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Simulations of Multiple Spacecraft Maneuvering with MATLAB/Simulink and

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DOI: 10.2514/1.35328

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 JOURNAL OF AEROSPACE INFORMATION SYSTEMS
Vol. 10, No. 7, July 2013

Simulations of Multiple Spacecraft Maneuvering with

MATLAB/Simulink and Satellite Tool Kit

Shawn B. McCamish,∗ Marco Ciarcià,† and Marcello Romano‡

Naval Postgraduate School, Monterey, California 93940
DOI: 10.2514/1.35328
A software interface between the MATLAB/Simulink environment and the Satellite Tool Kit Environment is
introduced. This research is based on the need for validating model performance and visualizing simultaneous
multiple-spacecraft proximity maneuvers for emerging missions. It is common for spacecraft systems to be modeled
with MATLAB and Simulink. Furthermore, the software package Satellite Tool Kit is often used for animating and
evaluating spacecraft maneuvers. In this research, a MATLAB/Satellite Tool Kit interface was developed to
propagate six-degree-of-freedom spacecraft models, compared against Satellite-Tool-Kit-generated ephemeris, and
Downloaded by UNIVERSITY OF CALIFORNIA on September 4, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.35328

animated for analysis. MATLAB script with necessary formatting is used for Satellite Tool Kit initialization and
animation. The MATLAB/Satellite Tool Kit simulation interface allows variations in number, shape, and dimensions
of spacecraft. Additionally, numerous model and simulation parameters can be selected and synchronized between
MATLAB and Satellite Tool Kit. Furthermore, either predetermined, or randomly distributed, initial spacecraft
positions and orientations are permitted by the interface. The paper gives enough details to allow the interested
readers to adapt to their needs and further develop the proposed software interface.

I. Introduction

M ODEL validation and simulation visualization are critical aspects of engineering analysis and performance evaluation for spacecraft
control algorithms [1]. An effective test scenario simulates the environment in which the control algorithm is expected to operate. For
spacecraft control system design, it is common for engineers to use The MathWorks, Inc. products MATLAB and Simulink [2,3] for dynamics and
kinematics modeling. These models are often independently developed and coded by separate researchers; therefore, modeling discrepancies can
be difficult to troubleshoot. This research suggests a method of spacecraft model validation by comparison with the Satellite Tool Kit (STK)
spacecraft analysis software [4]. STK, developed by Analytical Graphics Inc., can be used as an orbital propagator for both simulation and
emulation of the desired spacecraft models. In addition to spacecraft model validation, STK can be used for detailed animation of spacecraft
simulations.
In our research, a multiple-spacecraft six-degree-of-freedom (6-DOF) simulation was developed for the purpose of control algorithm
development during close-proximity operations. The simulator incorporates a 6-DOF MATLAB/Simulink numerical model with three-
dimensional (3-D) STK visualization. Both the model validation and 3-D visualization are intended to support engineering evaluation during
control algorithm development.
Since STK is not as commonly used in engineering fields as MATLAB, the developed simulation interface between the two software programs
is of high potential interest to many. In this research, MATLAB-developed spacecraft models were compared and validated based on the STK
standard. This paper serves an introduction to the capabilities of a MATLAB/STK simulation interface and gives enough details to allow the
readers to adapt and further develop it for their purposes [1]. As a sample case application of the developed software interface, we present the cross
validation of a multiple-spacecraft dynamic model and of a novel control algorithm. The paper is organized as follows. Section II introduces the
newly developed MATLAB/STK simulation interface, Sec. III reports the sample application of the developed interface for spacecraft modeling
verification, and Sec. IV introduces the use of the software interface for multiple-spacecraft model animation.

II. MATLAB/STK Simulation Interface

The developed MATLAB/STK interface takes advantage of STK’s standard connection protocol to initialize STK from MATLAB. STK
developers have enabled their code to be executed by MATLAB via an application program interface called AgConnect [4]. The connection
allows for properly formatted commands to be sent via a transmission control protocol/internet protocol (TCP/IP) port. By exploiting this feature,
formatted data, such as ephemeris and attitude data, can be passed between applications. For instance, the interface allows all spacecraft physical
characteristics and simulation parameters to be defined in MATLAB and related to STK. Also, STK data can be passed to MATLAB for analysis.
The general functions and information flow between MATLAB and STK are shown in Fig. 1.

