A potential field inspired approach to attitude motion planning with unit-quaternions

This paper presents a method of planning attitude motion with unit-quaternions in the presence of a single goal attitude, multiple obstacle attitudes, and forbidden axes of rotation. The method makes use of a potential field inspired approach that is utilized to generate a set of velocity directions that move the unit-quaternion towards a goal attitude and away from forbidden attitudes. A weighted sum of these directions is utilized to formulate an angular velocity vector where the weights are derived from a measure of the angular distance of the current attitude to both the goal and forbidden attitudes. The unit-quaternion state-transition matrix is utilized to propagate the unit-quaternion given this angular velocity vector thus insuring that the quaternion maintains unit magnitude. The method is demonstrated with an iterative example in which obstacles are strategically placed on previously generated attitude motion paths thereby highlighting the described technique's ability to generated paths that avoid forbidden attitudes.