Spatial statistical point prediction guidance for heating-rate-limited aeroassisted orbital transfer Pradipto Ghosh n , Bruce A. Conway Aerospace Engineering Department, University of Illinois at Urbana-Champaign, 319G Talbot Laboratory,104 S. Wright St., Urbana, IL 61801, USA article info Article history: Received 5 June 2014 Received in revised form 2 January 2015 Accepted 9 February 2015 Available online 17 February 2015 Keywords: Optimal feedback control Feedback guidance Trajectory optimization Spatial statistics Kriging Particle Swarm Optimization abstract Feedback control of constrained non-linear dynamical systems satisfying a certain optimality criterion and meeting a specified transfer objective in the state space is recognized as one of the most challenging problems in control theory. One approach to computing optimal feedback policies is the dynamic programming route of numerically solving the Hamilton–Jacobi–Bellman (HJB) partial differential equation directly. In this paper an alternate and more tractable dynamic programming approach, the optimal feedback synthesis method, is utilized. The effectiveness of this method is demonstrated through an explicit guidance scheme for the heating-rate-constrained maneuver of an Aeroassisted Transfer Vehicle (AOTV). In optimal feedback synthesis, a feedback chart is constructed from a family of open-loop extremals, thus ensuring optimality with respect to any initial condition in the family. This paper presents a solution to the AOTV optimal feedback synthesis problem using the Gaussian process spatial prediction method of universal kriging. A closed-form expression for a near-optimal guidance law is derived. Its performance is found to be very promising; initial atmospheric entry errors due to simulated thruster misfiring are seen to be accurately corrected while the algebraic state- inequality constraint is closely respected. & 2015 IAA. Published by Elsevier Ltd. All rights reserved. 1. Introduction Orbital transfers of spacecraft in low-Earth orbit may be categorized into one of the two major types: all propulsive transfers in which an orbit transfer occurs entirely using on- board fuel, and aeroassisted transfers, in which a part of the orbital transfer uses propulsion and the rest utilizes aero- dynamic forces via flight through atmosphere. The latter is also referred to as a synergetic transfer since the maneuver is accomplished through a combination of aerodynamic and propulsive forces rather than propulsion alone. The chief motivation behind the study of aeroassisted transfers is the potential fuel saving it affords. This is an important factor in missions involving small satellites for which the on-board fuel constraints may render all-propulsive maneuvers infea- sible, thereby necessitating aeroassisted transfers. In fact, it has been asserted that any mission involving changes in orbital altitude and/or inclination in the neighborhood of an atmosphere-bearing planet is a candidate for aeroassisted maneuvers [1]. The control and optimization of aeroassisted transfers have been actively researched since the introduction of this concept by London in 1961 [2]. However, the majority of efforts have focussed on the determination of fuel-optimal open-loop maneuvers [3–13]. But recognizing the presence of such factors as navigation errors and imperfections in the atmo- spheric, aerodynamic and gravitational models, coupled with Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/actaastro Acta Astronautica http://dx.doi.org/10.1016/j.actaastro.2015.02.013 0094-5765/& 2015 IAA. Published by Elsevier Ltd. All rights reserved. n Corresponding author. E-mail addresses: pradipto.ghosh@gmail.com (P. Ghosh), bconway@uiuc.edu (B.A. Conway). Acta Astronautica 111 (2015) 257–269