A. Overview of Spacecraft Dynamic Modeling in MATLAB/Simulink

Initially, generalized spacecraft characteristics were used to model the spacecraft in MATLAB/Simulink. All multiple-spacecraft simulation
parameters are assigned in MATLAB and implemented by a single Simulink model. Spacecraft states are concatenated into vectors and passed
through the Simulink model. A high-level Simulink spacecraft model is shown in Fig. 2.

Presented as Paper 2007-6805 at the AIAA Modeling and Simulation Technologies Conference and Exhibit, Hilton Head, SC, 20–23 August 2007; received 5
May 2008; revision received 10 December 2012; accepted for publication 23 January 2013; published online 26 July 2013. This material is declared a work of the
U.S. Government and is not subject to copyright protection in the United States. Copies of this paper may be made for personal or internal use, on condition that the
copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 2327-3097/13 and $10.00 in
correspondence with the CCC.
*Ph.D. Candidate, ECE Department, 700 Dyer Road; Major, U.S. Air Force; sbmccami@nps.edu.
†
Research Associate, Spacecraft Robotics Laboratory, Mechanical and Aerospace Engineering Department; mciarcia@nps.edu.
‡
Associate Professor and Director, Spacecraft Robotics Laboratory, Mechanical and Aerospace Engineering Department and Space Systems Academic Group;
mromano@nps.edu. Associate Fellow AIAA.
348
 MCCAMISH, CIARCIÀ, AND ROMANO 349

MATLAB &&SIMULINK
MATLAB Simulink Satellite
SatelliteTool Kit(STK)
Tool Kit (STK)
Version
Version7.3.0267 (R2006b)
7.3.0267 (R2006b) Version 7.0.1
STK 7.0.1
The MathWorks Inc Analytical Graphics, Inc

Spacecraft Orbital Dynamics Spacecraft Graphical Modeling

Spacecraft orbital dynamics Spacecraft Modeling
Spacecraft Attitude
Spacecraft attitude & Kinematics
and kinematics Spacecraft
Spacecraft Orbital
orbital Dynamic
dynamics

Spacecraft Control & Actuation Spacecraft Visualization

Spacecraft Characteristics Visualization of Spacecraft (Modeler)

Spacecraft State Data Spacecraft State Data

Spacecraft Model Validation Visualization of Multiple Spacecraft

Close proximity Operation
Fig. 1 MATLAB/STK simulation interface overview.
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Fig. 2 High-level Simulink model for multiple-spacecraft simulation.

Several parameters must be assigned before multiple-spacecraft simulations can be executed. These parameters can include the number of
simulations, initial time, selection of the acting perturbations, number of spacecraft and obstacles, selection of control algorithms, and duration of
simulation. For each simulation, a reference start time must be selected. In this research, the Universal Time (UT1) in the format of [year, month,
day, hour, minute, second] was used.
The inclusion of perturbations is critical to the fidelity of the 6-DOF spacecraft model. These perturbations forces and torques modify the
spacecraft’s simple two-body orbital propagation. Variations in the Earth’s shape and mass (J2–J4 coefficients), atmospheric drag on the
spacecraft, third-body (sun and moon) forces, and solar-radiation pressure result in disturbances in a spacecraft’s orbit [5] and attitude dynamics
(gravity gradient, and aero- and solar torque).
Once the number of chase spacecraft is selected, their initial positions must be assigned. These positions can be provided in classical orbital
elements, Earth-centered inertial (ECI), or target spacecraft’s RSW reference frame, as described in Fig. 3. Sample values of simulation conditions
are summarized in Table 1. Similar to chase spacecraft, stationary obstacles can also be included in the simulation. The control algorithm
development is discussed more in detail in [6,7].
For detailed 3-D simulations, each spacecraft’s physical characteristics must be further defined. The spacecraft size, shape, and mass are
variable for each simulation. The center of mass of the spacecraft is assumed to be located at the geometric center, and the moments of inertia are
calculated based on the spacecraft’s shape [8]. Each spacecraft is assumed to have six thrusters (for translational control) aligned along the positive
and negative primary body axes of the spacecraft. For the attitude control system, we consider three orthogonal reaction wheels aligned along the
primary spacecraft body axis. Selected spacecraft model characteristics for a sample spacecraft are listed in Table 2.
 350 MCCAMISH, CIARCIÀ, AND ROMANO
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Fig. 3 Relative reference frame.

