Launch Vehicle Guidance, Navigation, and Control

N. A. Bletsos

Getting a rocket safely from pad to orbit requires sophisticated, responsive flight software. Aerospace helps ensure that these mission-critical systems are fully qualified for the job.

A rocket's flight software (part of the avionics suite) has the difficult job of directing and controlling the vehicle from its initial position bolted down to the ground to its target location far above Earth. In modern rocketry, this is performed autonomously. To accomplish this challenging task, the flight software must correctly perform three basic functions: guidance, navigation, and control (GNC). Navigation is the process of determining the vehicle's position, velocity, and attitude in space. Guidance is the process of deciding how to steer to the desired target. Control is the process of implementing the guidance commands to achieve actual engine deflections or changes in thrust vector.

Guidance, navigation, and control functions are performed by the flight computer. A current navigation solution is computed using rates from the inertial measurement unit (IMU). Guidance uses the current navigated solution to determine the corrections that must be made to account for the vehicle's current location. The control system uses the commands from guidance along with high-frequency attitude information from the IMU to determine appropriate engine deflection angles (view larger image).

The Aerospace Corporation has historically been a major contributor to the development of launch vehicle GNC capabilities. In fact, in 1962, the Department of Defense commissioned Aerospace to design and develop the flight software for the Titan program, and this software has supported the program for more than 40 years. The unprecedented tasking of a federally funded R&D center as the prime contractor and developer has never been repeated; but Aerospace continues to support new and recurring launch programs through independent verification and validation, including modeling and simulation.

Navigation

Rocket navigation is managed by a device known as the inertial measurement unit or IMU, which is essentially an arrangement of accelerometers and gyros (rotation meters). An IMU operates on the same basic principle used for centuries by seagoing navigators—dead reckoning. Using this technique, the navigator would chart the speed and direction traveled from a known starting point to determine a new location, which in turn provided the starting point for the next computation. The process is a bit more sophisticated for launch vehicles: Given an initial position and velocity, the IMU integrates accelerations in three orthogonal directions to obtain velocity; this result is then integrated to determine a new position as a function of time. The process would be simple and accurate if not for four complications.

The navigation loop. The sensed acceleration (expressed in the working frame) drives the integrating loop from which position and velocity are determined. The attitude is determined by integrating the gyro data over time (in the case of a strapdown system) or by reading the gimbal angles (in the case of a gimbaled platform system). In the early days of launch vehicles, the gimbaled platform was extensively used. Today, strapdown systems, which are mechanically simpler but computationally more intense, are favored (view larger image).

First, accelerometers measure physical accelerations, but cannot measure field-induced accelerations such as gravity, which has a real effect on the vehicle's position and velocity. To obtain the total acceleration, the IMU must combine the accelerometer measurements with modeled gravitational acceleration. Second, acceleration integrations must be performed in an inertially fixed nonrotating frame. In such a "working" frame, the integration process is simple; however, a launch vehicle experiences roll (rotation), pitch (nose up or down), and yaw (nose left or right) motions during its flight. Therefore, the IMU must somehow resist or compensate for these motions to maintain an inertially fixed frame of reference. Third, accelerometers and gyros—like any instruments—are intrinsically prone to error. Instrument biases, scale factors, and misalignments are common sources of errors. Finally, the IMU requires an initial state from which to navigate. Errors in initial position can contribute to initial attitude and velocity errors, so the initial state needs to be extremely accurate (see sidebar, Alignment and Calibration ).

Aerospace has helped overcome many of these problems. For example, to enhance acceleration determination, Aerospace evaluates calibration techniques and investigates anomalous instrument behavior. Aerospace has also examined techniques for precision modeling of local gravity.

An IMU uses a coordinate frame to keep track of the accumulated motion. In the case of a strapdown system, the coordinate frame is computed. On the other hand, with a gimbaled IMU (shown here), the coordinate frame can be defined by the platform, which is held inertially fixed. The gyros on the platform sense any angular change and cause the torque motors to eliminate the rate, effectively holding the platform inertially stable. The accelerometers are free to integrate the translational motion without the complications of rotational motion (view larger image).

