Speed and morphology conditioned fourier gait synthesis for bipedal locomotion learning

Human gait is a quasi-periodic multi-channel signal whose cycle duration changes with walking speed, which makes it hard to feed to a model with a fixed-width input or output. FFT representation of a signal can be represented by fixed set of coefficients. This paper proposes a small network that maps walking speed and limb lengths to the harmonic coefficients, and uses the inverse transform to generate a joint-angle reference. A cycle of any duration thus becomes a fixed-dimensional coefficient vector, and the reconstruction is periodic by construction rather than learned. The proposed network is trained on a corpus of gait cycles and evaluated on held-out cycles. The network outperforms spline interpolation, recorded-cycle playback, a coupled oscillator, and PCA, recurrent and residual baselines on pointwise error, dynamic time warping distance and harmonic-magnitude fidelity. The network then serves as the reference generator for a torque-controlled 7-DoF planar biped trained with Proximal Policy Optimization (PPO) and an imitation reward. The resulting policies are tested off-distribution against reward-only and model-based baselines. The imitation-guided policies are more robust on slopes and rough terrain and keep a human-like joint pattern, while a reward-only PPO policy matches them on velocity tracking.