A motion-planning algorithm for control of an axis of miniature spacecraft using microactuators is presented in this paper. The axis determines the orientation of the spacecraft except for its spin about the axis. This work is motivated by a novel attitude control technique for miniature spacecraft using pseudo-wheels proposed in our prior work. A pseudo-wheel achieves net orientation changes using a sequence of fully reversed partial rotations by utilizing the non-commutative property of finite rigid body rotations. Finding the sequence for a desired change in orientation constitutes the inverse kinematics problem. Our prior work presented an approximate method for this problem for which the existence of the solution is not proved. In this paper, we simplify the problem by considering only the orientation of an axis attached to the spacecraft ignoring the spin about it. For this simplified problem, an accurate algorithm is presented using a technique called pair-wise rotation method, and the existence of the solution is proved. Several numerical experiments have been carried out to validate the new motion-planning algorithm. An axis-control has much practical utility for spacecraft in applications such as pointing solar panels or a camera.

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