Center of Mass (CoM)

The mass-weighted average position of an object, which behaves as if all its mass were concentrated there.

The center of mass is a mass-weighted average of position: r_c = Σmᵢrᵢ / Σmᵢ, where mᵢ is the mass of the i-th part and rᵢ is its position. In a uniform gravity field, the center of mass coincides with the center of gravity, so engineers often use the two terms interchangeably. For a robot, the center of mass governs balance: while standing still, its projection onto the ground has to land inside the support polygon — the region enclosed by the robot's ground-contact points — or the robot falls over. Gait control and zero-moment-point analysis for humanoids and quadrupeds are built around the center-of-mass trajectory. When an arm picks up a heavy object, the farther the payload's center of mass sits from the flange, the more torque the joints have to resist. Model files such as URDF require a mass and center-of-mass position for every link; getting these wrong makes simulation behave differently from the real robot.

ExampleTwo balls, 1 kg and 3 kg, sit at x = 0 and x = 4 meters. The center of mass is at (1×0 + 3×4) / (1+3) = 3 meters — closer to the heavier ball.

Also called

CoM, Center of Gravity (CoG)

Related

Support Polygon · Zero Moment Point · Centroidal Dynamics · Static Stability · Inertial Parameters · Payload

Sources

Wikipedia: Center of mass
Wikipedia: Support polygon