B. Overview of Satellite Tool Kit

The STK core modules allow for analytical and numerical orbital propagation of multiple spacecraft. An additional module, called AgConnect,
allows STK to be used in conjunction with MATLAB [4]. By transferring information between MATLAB and STK, MATLAB-constructed
simulation dynamics and kinematics can be verified and visualized. The STK/Connect module provides the means for STK to communicate with
applications, such as MATLAB, through the use of a TCP/IP socket. Additionally, the MATLAB/STK interface may use the STK/
Communications module to emulate signal propagation delays, frequency and bandwidth limitations, and bit error rates for each sensor and
spacecraft [9]. Typical STK users select scenario parameters via the STK graphical user interface (GUI) interface. This allows primary objects,

Table 1 Spacecraft maneuver parameters

Parameter Value
Target spacecraft Min altitude 300 km
Max altitude 2000 km
Chase spacecraft Number 1–12
Chase spacecraft R axis 1.0–1000 m
Initial position S axis 1.0–1000 m
W axis 1.0–1000 m
Chase spacecraft R axis 0 m∕s
Initial velocity S axis 0 m∕s
W axis 0 m∕s

Table 2 Sample spacecraft characteristics

Parameter Value
Physical properties Length/width 1.0 m
Height 1.0 m
Mass 100 kg
Moment of inertia X 16.67–50 kg · m2
Moment of inertia Y 16.67–50 kg · m2
Moment of inertia Z 16.67–50 kg · m2
Thrusters Number of thrusters 1–6
Propellant type Hydrazine
Max thrust per axis 1.0 N
Specific impulse 100–200 s
Steady-state impulse 200 s
Min pulse duration 0.05 s
Min Δv 0.0005 m∕s
Max total Δv 30–120 m∕s
Propellant mass 3% of total
Attitude actuators Reaction wheels (RWs) 3
RW max torque 0.055 N · m
RW max angular momentum 4–12 N · m · s
Initial RW angular rate 0 RPMa
RW spin axis inertia 0.1426 kg · m2
Magnetotorquers 3
Max dipole moment 100 A · m2
Docking tolerances Max axial
2.0 mm
Max lateral
2.0 mm
Max angular
0.1 deg
a
RPM denotes revolutions per minute.
 MCCAMISH, CIARCIÀ, AND ROMANO 351

such as spacecraft, to be loaded with desired constraints. Additionally, sensors can be defined and attached to the satellites. The GUI has dropdown
menus with layers to define basic characteristic: two-dimensional (2-D) graphic animation, 3-D graphic animation, and related constraints.
Several additional STK-supported modules may be useful for spacecraft proximity maneuver simulations. These modules supplement the core
STK visualization environment and assist in the evaluation of mission sequences. In particular, the Astrogator module can be used to support
detailed maneuver analysis and operations [10]. Similarly, the Advanced Close Approach Tool (ACAT) module may be useful in collision-
avoidance maneuver planning. This STK module allows for the additional situational awareness of any spacecraft or object in the referenced
database. The ACAT module enables proximity indications and visual cues for variable close-approach calculations.

