the elastomer but can improve energy efficiency through its rhythmic energy storage and discharge. The famous quadruped robot ANYmal is a successful application of this [13; 14]. However, the limitation of the stiffness and complexity of the structure with the above methods make the structural design more complicated and reduce the adaptability of the robot to complex terrain. Compared to the above strategies, passive locomotion seems to be the easiest way to improve energy efficiency. The three-dimensional passive walking robot designed by Cornell University [15] and inspired by [PERSON] [16] is representative. Not only can it walk stably on a slope, but it can achieve stable locomotion on a plane using motors and elastic mechanical springs in the ankle joint [17]. Unfortunately, such robots are developed for high energy efficiency and cannot be applied in practice. The most common method of motion optimization is to reduce the swing amplitude of the joint by optimizing the foot trajectory [18], which has obvious limitations for legged robots used in complex and unknown environments. With its excellent power-to-weight ratio, high robustness, and high bandwidth, hydraulic actuation is used in many successful legged robots, such as Bigdog and LS3. With the development of high performance hydraulic components, highly efficient hydraulic servo systems have developed rapidly and are used in many fields, such as the load-sensing servo systems, pump/motor-controlled servo systems [19], and independent metering systems [20; 21]. However, such systems are not suitable for legged robots. On the one hand, they are too complicated, and hydraulic components that can be applied to legged robots are relatively rare, while on the other hand, the performance of most of them is severely constrained by loads and the trajectory of the actuator, etc. The valve-controlled system [22] is still widely used on legged robots. It can provide good motion performance but cannot achieve its energy-saving potential. The energy efficiency can be significantly improved by using an ultra-low leakage valve or asymmetric spool servo valve [23], but such products with fast response and high control bandwidth are not only scarce but expensive. The hydraulic servo actuator with passive compliance (HPCA) [24] was designed to improve the response of the actuator to impact forces between a robot's feet and the ground. The micro-hydraulic accumulator is connected to the piston chamber of the actuator, and its performance is also improved by various oil circuits and control valves.