Randomness in appendage oscillations helps a robot self-right

Uncertainty is usually avoided or mitigated in control of robot locomotion. When flipped over, the winged discoid cockroach rights itself by repeatedly opening and closing its wings to push against the ground and flailing its legs, both with substantial randomness. A cockroach-inspired robot also uses coupled oscillations of wings and a tail-like appendage (mimicking flailing legs) to self-right but is well controlled. Can randomness be used to improve performance? Here, we test this idea using an experimentally validated multi-body dynamics simulation of the robot. As appendage oscillation randomness (coefficient of variation) increased from 1% typical of the well-controlled robot to 20% typical of the animal, the robot self-righted more often (43% vs. 69%) and more quickly (6.8 ± 3.9 s vs. 5.2 ± 3.8 s) (P < 0.001, ANOVA). We discovered that an appropriate phase offset between the two oscillations was critical to self-righting. Periodic oscillations limited the coupled-oscillator system to visiting only a few phase offsets, causing it to often be trapped near failure limit cycles. Added randomness in appendage oscillations allowed the system to explore more phase offsets, increasing probability and reducing time to escape from failure limit cycles and self-right.