Adaptive atmospheric reentry guidance for the Kistler K-1 orbital vehicle

The Kistler K-l is designed to be a fullyreusable, two stage launch vehicle for economical delivery of small satellite ,payloads to low earth orbit. Greatest efficiency and, hence, lowest cost are achieved by flyback of both vehicle stages to the near vicinity of the launch site. The second stage Orbital Vehicle (OV), after deploying the payload and performing necessary phasing maneuvers, performs a deorbit burn to achieve the desired trajectory conditions at atmospheric entry. After entering the atmosphere, the OV is steered aerodynamically until reaching the deployment point . for a stabilization parachute. Subsequently, drogue and main parachutes complete deceleration of the vehicle for landing orrairbags. This paper presents the design of an atmospheric guidance algorithm for bank-to-turn steering of the OV prior to deployment of the stabilization parachute. Reentry guidance targets a desired geographic position for deployment of the drogue parachute. The algorithm employs a numerical predictor/corrector technique to compute the bank angle and the start time of a single bank reversal required to null the predicted target position miss. Aerodynamic loads and heating are limited implicitly by selection of deorbit target conditions for reentry trajectory shaping. Results obtained using the Draper Laboratory K-l Integrated Vehicle Simulation illustrate guidance performance under nominal and dispersed conditions. * Senior Member of the Technical Staff, Member AIAA. Introduction The K-l Orbital Vehicle (OV) is cylindrical in shape, with a blunt nose and a flared skirt on the aft end (Figure 1). The vehicle trims at an angle of attack of approximately 11 to 12 degrees over the Mach range experienced during reentry. This results in a lift-todrag ratio ranging from 0.1 to 0.15. The only control effecters available are 12 small attitude control system (ACS) jets that are used to provide three-axis attitude stabilization and control. Due .to jet size limitations, alteration of the vehicle angle of attack from the trim condition for purposes of trajectory control is not feasible. Thus, active control of the vehicle trajectory is possible via bank maneuvers only. Given the vehicle mass characteristics and ACS jet properties, the bank acceleration is limited to approximately 2.5 deg/sec/sec. A maximum sustainable bank rate of approximately 15 deg/sec is possible; however, 10 deg/sec is used as a practical limit to avoid excessive Euler coupling (and, hence, fuel usage). Figure 1. Kistler K-l Orbital Vehicle (OV) Copyright 01999 by The Charles Stark Draper Laboratory, Inc. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission: 1275 (c)l999 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization. When the Mach number decreases to 2.5, a stabilization parachute is --deployed to stabilize the vehicle about the pitch and yaw axes in the low supersonic and transonic regimes. When a specified altitude is reached a drogue parachute and main parachutes are deployed to decelerate the vehicle for subsequent landing. on airbags. The landing site may be located either at the Nevada Test Site (NTS) or in Woomera, Australia. The key requirement levied on the reentry guidance is to steer the vehicle to the proper conditions for parachute deployment to achieve the landing target position with a given accuracy. This must be accomplished without exceeding specified aerodynamic loading and heating rate limits (8 g longitudinal, 4 g lateral, and 58 BTU/sq ft/sec, respectively). ACS fuel usage must be limited in the process. These requirements must be satisfied in the presence of potentially significant known and unknown dispersions in vehicle mass and aerodynamics properties, deorbit trajectory, and atmospheric conditions. An adaptive atmospheric reentry guidance algorithm has been designed which, as part of an overall guidance, navigation, and control subsystem, addresses the above vehicle characteristics and mission design requirements. The algorithm uses a numerical predictor/corrector technique to solve for a bank angle magnitude and the start time of a single bank reversal that will null the predicted target position miss. Numerical predictor/corrector guidance has been suggested previously for application to aerobraking and aerocapture.“2’3 -While computationally intensive, this technique allows the use of relatively high-fidelity models of vehicle and environmental characteristics, with ,correspondingly increased accuracy over analytic techniques. This paper presents a discussion of the decision’ process leading to the guidance design in addition to a detailed description of the key elements of ‘. the guidance algorithm. Details of the flight software implementation of the guidance algorithms are included where beneficial. Finally, simulation results are supplied to illustrate guidance performance. under nominal and dispersed-conditions. Reentry Dynamics Figure 2 is a free-body diagram of the OV during atmospheric reentry. The lift and drag accelerations experienced by the vehicle are expressed as where. . p f atmospheric density Vd = velocity relative to air mass C, , C, = vehicle drag and lift coefficients