Six-Degree-of-Freedom Digital Simulations for Missile Guidance, Navigation, and Control Patricia A. Hawley and Ross A. Blauwkamp his article presents a brief history of missile simulations and a discussion of the programming languages and paradigms used for developing them. Evolv- ing language and programming paradigms elicit requirements for new simulation architectures. Within this execution framework, engineering-level guidance, navigation, and control simulations must include certain functional modules to capture the performance characteristics of the missile system. The level of model sophistication required depends on the particular engineering question to be answered. Six-degree-of- freedom simulations are effective tools for cost and risk reduction during the develop- ment and deployment of missile systems. INTRODUCTION The DoD definitions1 of the terms model and simula- navigation, and control (GNC) analysis, the number tion are as follows: of assets is more limited, and the simulation is at the • Model: A physical, mathematical, or otherwise logi- engineering level—although the level of sophistication cal representation of a system, entity, phenomenon, of the models used varies with the system questions to or process. be answered. • Simulation: A method for implementing a model This article discusses the engineering questions, over time. model implementations, and simulation architectures Models and simulations are further classified by the used in a GNC simulation. We start with a brief his- DoD into four levels: campaign, mission, engagement, torical review of GNC simulations and their uses, and and engineering. These four levels are shown and then we examine the requirements of a digital simula- defined in Fig. 1. A campaign-level simulation includes tion independent of the models and outline current such a large number of model elements that using engi- simulation designs. Finally, we characterize the essential neering-level models on a single computer would prob- models for a GNC simulation and the different levels of ably take years of execution time. Typically for guidance, detail for these models. Additionally, we consider some JOHNS HOPKINS APL TECHNICAL DIGEST, VOLUME 29, NUMBER 1 (2010) 71­­­­ P. A. HAWLEY and R. A. BLAUWKAMP ballistic missiles. During World War II, German engi- neers improved on the launch mechanism of their bal- Campaign listae by adding rocket propulsion and a simple azimuth control for rudimentary guidance. The performance of these first guided missiles was poor, but it was sufficient Mission to inspire an entire segment of today’s defense industry. The first “simulation” of a missile consisted of a rocket engine burn time and the ballistic equation of motion to determine the missile’s achievable range, as well as Engagement a heading to determine its approximate impact point.2 Current missile systems are described by nonlinear dif- ferential equations, partial differential equations, and/ Engineering or discrete-time equations. These models may encom- pass high-fidelity aerodynamics involving tables of 3 Figure 1. These four levels of simulation reflect the level of detail wind tunnel measurements, time-varying propulsion in the simulations and the scope of the questions being asked. characteristics, digital autopilots, one or more homing Starting at the most detailed level, an engineering simulation sensors, inertial sensors, communication links, and one models a missile system’s components and their interactions or more guidance laws. The complexity of these mis- to the highest fidelity possible. Next, an engagement simula- siles is reflected in the costs and the capabilities of such tion omits some of the detail of the engineering simulation but systems. Instead of simply hitting a target as large as a includes models for launch platforms and threats so that the sys- London neighborhood (the goal of the German missiles tem’s effectiveness at neutralizing the threat can be ascertained. A of World War II), current interceptors are expected to mission-level simulation omits more details and aims to address impact within centimeters of the aimpoint. Given the the tactical effectiveness of the missile system to perform a spe- expense of testing such complex systems, and the dif- cific mission (e.g., air defense). Finally, a campaign-level simulation ficulty in fully evaluating all components to their full seeks to determine the best capability mix of “blue” forces against range of capability, simulations are an effective means of “red” forces by focusing on order of battle and probability of kill. cost and risk reduction. Ideally, all available engineering details would be included at all levels of simulation, but this is generally not feasible. PROGRAMMING LANGUAGES AND PARADIGMS The first digital programs were written in assembly engineering questions that the simulation may answer language, and the combination of hardware and lan- based on the level of model fidelity. guage limited their scope. Fortunately high-level pro- gramming languages provided engineers with more sophisticated tools for building programs. One of the HISTORY first high-level programming languages was FORTRAN, Orville and Wilbur Wright did not simulate air- the IBM Mathematical FORmula TRANslation System. frames; they prototyped them. As pilots, they acted as FORTRAN allowed engineers to write mathematically the guidance and navigation subsystems, and they solved sophisticated equations to model missile systems. The any unstable control systems problems with the airframe challenge then was to write equations that were suc- during flight testing by improvising attitude commands cinct enough to execute on the slow memory-limited and after landing by modifying the control surfaces to early digital computers—without any particular software achieve, after an iterative process, safe and stable per- architecture. To achieve real-time performance with formance. Their successes triggered the development of hardware in the loop, engineers used analog comput- airplanes around the world, but their methodology was ers rather than slower digital ones. An analog computer costly both in terms of material and in the health and uses the voltages and currents of electrical components safety of the pilot. It also was impractical for unmanned as surrogates for the state variables in differential equa- airframes such as missiles. tions and, therefore, could represent the operating con- The first missiles were the Greek and Roman ballis- dition for a missile during testing of subsystems such as tae, whose motion gave us the term ballistic trajectory. tail actuators or seeker heads. Because analog comput- Their designers and users determined the performance ers require special-purpose hardware and configurations characteristics of these weapons empirically and incre- and are limited by noise, nonlinearities, and parasitic mentally modified and improved them over the years. It effects, they have been replaced by digital computers as wasn’t until Sir Isaac Newton supplied the mathematical the speed and memory capacity of the digital computers and physical language to describe this motion that engi- have improved.4 Invariably, with each increase in hard- neers could more accurately predict the performance of ware performance, engineers increase the complexity of 72 JOHNS HOPKINS APL TECHNICAL DIGEST, VOLUME 29, NUMBER 1 (2010) 6DOF DIGITAL SIMULATIONS FOR MISSILE GNC SystemRoot Ship ThreatObjects ReentryVehicle Launcher ShipMotion Booster ShipSensor Decoy Missile HomingSensors FlightController IRSensor BoostAutopilot INS RFSensor Airframe Seeker BoostGuidance WarheadSection Propulsion Fuze InertialSensors TVC Autopilot Gyros Dynamics Servos FinActuators IMU MidcourseGuidance TerminalGuidance Accelerometers Gyros Figure 2. This tree shows a hierarchical model tree for a missile system. The SystemRoot in cyan connects the tree to the simulation executive. The top nodes—Missile, ThreatObjects, and Ship (in blue)—correspond to the top-level functional descriptions of objects that would appear in a mission or engagement simulation. The pink nodes are higher-level models composed of the more detailed models that are the leaves of the tree (in green). These leaves correspond to the engineering models that would appear in a 6-degree-of-freedom (6DOF) simulation. the models that they describe in computer code. Logi- ment of structured programming: a top-down software- cally, there should be a corollary to Moore’s Law (which development methodology that imposed a disciplined states that the power of digital hardware doubles approxi- breakdown of the data flow in a simulation. Operations mately every 2 years) to indicate that the models coded on the data were partitioned into modules or procedures on these rapidly advancing computing platforms double and executed sequentially, and the system states often in complexity every 2 years. were represented by an appropriate set of data structures. FORTRAN is a high-level procedural programming This methodology exposed the control flows that pro- language with high-quality mathematical libraries for duce spaghetti code, namely the infamous GOTO state- numerical computations, but initially there were few ment and the equally nefarious FORTRAN COMMON data structures—only scalars, arrays, and COMMON block, but did not eliminate the problems associated with blocks—and few control constructs—IF, GOTO, and global scoping of variables in a simulation. Data flowing DO; so, as the size of the code blocks and