The COM(Center of Mass) is as one might imagine, the equivalent center of collection of mass bearing particles. It can be calculated by averaging the position of each particle and weighing it by its mass:

$x_{com}=\frac{\sum_{i=0}^{N}x_{i}m_{i}}{\sum_{i=0}^{N}m_{i}}$

The mass of the COM is equivalent to the sum of the masses of its constituent particles.

The position of the COM can be used to give a estimate of the robots stability. Generally speaking, when the COM is outside the support area then the robot has a risk of falling over however this is not always so. In particular when the velocity of the COM is in a direction of moving back into the support area then this  may not be a problem at all and such movements are commonly used in modern biped robots.

Finally note that in the situation of zero acceleration, the ZMP point is located just beneath the COM as can be seen from the model based ZMP equation

 $x_{zmp}=x_{com}-\frac{zh}{g}\ddot{x}_{com}$

This means that under static conditions the robot is able to maintain balance as long as its COM is inside the support polygon and unable to do so when the COM is outside the support polygon.

Next: Support Area

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### One Response to “Center of Mass”

1. I want to be a biped robot with 1.6m, but I don’t know how to do a flexible foot and thigh joint, which can make the robot walk smoothly.