| The problem of capturing and despinning a satellite in an uncontrolled three-axis tumble is addressed. The proposed solution is a device which resembles a hollow cage. Thin cylindrical elements are arranged in a regular octahedron, forming a three-dimensional space truss with masses mounted at each comer of the octahedron. The device, which is larger than the tumbling satellite, opens at one end and engulfs the satellite. The device maneuvers such that its center of mass is coincident with the satellite's center of mass. By adjusting the corner masses, the device can match the satellite's moment of inertia ratios. Torques are then applied to the device to cause it to match the tumble rates of the satellite. Once this occurs, the torques can be neutralized and the device will follow the satellite's motion in a torque-free tumble. The target (i.e., the satellite) is then motionless in the reference frame of the retrieval device and the satellite can be grappled without fear of damaging solar panels, antennas, or other equipment. Equations are derived which show how the device can vary the mass distribution to match any set of inertia moment ratios. The physical system is shown to be controllable. An optimal control algorithm for tumble matching is then derived and a computer simulation is developed. The results of the computer simulation show that the control algorithm is stable for four test cases involving different satellites in different tumbles. |