C. MATLAB/STK Interface
The MATLAB/STK interface allows overall simulation parameters and spacecraft physical characteristics to be defined in MATLAB and
related to STK via the mexConnect MATLAB commands or formatted native STK commands. This interface technique takes advantage of STK’s
standard connection protocol for initializing STK from MATLAB. Once it is initialized, native STK commands can be called from MATLAB. In
addition, formatted ephemeris and attitude files can be passed from MATLAB to STK. Similarly, data can be retrieved from STK by using the
stkReport command. Getting ephemeris from STK and passing it to the MATLAB engine allows for comparison of independently generated
STK and MATLAB spacecraft propagation. Evaluating the results of this comparison allows for validation of a developed MATLAB model based
on the STK’s High-Precision Orbital Propagator (HPOP). The satellite of interest must be initialized and assigned with HPOP before the
propagation parameters and perturbations can be tailored via HPOP commands.
The MATLAB/STK simulation interface code was written in MATLAB (.m file format) with some MATLAB/Simulink files nested within it.
Downloaded by UNIVERSITY OF CALIFORNIA on September 4, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.35328

These subfiles serve as modular components of the MATLAB/STK interface, allowing easier simulation variation and modification
between users.
For the standard MATLAB/STK connection, both MATLAB and STK applications should be loaded and launched. Once launched, STK can be
initialized from MATLAB by using the commands stkInit or agiInit. Information on the path setting established can be found by using
agiGetConfig. The next step in the connection processes is to open a socket by using stkOpen. This configures the path and assigns a socket
variable and a MATLAB variable, called STKError, for reference. Via the established MATLAB/STK connection, STK can be commanded by
using either a select number of mexConnect commands or native STK commands. The command paths for these two methods are slightly
different. The mexConnect commands are a limited subset of core MATLAB/STK interface commands that can be found by exploring the
MATLAB help menu. These mexConnect commands are all prefixed with stk, such as the stkInit commands mentioned previously. Since
the mexConnect commands are limited, there is a general command that allows native STK commands to be executed from MATLAB. The
general execution of STK commands via MATLAB can be conducted by using stkExec(ConID, ‘Command Path Parameter’). A full
listing of native STK commands that can be implemented in this fashion are listed in the STK help menu under the path <Automate/Extend/
Integrate>, <Command Listings>, <Alphabetical Listing>. The first step is usually to open a new STK scenario and ensure that any previous
scenarios are closed. The initial MATLAB/STK interface code is listed in MATLAB code excerpt 1 (Fig. 4). The conID variable serves as a
numeric representation of the established connection, and it will be used often in stkExec commands. The STK scenario name was determined
by a MATLAB variable, such as CONST.simnum, which can be selected by the user to represent the number of simulations or scenarios desired.
The same name was then used to establish the new STK scenario. The stkNewObj command path is establishing the new scenario at the highest-
level path level. All subsequent STK objects, such as spacecraft, will be assigned under this current scenario.
The selected simulation initial date and time must be properly formatted and passed to STK. For STK applications, the date and time must be
rearranged and passed in the format of [21 Jul 2007 12:30:00.0]. If the MATLAB datestr command is used to determine the date and time, then
a method of reformatting and passing the date and time to STK is listed in MATLAB code excerpt 2 (Fig. 5).
In the newpara variable, the second-to-last number is the animation time step in seconds, and the last number is the highest speed or refresh
rate in seconds. The scale of these rates will influence the simulation by changing the animation of the scenario. These values can also be assigned
as variables in the stkConnect command, where the variable scen_nam is used.
Multiple-spacecraft simulations require several spacecraft to be created. The sample code in MATLAB code excerpt 3 (Fig. 6) shows a
spacecraft, called target, being created. The visualization option (VO) command is used to call a general spacecraft graphical model that is
available to STK. The spacecraft graphical model can be selected from a default list, usually located at C:\Program Files\AGI\STK 7
\STKData\VO\Models\Space, or a custom user-generated spacecraft graphical model. The development of simple spacecraft graphical
models will be discussed in more detail in Sec. IV.

