Divergent Component of Motion

The part of a biped's center-of-mass motion that diverges exponentially; controlling it is enough to keep the robot balanced.

The divergent component of motion is a state variable used in biped walking control: ξ = x + ẋ/ω, where x is the center-of-mass position, ẋ is its velocity, and ω = √(g/z₀), with g gravitational acceleration and z₀ the center-of-mass height. Honda's Takenaka and colleagues coined this name in their 2009 work on real-time gait generation. In the linear inverted pendulum model — which simplifies the robot to an inverted pendulum with constant center-of-mass height — the motion splits into two parts: the center of mass automatically converges toward ξ, while ξ itself moves exponentially away from the zero moment point (where the resultant force under the foot acts). So it's enough to plan and control ξ alone; the center of mass will naturally follow. It is the same point as the capture point introduced by Pratt and colleagues in 2006. Researchers at the German Aerospace Center (DLR), led by Englsberger, extended it to three dimensions between 2013 and 2015, introducing the two auxiliary points eCMP and VRP along the way.

ExampleWith the center of mass at a height of 0.8 m, ω = √(9.8/0.8) ≈ 3.5 s⁻¹; if the center of mass is directly above the support point and moving forward at 0.35 m/s, ξ sits 0.35/3.5 = 0.1 m ahead of it. If the front edge of the foot can't reach that far, the robot has to take a step.

Also called

DCM, Capture Point (equivalent)

Related

Capture Point · Linear Inverted Pendulum Model (LIPM) · Zero Moment Point · Centroidal Moment Pivot · Bipedal Locomotion · Balance Control

Sources

Takenaka et al., Real time motion generation and control for biped robot – 1st report (IROS 2009)
Englsberger, Ott, Albu-Schäffer: Three-Dimensional Bipedal Walking Control Based on Divergent Component of Motion (IEEE T-RO 2015)
Stéphane Caron: Capture point