HOW TO REDUCE CROSS COUPLING
OF AIRBORNE CAMERAS and other gimbaled sensors

This camera has an unbalance.

It is statically unbalanced because the center of gravity of this assembly is not at the center of the cylinder, and therefore not at the intersection of the axes.

It also has a dynamic unbalance about the azimuth axis. Spinning this object about the azimuth will result in forces that tend to make it spin about the elevation axis until it finds a stable position.

In order to compensate for the unbalance we add a weight on the opposite side.

Our camera is now statically balanced (the center of gravity is at the intersection of the axes at the center of the cylinder). It is capable of looking at a slow moving target and be jitter free. This configuration eliminates most of the jitter.

This static balancing process is done using a gimbal balance machine.

The camera is still dynamically unbalanced about the azimuth. This object still rotates about its elevation axis when it is spun about the azimuth.

Let us now compensate for the dynamic unbalance. We add two weights opposite of the ones that created the dynamic unbalance.

Several methods can be used for dynamic balancing, including the use of spin balance machines or moment of inertia instruments to determine the cross products (also called products of inertia). The technique used depends on each gimbal. Considerations such as travel angles on each axis, mass and inertia distributions, gimbal type, rotational speed, and tolerable residual unbalance determine which method can be used.

The gimbaled camera is now dynamically balanced about both azimuth and elevation. It is both statically and dynamically stable. We have eliminated the cross coupling (or cross product or product of inertia).

In an ideal world the job is done.

Unfortunately (from a balancing standpoint) most gimbaled sensors have internal adjustments. A gimbaled camera can have a zoom that changes its configuration. Or the gimbal has more than 2 axes. These provoke changes of configuration that affect balancing.

The figure on the left represents a rotation of the inner axis (elevation) to track a target. Because of this rotation the outer axis (azimuth) is now experiencing a product. The camera is dynamically unbalanced about the azimuth axis again.

In real situations, dynamically balancing a gimbal means finding a compromise that will lead to the best performance in a range of specified configurations.