III. Spacecraft Model Verification

High fidelity 6-DOF spacecraft model dynamics can be verified by comparison of MATLAB and Simulink propagation with a custom STK
propagator. The STK HPOP was used to ensure spacecraft propagation conditions matched all model variations. Details on numerical integration
applied to orbital propagation are provided in [7]. The modeled space environment perturbations, including variations in the Earth’s shape and

Fig. 4 MATLAB code excerpt 1: initializing STK scenario via MATLAB.

 352 MCCAMISH, CIARCIÀ, AND ROMANO

Fig. 5 MATLAB code excerpt 2: date and time formatting.

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Fig. 6 MATLAB code excerpt 3: spacecraft object creation.

Fig. 7 MATLAB code excerpt 4: spacecraft propagation.

mass (J2–J4 coefficients), atmospheric drag on the spacecraft, third-body (sun and moon) forces, and solar-radiation pressure, were sequentially
evaluated. Table 3 reports the average differences, in terms of position and velocity, of several low-Earth-orbit orbital propagations of 10
spacecraft at various initial conditions. Each orbit was propagated for 30 min and 1 min durations with fixed 1 s step sizes [11].
The HPOP command allows for assignment of both a numerical integration method, such as the fourth-order Runge–Kutta, and an Earth
gravitational model (EGM), such as EGM96 [2,3,5]. The HPOP command is of the general form stkExec(ConID, ‘HPOP Path
Parameter’). Once the HPOP is assigned to a spacecraft, the perturbation forces can be further defined. The desired perturbations can be
related to the enabling condition on the Simulink model so that the various perturbations can be independently evaluated.
Selection of the perturbation parameter, CONST.PERT.choice, activates the desired perturbation code. The coefficients can be
synchronized with any particular user-defined model by modifying the .grv file selected. As previously discussed, the variable can be passed into
the STK command. For instance, the coefficient of drag, represented by Cd, was incorporated into the Drag and SolarRad command settings.
Once the HPOP settings are completed, the actual propagation can be computed. The initial stop time, tstopdummy, is replaced with the final
desired propagation time, tstop. The spacecraft propagation command is listed in MATLAB code excerpt 5 (Fig. 7), where the propagation
parameters of stepsize, orbitepoch, STATE.ri, and STATE.vi are the same as in the initial propagation command.
The data from STK propagation can be passed to the MATLAB workspace. This will allow any desired postprocessing and evaluation of the
data. STK spacecraft state data can be passed in several formats. For this research, the ECI position and velocity were desired. The sample code for
passing spacecraft ephemeris is listed in MATLAB code excerpt 5 (Fig. 8), with the variables, prefixed with STATE.STK, arbitrarily assigned. The
STK ephemeris data are in column format, with each row representing a numerical integration step. Although not the focus of this research, the
user can also pass spacecraft attitude data back to the MATLAB workspace as shown in MATLAB code excerpt box 6 (Fig. 9).

IV. Spacecraft Model Animation

Multiple spacecraft maneuvers can be simulated via MATLAB and animated via STK. The MATLAB initiates an STK TCP/IP connection to
send commands over a specified port. The STK scenario is developed by executing STK commands. Spacecraft dimensional models for STK

Table 3 Average differences of MATLAB and STK propagation (1 s fixed

step size integration)
Perturbation model Average difference 30 min 1 min
Simple two body Position 8.237 × 10−10 m 3.391 × 10−10 m
Velocity 6.890 × 10−13 m∕s 6.082 × 10−13 m∕s
J2 perturbation Position 4.650 × 10−1 m 1.102 × 10−3 m
Velocity 6.908 × 10−4 m∕s 5.346 × 10−5 m∕s
J4 perturbation Position 8.286 × 10−1 m 1.452 × 10−3 m
Velocity 1.256 × 10−3 m∕s 7.183 × 10−5 m∕s
Aerodynamic drag Position 2.904 × 10−9 m∕s 6.291 × 10−10 m∕s
Velocity 2.904 × 10−9 m∕s 6.291 × 10−10 m∕s
Solar drag Position 2.075 × 10−3 m 6.656 × 10−8 m
Velocity 4.267 × 10−6 m∕s 3.277 × 10−9 m∕s
Third-body effects Position 5.271 × 10−2 m 6.330 × 10−5 m
Velocity 1.065 × 10−4 m∕s 3.777 × 10−6 m∕s
Total perturbation Position 1.360 m 3.739 × 10−3 m
Velocity 2.047 × 10−3 m∕s 3.357 × 10−4 m∕s
 MCCAMISH, CIARCIÀ, AND ROMANO 353

Fig. 8 MATLAB code excerpt 5: STK spacecraft ephemeris data.