To maintain an inertially fixed working frame, an IMU is typically designed to follow one of two main approaches. In the first, the accelerometers are mounted on a gimbaled platform held steady by servomotors that respond to gyro inputs. This type of IMU is known as a platform IMU. In the second approach, the accelerometers are allowed to rotate with the vehicle while gyros determine the change in attitude. In this case, the inertial working frame is a computational entity. This second type of IMU is known as a strapdown IMU, and it has grown more popular with advances in computing power. To enhance IMU capability and applicability, Aerospace has been studying gyro technology in the lab, looking at both high-precision small-range gyros for platform applications and less precise large-range gyros for strapdown applications. Aerospace is also developing new gyro technologies and computational algorithms.

To assess the effects caused by sensor error, Aerospace has developed sophisticated simulation and error-analysis tools. One such tool, NavFil (Navigation Filter), evaluates the expected navigational accuracy of launch vehicles. The program reads in the nominal launch trajectory obtained from high-fidelity simulations and propagates the state-error covariance statistics using measured sensor-error statistics. A second statistical program, PRTORB, then computes the orbital dispersions for a given position and velocity error range, which is output from NavFil. The program generates a statistical population of perturbed orbits about the nominal. From this population, the sample mean, sample variance, probability density, and cumulative distribution function for each orbital element are determined. Tools such as NavFil and PRTORB help ensure mission success by determining the likelihood of navigation-related orbital constraint violations. In fact, when these tools indicate a substantial risk of such a violation, the contractor may choose to reoptimize the trajectory or seek a different IMU with higher performance.

Guidance

Guidance can be defined as the process of steering to generate a trajectory that will achieve target conditions despite continuous changes in the launch vehicle and its environment. If the vehicle state and environmental conditions were exactly known and did not change, guidance would be a relatively simple matter, requiring only open-loop schemes. In practice, unknown system variations force the need for closed-loop guidance steering in which vehicle position and velocity are used as feedback in the guidance algorithm.

Guidance schemes are as varied as the systems they control. There is no generic guidance theory, but most mission-specific functions have three phases: atmospheric flight, exoatmospheric flight, and coast flight.

During atmospheric flight, the primary goal is to minimize aerodynamic loading and heating—that is, to prevent the vehicle from breaking or burning up. These atmospheric forces are a function of angle of attack; hence, a trajectory must be designed to minimize the angle of attack in the region of high dynamic pressure. This trajectory is typically designed prior to flight and input as open-loop attitude steering commands to the vehicle.

Leveling is the process of determining initial vertical orientation on the launchpad using measured acceleration data from the accelerometers in the IMU. The idea is comparable to taking a ball in a tube balanced on a fulcrum and finding the angle of the tube that causes the ball to remain balanced and stationary inside it. This gives local level in one direction. The process can be repeated in another direction to determine level relative to both north and east directions.

Exoatmospheric steering usually involves large closed-loop algorithmic solutions to the two-point boundary value problem—that is, how to get from point A to point B. Because of the computational complexity involved, real-time onboard optimization is rarely implemented. Various algorithms can be applied. For example, the Titan and Centaur vehicles use an iterative method to find a set of guidance parameters that satisfy the end condition for a guidance law given in functional form. In contrast, the Inertial Upper Stage (IUS) iteratively searches through all trajectories from the starting point to the target point until a suitable path is determined; this method is quite powerful but requires significant computational resources. On the other hand, the Delta employs a scheme that uses open-loop attitude commands and an open-loop trajectory-acceleration profile, determined a priori, as the basis for the steering; the system continually measures deviations from nominal and makes appropriate adjustments to the nominal commands.

Aerospace typically reviews and analyzes new or updated guidance algorithms. This involves independently implementing the proposed guidance scheme in a computer simulation to verify the algorithm convergence and targeting procedure. Using the flight software provided by the contractor (which includes the guidance algorithm), a large number of runs are made to stress the guidance function under dispersions to ensure that the flight software can safely operate and deliver the payload to the targeted orbit. The importance of this Aerospace activity was demonstrated recently when a contractor's initial guidance algorithm was found to be unstable under dispersions. A targeting parameter had to be modified to correct the instability.

