Gait Phase Variable / Clock Input (sin/cos Phase Encoding)

Encoding gait phase as a pair of numbers, sin and cos, fed into the policy network so it knows the beat.

This is how gait phase gets used concretely in learned locomotion control: when training a reinforcement-learning walking policy, in addition to joint angles, angular velocities, and velocity commands, sin(2πφ) and cos(2πφ) are also fed in as observations, where φ cycles through 0–1. φ isn't fed in directly because it jumps discontinuously from 0.99 back to 0, whereas sin/cos correspond to a point on a circle and stay continuous, letting the network see that these two moments are actually adjacent. With this external beat available, even a memoryless feedforward network can output a stable periodic gait, aligned with the stance/swing schedule used in a periodic reward. Walk These Ways (Margolis and Agrawal) feeds each of the four legs its own sinusoidal timing signal, and uses stepping frequency and inter-leg phase offset as commands, letting it switch online among trotting, pacing, bounding, and other gaits.

Exampleunitree_rl_gym's G1 environment appends sin(2πφ) and cos(2πφ) to the end of the observation vector, alongside angular velocity, projected gravity, velocity commands, joint positions and velocities, and the previous action, all fed into the policy network together.

Also called

Clock Input, Phase Observation, sin/cos Phase Encoding

Related

Gait Phase (Phase Clock) · RL-based Locomotion Control · Walk These Ways · Observation · Stance Phase / Swing Phase · Positional Encoding

Sources

unitree_rl_gym: legged_gym/envs/g1/g1_env.py
Siekmann et al., Periodic Reward Composition (arXiv 2011.01387)