Fig. 9 MATLAB code excerpt 6: STK spacecraft attitude data.

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visualization are prewritten in STK Modeler. Once the model is loaded and the scenario is established, data can be passed between STK and
MATLAB. For this research, visualization included basic cubic, spherical, and cylindrical spacecraft graphical models. A snapshot of a sample
3-D animation of multiple spacecraft is shown in Fig. 10. Three cubic chase spacecraft are shown converging toward a common target spacecraft,
with a spherical obstacle in the background on the right.

A. STK Spacecraft Model

For standard STK model assignment, a STK .mdl file must be available. This file is assigned to the desired STK satellite object using the
command listed in MATLAB code excerpt 7 (Fig. 11), where isi is a numerical variable that was used to distinguish multiple uses of the same
basic model file. This is useful to model multiple spacecraft with the same basic properties. A sample spacecraft model filename may be
mdl_cube1.mdl. This would assign the STK satellite object named targe, with the model spacecraft model described by mdl_cube1.mdl.
The VO command can be used to call a general spacecraft model, which is available in STK. The spacecraft model can be selected from a default
list, located at C:\Program Files\AGI\STK 7\STKData\VO\Models\Space, or a custom user-generated spacecraft graphical model.

1. STK Graphical Model Development

Three simple and distinctive spacecraft models were developed in this research. They are based on simple spherical, cylindrical, or cubic
spacecraft designs. Once again, the fprintf command serves as our primary formatting tool. In this example, the cubic shape serves as the
primary body component with supplemental docking ports and thrusters components. The sample cubic spacecraft model code is presented in

Fig. 10 Sample 3-D STK view animation frame.

Fig. 11 MATLAB code excerpt 7: spacecraft model assignment.

 354 MCCAMISH, CIARCIÀ, AND ROMANO

MATLAB code excerpt 8 (Fig. 12). The variable L represents user-defined dimensional parameters that can be implemented in the model. In this
code, the face component was defined first. Next, this component was translated and rotated as necessary to determine all sides of the cubic
spacecraft. Additional components (cone, cylinder, etc.) can also be defined. More detailed components can be generated by combining additional
subcomponents.
Once the primary spacecraft components, including the cubic faces, docking ports, and thrusters, are defined, they can be assembled. Each of
the six cubic components will make the basic spacecraft shape. Next, a thruster with flame articulation will be centered on each face of the cubic
spacecraft. Finally, the desired number of docking ports will be added based on the total number of spacecraft.

2. STK Three-Dimensional Visualization Options

Several graphics and VO parameters can be tailored for clear visualization of multiple-spacecraft maneuvers. The primary scaling of the model
view is accomplished by selecting the following VO command in MATLAB code excerpt 9 (Fig. 13). Ratio is a scaling factor which determines
the spacecraft dimensional appearance during the animation, which is chosen to be equal to one in our case. The label and graphic features of the
spacecraft can be modified, as in MATLAB code excerpt 10 (Fig. 14).
The orbital path is typically shown for spacecraft propagation. However, for multiple spacecraft, these projections can result in visual
confusion. These orbital pass projections can be modified as in MATLAB code excerpt 11 (Fig. 15). In addition to labeling the spacecraft,
inclusion of a body axis may be useful for attitude reference. A 3-D spacecraft body reference frame can be added to a model, as in MATLAB code
excerpt 12 (Fig. 16). Besides straightforward labeling and graphics modifications, additional sensors may be desired. These sensors may represent
actual ranging and communication devices, or useful visual projections for engineering analysis. Each sensor must be uniquely named. In this
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research, a conical ranging and docking sensor was added to each chase spacecraft. The ranging sensor represents the local sensor view from the
chase spacecraft to the target spacecraft, or position. The simple conic range sensor is assigned in MATLAB code excerpt 13 (Fig. 17). First, the
sensor is positioned and defined on a spacecraft with an exclusive name. In this example, Chase is an alphanumeric label unique to each chase

Fig. 12 MATLAB code excerpt 8: sample cubic spacecraft model.

