The Poppy Humanoid is an open-source, low-cost robot suitable for research and education in artificial intelligence. However, we are unaware of any published methodology that achieves reliable, unassisted bipedal locomotion on the standard Poppy hardware. This paper contributes a functional closed-loop walking controller for Poppy, based on the linear-quadratic regulator (LQR) framework for trajectory tracking. Starting with data collected from open-loop playback of a nominal walking trajectory, our proposed method learns a quadratic cost function for an LQR controller that substantially improves the reliability of the motion. The closed-loop controller is validated empirically, demonstrating statistically significant improvements in walking performance compared to open-loop trajectory playback.
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Figure 1: The Poppy hardware and four locations used in our experiments. To prevent hardware damage during falls, we fashioned an experimental harness from a consumer clothing rack and camera strap, with a custom wooden insert to avoid pressure on the sides of the head when the strap is taut. We only count footsteps as “successful” if the strap is slack for the entirety of the motion without any human intervention or assistance.
Figure 2: Nominal trajectory (solid lines) and recorded joint angles (dashed lines) from a representative hardware run. Circles indicate the timing of the waypoint commands. Only a subset of joint motors are shown for figure legibility, labeled at right according to the standard Poppy naming convention.
Figure 3: Histogram over open-loop runs of the number of successful footsteps before a fall (trajectories were 6 footsteps long, so 6 successful footsteps means no fall during the episode). The left panel is for noiseless trajectories only ( σ=0.0 , see text); the right panel is over all runs.
Figure 4: Per-run, per-timepoint Euclidean distances from current joint observations to average successful run (left) or initial stance pose before each footstep cycle (right). On right we only show the timepoints at the boundary of each cycle. Each transparent curve is a separate run, and opaque curves show the means over all runs in their respective categories. Data from failure runs after the recorded fall step are omitted from the plots.
Figure 5: Left: Mean absolute deviation between dynamics model predictions and observed data. Right: Condition number of fitted dynamics matrix.
Figure 6: Left : Cumulative products Λn of maximum eigenvalue magnitudes of An+BnKN , for several ϵ . “Open-loop” refers to “passive” residual dynamics with no LQR adjustments, i.e., using maximum eigenvalues of An . Middle: Eigenvalues of the cost coefficient matrices Cn . Each scatterpoint is an individual eigenvalue and solid lines show minimum eigenvalue for each ϵ and n . Right: Violin plots showing cost distributions over failed and successful runs in the open-loop data for ϵ=−2.0 (each scatterpoint is a run with horizontal noise added for legibility).