Centroidal Dynamics

Dynamics that track only how a robot's center of mass and overall momentum change under external forces.

Orin, Goswami, and Lee gave a systematic treatment of this concept in a 2013 Autonomous Robots paper: convert every link's momentum to the whole robot's center of mass and sum them, yielding a 6-dimensional centroidal momentum — 3D linear momentum plus 3D angular momentum about the center of mass. Its rate of change depends only on external forces: the change in linear momentum equals the sum of all contact forces plus gravity, and the change in angular momentum equals the sum of the moments those contact forces produce about the center of mass. These equations are exact for the whole robot, not an approximation — they simply don't encode limits like maximum joint torque or how far a leg can reach. Because the representation is low-dimensional, planning and model-predictive control for humanoids and quadrupeds often first solve for contact forces and the center-of-mass trajectory in this model, then hand the result to a whole-body controller to realize at each joint.

ExamplePlanning a vertical jump: first use the centroidal dynamics model to compute how much ground-reaction force each foot must push off with and how the center of mass and angular momentum should evolve, then have the whole-body controller convert those targets into torques for each joint.

Also called

Centroidal Momentum Dynamics

Related

Centroidal Momentum Matrix · Single Rigid Body Dynamics Model · Angular Momentum · Whole-Body Control · Model Predictive Control · Contact Force

Sources

Orin, Goswami, Lee: Centroidal dynamics of a humanoid robot (Autonomous Robots, 2013)
Underactuated Robotics（Tedrake）: Highly-articulated Legged Robots 一章 (Chinese)