Fig. 13 MATLAB code excerpt 9: spacecraft model size scaling.

Fig. 14 MATLAB code excerpt 10: spacecraft model graphic features.

Fig. 15 MATLAB code excerpt 11: spacecraft orbital path projections.

 MCCAMISH, CIARCIÀ, AND ROMANO 355

Fig. 16 MATLAB code excerpt 12: spacecraft model 3-D body reference frame.

spacecraft. Next, the pointing direction of the sensor is determined. The range sensor continually points toward the target spacecraft and adjusts its
projection based on the relative distance from the target, represented by rsw_norm. This modification of the projection may not be necessary for
most sensor applications. Finally, the color of the sensor projection can be modified as desired. Similarly, a docking sensor may be added to the
spacecraft graphical model, as listed in MATLAB code excerpt 14 (Fig. 18).
The docking sensor is located at the same position, but it has a much wider cone of 45 deg. The docking sensor points in a fixed direction from
the spacecraft body axis, with a limited projection of half of the spacecraft’s length. Next, the sensor projection color is selected from a matrix,
called dockc. These simple sensors are useful in visually representing ranges and fields of view (FOVs) as spacecraft are animated through their
dynamics and kinematics. A sample cubic spacecraft with labels and sensor projections is shown in Fig. 19. The three-body axes are labeled
“Body X”, “Body Y”, and “Body Z”. The projection on the right side of the spacecraft is the docking sensor projection, and the small line
extending to the bottom left is the range sensor. The white protrusions on the top and right are thruster firings.
One additional sensor projection was useful in visualizing spacecraft exclusion regions during close-proximity operations. A boundary sensor
projection was placed around regions that spacecraft were intended to avoid. These areas were referred to as obstacles and labeled with Obstcl.
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Spherical projections encompassing these regions can be generated using a conical sensor defined with a 360 deg FOV, such as listed in MATLAB
code excerpt 15 (Fig. 20). The spherical sensor projections were made translucent in order to not obscure the view of maneuvering spacecraft. A
sample spherical boundary sensor projection about a spherical object is shown in Fig. 21. The sensor projection is the globular grid with the chase

Fig. 17 MATLAB code excerpt 13: simple conic range sensor for spacecraft model.

Fig. 18 MATLAB code excerpt 14: simple conic docking sensor for spacecraft model.

Fig. 19 Sample cubic spacecraft graphical model.

 356 MCCAMISH, CIARCIÀ, AND ROMANO

spacecraft in the upper right. These sensors allowed for robust engineering evaluation of the collision-avoidance function of spacecraft control
algorithms [6,7,12,13]. From these basic examples, the user can develop a vast array of representative sensors. Sensor projection ranges and colors
can be varied based on logical condition. For instance, ranging sensors may be programmed to modify their color as the distance to a target varies.
This may allow for quick visual analysis of multiple-spacecraft maneuver performance.

