Aerospace and Electronic Systems Magazine April 2018 - 4

Feature Article:

DOI. No. 10.1109/MAES.2018.160162

Nonlinear Receding Horizon Control-Based Real-Time
Guidance, Navigation, and Control Architecture for
Launch Vehicles
Eric Wahl, Kamran Turkoglu, San Jose State University, San Jose, CA, USA

HISTORICAL PERSPECTIVE
For almost as long as the Western world has had rockets and
missiles, people have been interested in incorporating guidance
systems into them [1], [2]. Robert Goddard experimented with
rudimentary gyroscopic systems as early as the 1930s. Under
the leadership of Wernher Von Braun and his team in the 1940s,
V2 rockets used gyroscopes and an accelerometer, along with a
simple analog computer, to help adjust their azimuth. Advancements continued to be made after World War II, including the
development of guidance systems that adhered as closely as possible to a preplanned reference trajectory [1]-[3]. Expanding on
this, studies (such as Launius and Jenkins [4]) provide a broader
perspective into the history of the launch vehicle control problem. In his doctrine, Friedberg touches upon the history of U.S.
launch vehicle missions [5], while Bilstein sheds light on the
Apollo/Saturn launch vehicle program [6]. Such systems, and
their offshoots, used differences in the actual velocity vector vs.
the expected velocity vector, as well as vector cross products
and partial derivatives, to determine what corrective guidance
actions to take.
In recent years, more sophisticated attempts at control systems
have been proposed or implemented. Although by no means an
exhaustive list, these include the use of neural networks [7]; multiple-timescale, continuous sliding modes [8]; adaptive guidance
technology [9]; and model predictive control (MPC) [10], [11].

CONTROL METHODOLOGIES
It is the intention of this paper to propose a guidance system that
may be used on a nontraditional type of launch vehicle, such as
one launched from a moving platform (including ships or airAuthors' current address: E. Wahl, K. Turkoglu, San Jose State
University, Aerospace Engineering, 1 Washington Sq., ENG
272C, San Jose, CA 95192, USA, E-mail: (kamran.turkoglu@
sjsu.edu).
Manuscript received July 29, 2016, revised January 2, 2017,
May 30, 2017, October 5, 2017, and ready for publication
October 6, 2017.
Review handled by H. Liu.
0885/8985/18/$26.00 © 2018 IEEE
4

planes) and especially one that needs to have its payload inserted
into a certain precise orbit. Furthermore, because it is desirable
to minimize the weight of launch vehicles, this research also
tries to optimize the control effort exerted during the flight of the
vehicle to minimize the amount of fuel that is used. The guidance system must be able to adapt to unknown (and potentially
highly variable) conditions that occur during the launch process,
including variations in position, velocity, and attitude at launch
time. Therefore, some previously mentioned sophisticated control systems have been investigated and considered for further
development. In the end, this paper proposes a system based on
a version of MPC.
MPC, sometimes known as receding time-horizon control,
uses a plant model, an optimization cost function, and iterative calculations of optimal outcomes (and their associated control efforts)
over a receding time horizon [10]. MPC also lends itself to the use
of nonlinear dynamics, which may result in more accurate plant
models (and therefore better control predictions) than linearized
control schemes. As has been stated in Menon et al. [12], although
the study of linearized systems is fairly mature, there is still room
for development in nonlinear systems.
One potential disadvantage of real-time nonlinear controls is
that they tend to result in a higher computational load (in terms of
control action calculations) than equivalent linear control efforts
because of a highly coupled and complex structure. However, the
computing power of small single-board computers, in the size and
weight range that would be desired for a modestly sized launch
vehicle, has increased dramatically over time. With developments
in recent years in microprocessor technologies, it is possible to
execute online (and real-time) calculations in the 500-Hz to 1-kHz
range with a small, yet powerful, credit card-sized computer [17],
[18]. The abilities of microcontrollers such as Odroid, BeagleBone
Black, and Raspberry Pi are superior to onboard computing systems of decades past while being smaller, lighter, and less expensive and consuming less power. It is an additional aim of this paper
to show that such a system may be used to implement the nonlinear receding horizon control (RHC) scheme developed therein.
Presented herein is the contribution of the research in complement
to the existing studies.
Several important points distinguish presented efforts in this
study with respect to Wahl and Turkoglu [19]. In this study, the

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