Development of angular velocity vector measurement of a spherical rotor based on color sensors

Spherical actuators have many applications in satellite attitude control. It is very important for closed-loop control to measure the angular velocity vector of the spherical rotor accurately and quickly. This paper proposes one non-contact method for measuring angular velocity vector of a spherical rotor, using four color sensors. The spherical rotor surface should be color-coded with red, blue, green, magenta, yellow, cyan, black and white, while each color covers an octant in sequence. Four color sensors are mounted about the vertexes of a tetrahedron, used to sense the color of the spherical surface and transform them into angular velocity vector. Simulations approve the correctness of this method, within a module error of approximately 5.2 rpm and a direction error of 0.88 degree within 4000 rpm. Experiments verify that the random error is smaller than 2.7 rpm and direction error smaller than 1.1 degree within 2000 rpm.