B. Formatting MATLAB Data for STK Files

The visualization and animation of the MATLAB/Simulink data with the desired spacecraft model is a useful tool for engineering analysis and
evaluation. In particular, it was vital in the development of a multiple-spacecraft control algorithm during simultaneous close-proximity
operations [6,7]. The3-D representation for spacecraft during collision-avoidance maneuvers enabled effective troubleshooting. For instance, the
undesired clipping of the corners of chase spacecraft while converging to the target spacecraft during docking maneuvers was easily shown in STK
animation. Due to this evaluation, the control algorithm collision-avoidance logic was modified and its performance robustness was improved.
Additionally, visualization of the simultaneous multiple-spacecraft maneuvers in STK allows for logical point-of-view changes and animation
rate changes.
The animation of the spacecraft can be based on the data generated by STK or the MATLAB/Simulink model. STK-generated data are already
in the proper format. However, MATLAB/Simulink data must be properly formatted in order to be used by STK. STK allows for several specific
data file formats, such as STK ephemeris and attitude files. These files can be properly written by executing short MATLAB scripts using
fprintf commands. A sample STK ephemeris file can be created, such as in MATLAB code excerpt 16 (Fig. 22). The STK ephemeris file name
and path, in the first line, are arbitrary, as long as it has the proper .e suffix. Although, it is useful to save all related STK scenario files in the same
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folder. The first few fprintf lines are used to establish the desired reference frame and interpolation for the data. The variables STATE.time and
para_now are used to synchronize the data points with the time constraints, as discussed in Sec. I.C.2. The data are formatted into seven
columns, represented by time, position vector, and velocity vector. Each row represents an iteration, or step size, of the data. Similarly, a STK
quaternion attitude file can be created, such as in MATLAB code excerpt 17 (Fig. 23). The STK attitude file name and path are arbitrary, as long as
it has the proper .a suffix. This sample STK attitude file is formatted into five columns with time, the three-element quaternion vector, and the
quaternion scalar (rotational) term.

C. Sample Visualization
STK scenarios can be made into video files that can offer useful representation of complex situations and maneuvers. For instance, a sample
visualization of a docking maneuver between seven cubic spacecraft is shown in Fig. 24. The docking maneuver consists of a target spacecraft at
the center of the screen with six chase spacecraft converging from different initial positions. The six chase spacecraft are labeled Chase1–Chase6,

Fig. 20 MATLAB code excerpt 15: obstacle region of influence projection.

Fig. 21 Sample spherical boundary sensor.

 MCCAMISH, CIARCIÀ, AND ROMANO 357

Fig. 22 MATLAB code excerpt 16: formating MATLAB/Simulink ephemeris data for STK.
Downloaded by UNIVERSITY OF CALIFORNIA on September 4, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.35328

Fig. 23 MATLAB code excerpt 17: formating MATLAB/Simulink attitude data for STK.

respectively. Chase spacecraft 1 through 3 have obstacles placed along their primary maneuver paths. The three obstacles are labeled Object1–
Object3, respectively. The obstacles are 2.0 m spheres with globular mesh region of influence projections.
The solid line through the center of the screen is the targets spacecraft’s orbital path. The lighter lines are range sensors from each chase
spacecraft toward the target spacecraft. The Earth’s horizon can be seen at the bottom of the figure.
This sample animation was developed to the collision-avoidance and close-proximity maneuver capabilities of a novel new control algorithm
described in detail in [6,7]. This sample animation has been made available online.

Fig. 24 Sample visualization of multiple-spacecraft maneuver.

 358 MCCAMISH, CIARCIÀ, AND ROMANO

V. Conclusions
A MATLAB/ Satellite Tool Kit (STK) simulation interface was developed for spacecraft model validation and visualization. By using the
proposed interface, the spacecraft characteristics and parameters, together with simulation results, can be interchanged between MATLAB/
Simulink and STK. In particular, using STK via MATLAB is a versatile and effective method of animating six-degree-of-freedom spacecraft
models. The resulting STK animation of spacecraft propagations is useful for engineering evaluation and result presentations.
The proposed interface was used during the development of a multiple-spacecraft control algorithm for close-proximity operations. Model
validation gave confidence in the performance results, and visualization allowed for straightforward evaluation. The animation allowed for
immediate identification of undesirable performance, such that modifications and improvements could be made to the control algorithm.

Acknowledgments
This research has been supported in part by the U.S. Department of Defense. S. B. McCamish gratefully acknowledges the support from both
faculty and students at the Naval Postgraduate School.

References
Downloaded by UNIVERSITY OF CALIFORNIA on September 4, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.35328

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G. Brat
Associate Editor

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