# Pace Running of a Quadruped Robot Driven by Pneumatic Muscle Actuators: An Experimental Study
## 1 Introduction  
Legged robots can move over a high obstacle more easily than wheeled and tracked vehicles, and especially, quadruped robots are more stable than biped robots. Therefore, a quadruped robot is expected to assist people in many activities conducted over rough terrain, such as a rescue mission over rubble and construction work in fields filled with many obstacles, in the future. Although we focus on a pace running on flat terrain in this paper, running over rough terrain is our following target. Quadrupeds change their gait according to speed and typically choose a trot or pace at medium speed running [1]. A trot is a gait in which the diagonal pairs of legs move in phase, while the two pairs together move out of phase. A pace is a gait in which the ipsilateral pairs of legs move in phase, while the two pairs together move out of phase. Although a vast number of quadruped robots using a trot gait have been developed, a smaller number of quadruped robots using a pace gait have been developed [2; 3; 4; 5; 6; 7; 8; 9; 10], of which limited ones [2; 4; 7] can run. Pacing can be generally observed in long-legged quadruped animals, such as giraffes and largedogs, because the ipsilateral legs being swung in phase can prevent the legs from bumping into each other [11]. The ipsilateral legs of general mammalian quadruped robots whose degrees of freedom are limited tend to move on the same sagittal plane, causing even a short leg to have a risk of bumping into one another, especially while running with longer strides. Therefore, a quadruped robot that chooses a pace for running at a medium speed is considered practical. Although the locomotion abilities of contemporary quadruped robots, such as Spot [12], Unitree [13], Mini-Cheetah [7], and Anymal [14], have been rapidly progressing, most of them use electromagnetic motors as their actuators, causing concern for energy efficiency. Animals achieve energy-efficient locomotion because of effective energy conversion between chemical compounds and force of contraction in muscles, and more energy-efficient in running by making use of the muscles' elasticity. Therefore, next-generation artificial muscle actuators are expected to be used for prospective quadruped robots. Another advantage of using muscle actuators is durability because their softness can absorb shocks from the ground when the robot falls over. We aim to achieve a steady pace running by a bioinspired quadruped robot driven by artificial muscles in our present study. Our goal is to develop a controller for walking and running for a bioinspired quadruped robot that will be driven by next-generation artificial muscles in the future. To target this, we reported uneven terrain walking by a simulated quadruped model (Figure 1a) [15] and stepping on a treadmill by a two-hind leg robot driven by McKibben-type pneumatic artificial muscles [16] with the constrained torso (Figure 1b) [17]. In the simulated model and robot, each leg consisted of three joints around the pitch axis (without any joints around the roll or yaw axis) driven by four single-joint muscles and two two-joint muscles, based on muscles that are mainly used for a cat's locomotion [18; 19]. To drive the biomimetic leg along a leg trajectory similar to that of an animal's, we must synergistically activate a different set of the six muscles in each of the typical four sequential leg phases (i.e., swing, touchdown, stance, and liftoff) in one cycle [18]. To achieve this, we used a central pattern generator (CPG) for each leg, which exists in a spinal cord of an animal and produces the rhythmic motion of the leg [20; 21]. We improved a realistic neuromorphic two-level CPG proposed by [PERSON] et al. [22; 23] to achieve the realistic motion of each leg with the six muscles. In addition, we demonstrated that leg loading feedback to the CPG played an important role in the uneven terrain walking [15] and hind-leg stepping [17].