Adaptive-Frequency Central Pattern Generator with Multi-Scale Feedback for Dynamic Quadruped Locomotion

This paper studies a MuJoCo-based locomotion framework that couples an adaptive-frequency central pattern generator (AFCO-CPG) with single rigid-body dynamics model predictive control (MPC) for the RENS Q1 quadruped with elastic parallel knee joints. AFCO-CPG combines multi-scale phase coordination, saturated phase correction, and load-gated feedback, while MPC supplies feasible ground-reaction forces and returns load cues to the timing layer. In MuJoCo, the controller achieves stable diagonal-trot speed tracking from 0.4 to 1.2 m/s and recovers from short external pushes. A matched elastic-versus-rigid timing sweep shows a favorable flat-ground parameter band around ω=1.8 Hz, with a best-case cost-of-transport reduction of 12.83% for the elastic model under identical controller gains. A flat-to-slope ascent case further verifies that AFCO timing is modulated when load conditions change. Ablation across nine controller variants shows that multi-scale coordination is the dominant component, causing a 135% increase in phase error and a 536% increase in recovery time when removed. A reduced-order early/late-contact benchmark further confirms faster re-locking than diagonal-only and minimal variants. The results support the value of combining neural timing, predictive force optimization, and compliant-leg feedback in high-fidelity simulation, while hardware validation remains future work.