# Pace Running of a Quadruped Robot Driven by Pneumatic Muscle Actuators: An Experimental Study
## 1 Introduction
It is reported in biology that leg load is fed back to the CPG such that the activity of a flexor neuron in the CPG is inhibited when a load is applied to the leg, resulting in activating an extensor neuron and extending the stance phase to support the body [24; 25]. Specifically, we input leg load multiplied by a gain to the flexor neuron of the corresponding CPG in an inhibitory manner. As a result, the simulated quadruped model demonstrated being capable of safely walking over a step and a slope [15]. Although the model only with joints around the pitch axis was often inclined sideways, the model extended the stance phase of each leg on the side toward which the body was inclined and avoided falling toward the side. The hind-leg robot with pneumatic artificial muscles demonstrated adaptive stepping by automatically changing the locomotion speed according to the gradual speed variation of a treadmill [17], similar to a mesencephalic cat's reaction [26]. These two results suggested that our proposed two-level CPG with leg loading feedback enhanced walking stability and adaptability to external speed variation. In this study, we build a quadruped robot in which forelegs are added to the previous hind leg robot in Figure 1b, and control it with the four two-level CPGs with leg loading feedback coupled to produce a pace gait. Then, we demonstrate that the coupled two-level CPGs can achieve a stable pace running based on experiments at steady speeds on a treadmill. It is reported in neurophysiology that changing connection strengths between the CPGs of the four legs can produce a variety of gaits [20,21]. Thus, to simply reproduce a pace gait for our quadruped robot in our present study, we first connected the ipsilateral CPGs and contralateral CPGs in strongly excited and inhibitory manners, respectively, without leg loading feedback to the CPGs. However, our robot failed in steady pace running because the oscillation of each leg swung by the dominant CPG was not able to synchronize with the roll body oscillation. The same results were observed even with leg loading feedback. Therefore, when we weakened the connection strengths, the coupling between the CPGs did not affect locomotion, and the quadruped robot steadily runs with a pronk, which is a gait in which all the four legs moved in phase. Subsequently, when we added leg loading feedback to the CPG, resulting in the robot achieving a steady pace running at a constant speed. Since the body oscillated around the roll axis on the treadmill, a load applied to the ipsilateral pairs of legs toward which the body inclined increased. This allowed the stance phases of the ipsilateral legs to be simultaneously extended because of leg loading feedback, preventing the robot from falling toward the side. The robot alternated this adaptation on both sides, leading to a pace gait. In short, the cycles of each CPG and the roll body oscillation were autonomously synchronized through leg loading feedback. Interestingly, when we used leg loading feedback with the weakly coupled CPGs, the oscillation of each CPG was entrained in the roll body oscillation and autonomously converged to an arbitrary cycle, which was different from the original cycle of the CPG without leg loading feedback and suited the roll body oscillation. As a result, our robot safely pac by swinging each leg at a suitable cycle to suit the roll body oscillation without any joints around the roll axis or any instruction of the desired cycle. The present results demonstrated that the two-level CPG with leg loading feedback that we proposed can be used for steady pace running of a musculoskeletal quadruped robot as well as uneven terrain walking [15] and autonomous adaptation to external speed adaptation [17]. This paper is organized as follows. Section 2 introduces our quadruped robot, devices, and two-level CPGs. Section 3 shows the robot's experimental results of pronking without leg loading feedback and pacing with it. Section 4 presents the conclusions of our study.