A mixed integer convex programming approach to Constrained Attitude Guidance

This paper introduces a new algorithm for attitude motion planning, Constrained Attitude Guidance (CAG) problem, in the presence of angular rate constraints and conic exclusion regions (pointing constraints). The CAG problem is solved by considering only the quaternion kinematics in the formulation and using constraints on quaternions and its time derivatives to indirectly apply bounds on the angular rates and accelerations. The CAG formulation makes use of Mixed Integer Convex Programming (MICP) in order to impose, approximately, the unity constraint on the quaternion magnitude, where the approximation accuracy can be set to a desired accuracy. The solution complexity of the MICP formulation increases exponentially with the number of binary variables that are used to impose the unit norm constraint on the quaternion. Since this number is independent of the number of exclusion pointing constraints, the solution approach has favorable complexity in terms of the number of pointing constraints. The paper also provides a numerical example that incorporates both angular rate and pointing constraints.