A general problem in spaceflight since its beginning is attitude guidance: how to turn a spacecraft — also called a slew — so as to point science instruments at their targets. The slew must be done while avoiding pointing sensitive science instruments (e.g., a camera) and attitude sensors (e.g., a star tracker) at bright objects in the sky (e.g., the Sun or the Moon).

To formalize pointing constraints, the spacecraft instruments and sensors — referred to collectively as sensors — are specified as direction vectors in a spacecraft body frame. The bright objects are specified as direction vectors in an inertial frame. Each sensor also has a field of view that bright objects must not enter. Hence, the pointing constraints consist of a list of body vectors with each body vector having an associated and independent list of pairs of inertial vectors and “keepout” angles. For example, the star tracker cannot be pointed within 30° of the Sun nor within 15° of the Moon. These types of constraints are called hard pointing constraints.

The constrained attitude guidance (CAG) problem considered is to find a spacecraft attitude history that points a specified body vector in a specified inertial direction in a given time while not exceeding spacecraft acceleration and velocity limits, and while satisfying all hard pointing constraints. The CAG is solved by formulating it as a mixed-integer convex optimization (MICO). Then standard tools for MICO problems can be used when computing on the ground.

Hence, the significant contribution in this report is the formulation. The formulation includes all the required constraints, handling an arbitrary number of hard pointing constraints, and can be extended to include soft constraints at the cost of drastically increased computation time. The formulation is conservative, with a design parameter that allows the conservatism to be reduced at the cost of computation time. Finally, for a given slew time, the minimum-energy slew is found, in that the sum of the acceleration is minimized in the formulation. While nominally a minimum-energy solution, an approximate minimum time slew can be found with this new formulation by reducing the specified slew time and repeating the optimization until the MICO solver fails to find a solution.

The significant advantage of the MICO formulation is that it is global: it finds a best slew. And even though solving a MICO problem can be time-consuming, slew sequences for flybys of celestial bodies are planned well in advance to maximize science return. With MICO-based CAG, slews will be optimal and more science should be achieved from each flyby.

This work was done by Utku Eren and Behçet Açıkmeşe of the University of Texas at Austin, and Daniel P. Scharf of Caltech for NASA’s Jet Propulsion Laboratory.

This software is available for commercial licensing. Please contact Dan Broderick at This email address is being protected from spambots. You need JavaScript enabled to view it.. Refer to NPO-49685.

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This article first appeared in the April, 2016 issue of NASA Tech Briefs Magazine.

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