Control

The basic purpose of the flight control system, or autopilot, is to maintain the vehicle attitude commanded by the guidance program. The autopilot senses the vehicle attitude via an inertial measurement system and commands the appropriate change in the engine thrust vector to achieve the commanded attitude. Design of the launch vehicle autopilot must satisfy three main, often conflicting, requirements: stabilize the vehicle, ensure adequate response to guidance commands while minimizing trajectory deviations, and minimize angle of attack to ensure structural integrity of the vehicle.

Vehicle stability is the primary and most difficult criterion to meet, and its design requirements are often contradictory to the speed of response of the autopilot. Vehicle stability is hampered by vehicle flexibility, which causes local elastic deflections that are sensed by the attitude and rate sensors used by the autopilot for attitude control. Minimizing the aerodynamic loads on the vehicle often requires a load-relief loop in the autopilot, which is typically a sensed lateral acceleration feedback loop that can cause deviations from the guidance commanded trajectory. Further complicating matters, the mass, aerodynamics, and slosh and bending characteristics of the vehicle vary rapidly as propellant is consumed.

A typical launch trajectory. A launch vehicle operates in a wide range of environments, from the sea-level atmosphere to the near vacuum of space. The mass properties of the vehicle change continually during powered flight as fuel is used and discretely as components are jettisoned. The control and guidance systems must properly operate in all of these environments and must also account for the vehicle mass property changes to remain stable and on course to the targeted delivery point.

Because of these complexities, the design of the autopilot is performed in stages, beginning with highly simplified models. The process may be divided into four parts: point-mass determination of a reference trajectory; rigid-body autopilot design; slosh and flexible body design to determine filters, gyro locations, and stability characteristics; and nonlinear time-varying simulations to determine both stability and performance characteristics in the presence of wind.

In the first phase, a reference trajectory is designed using a three-degrees-of-freedom simulation. During the second phase, the basic control gains are calculated. Because vehicle properties change over time, a "time-slice" design approach is used. This approach freezes the time-varying properties while making use of linearized vehicle equations of motion. The time slices are taken along various points in the trajectory, and the autopilot gains are linearly interpolated between them. This approach continues in phase three of the process, which considers slosh and flexible body dynamics. This is the most difficult and time-consuming phase of the design. When the third phase is complete, a nonlinear time-varying simulation is performed to ensure that the stability and performance of the autopilot are satisfactory. Iterations on each of these phases may be necessary before a final design is achieved.

Range safety network incorporating GPS. Radar and IMU navigation data would be used to verify that a launch vehicle is safely on course. With a GPS receiver on the rocket, a separate independent navigation measurement can be provided, virtually eliminating scrubbed launches caused by tracking-station failures.

Aerospace has developed tools for quickly analyzing vehicle stability under both nominal and off-nominal conditions, such as dispersed mass properties, aerodynamics, and flexible body parameters. These tools account for vehicle flexibility, propellant slosh, engine inertia, and engine actuator characteristics; they are used to assess the adequacy of the control system prior to launch and also to resolve anomalies seen during flight. These tools were critical in certifying a recent launch. Aerospace postflight analysis from an earlier mission found that the first structural bending mode frequency was significantly higher than predicted. This caused concern for a second mission scheduled to carry the same payload. Aerospace performed a stability analysis and showed that the autopilot could handle the frequency discrepancy in addition to the other modeled structural uncertainties. Thus, the autopilot was cleared for the mission.

Summary and Future Plans

The final responsibility for the success of a mission rests with the successful operation of the guidance, navigation, and control system. Aerospace has played a vital role in certifying these systems to ensure their accuracy and reliability.

The Aerospace role in GNC continues to expand. The corporation has initiated a series of independent research and development programs to evaluate and improve advanced GNC architectures, including the use of adaptive autopilots, integrated GPS/IMU navigation, and in-flight retargeting (see sidebar, GPS for Rocket Navigation). In addition, Aerospace is supporting the Land Based Strategic Deterrent Analysis of Alternatives, a program to replace the current ICBM fleet of Minuteman and Peacekeeper missiles. The specifications levied upon the new system will necessitate the use of advanced GNC technologies.

Acknowledgements

The author would like to thank M. A. deVirgilio, G. L. Fay, J. K. Hui, D. K. Kamimoto, J.-S. Leung, J. C. Liau, A. Omar-Amrani, S. L. Osburn, and W. R. Vitacco for their contributions to this article.

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