This paper describes a new control algorithm for achieving any arbitrary attitude and angular velocity states of a rigid body, even fast and complicated tumbling rotations, under some practical constraints. This technique is expected to be applied for the attitude motion synchronization to capture a non-cooperative, tumbling object in such missions as removal of debris from orbit, servicing broken-down satellites for repairing or inspection, rescue of manned vehicles, etc. For this objective, we have developed a novel control algorithm called Free Motion Path Method (FMPM), which enables us to completely ignore a non-linearity effect in the dynamics by concentrating on some conservative quantities of the system. FMPM is an on-line control method and can be formulated as an open-loop or a closed-loop system. With FMPM, we can explicitly specify the maximum control torque constraint and also it realizes a certain kind of optimality. This paper examines an open-loop formulation of FMPM with some theoretical analyses and computer simulations.
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