# Pace Running of a Quadruped Robot Driven by Pneumatic Muscle Actuators: An Experimental Study
## 2 Quadruped Robot and Control Method
### Motion Generator  
#### 2.3.1 Two-Level CPG with Leg Loading Feedback  
The aforementioned representative quadruped robots [7; 12; 13; 14], which are driven by motors, have each simplified leg consisting of two links. Unlike these, to move a three-link leg along an animal-like leg trajectory, the robot has to drive each leg through the four sequential phases (touch-down, stance, lift-off, and swing) in one cycle, as shown in Figure 4. An animal synergistically activates a different set of muscles (the red muscles in Figure 4) in each of the four phases [18]. To realize the synergistic activation of muscles, we previously proposed two-level CPG, as shown in Figure 5[15; 17]. This was improved from the CPG proposed by [PERSON] et al. [22; 23]. We use the two-level CPG for our present running quadruped and drive its legs along the animal-like leg trajectory in Figure 4. The parameters are modified such that the quadruped robot can safely run. The CPG's equations are shown in Appendix A, and we briefly explain the functions below.  
Figure 3: Configurations of the fore and hind legs (**a**), and an image of our quadruped robot (**b**).  
As shown in Figure 5, the CPG is divided into two parts, namely rhythm generation (RG) and pattern formation (PF). The RG part receives a constant tonic descending input when locomotion speed is constant and produces a basic locomotion rhythm for a single leg, which is generated by the mutual inhibitory connections between the extensor neuron (RG-E) and flexor neuron (RG-F). The PF part has the four PF neurons (PF\({}_{\text{td}}\), PF\({}_{\text{st}}\), PF\({}_{\text{lf}}\), and PF\({}_{\text{sw}}\)), which manage the four leg phases (touch-down, stance, lift-off, and swing).  
Figure 4: Cycle of the four leg phases (touchdown, stance, liftoff, and swing).  
Figure 5: Diagram of the two-level central pattern generator (CPG) for each leg.  
shown in Figure 4, respectively. While each PF neuron rhythmically bursts by receiving inputs from the RG neurons, the four PF neurons activate at different timings by mutually inhibiting each other. Eventually, the outputs from several of the PF neurons multiplied by different gains, which are shown by the thickness of the arrows from PF neurons to motoneneurons, are integrated into each motoneuron to drive the corresponding muscle, as shown in Figure 5. The neural system activates the different sets of muscles in each of the four sequential phases, as shown in Figure 4. For example, in the forelegs, \(\text{PF}_{\text{td}}\) in Figure 5 is input with relatively strong gains to \(\text{Mn}_{1}\), \(\text{Mn}_{4}\), and \(\text{Mn}_{6}\) for the scapula flexor, shoulder extensor, and two-joint muscle for shoulder and elbow joints, respectively, which show the three red muscles in the case of touch-down in Figure 4. This leads the foreleg to the touch-down phase.  
We apply leg loading feedback to the CPG, which is crucial to adjust the rhythm and support the body [25]. Specifically, leg load is inputted to the RG flexor neuron in an inhibitory manner, as shown in Figure 5, based on biological findings [25; 31]. The feedback inhibits the activation of the RG flexor neuron in the stance phase, causing the extension of the stance duration. Similar to our previous hind leg robot [17], we estimate the leg load from tension applied to the two-joint muscle actuator for the shoulder/knee and elbow/ankle joints, which covers an elbow or ankle joint extensor, based on many locomotion experiments of decerebrate cats [25].