Jonathan Rogers

Control Authority of a Projectile Equipped with a Controllable Internal Translating Mass

control authority requirements. The work reported here considers a vibrating internal mass control mechanism applicableto both fin-and spin-stabilized configurations.To investigate the potential of this control mechanism, a7degree-of-freedom flight dynamic model of a projectile equipped with an internal translating mass is generated. By vibrating the internal translating mass normal to the axis of symmetry and at the roll rate frequency, significant control authority can be attained with a relatively small internal mass on the order of a percent or so of the total projectile mass. Interestingly, control authority increases proportionally with increasing roll rate and also with increasing station-line cavity offset from the mass center. Trajectory changes are not caused by lateral mass center offset and drag but rather by dynamic coupling between internal mass vibration and the projectile body. Nomenclature AT = internal translating mass oscillation amplitude aC=I = translational acceleration vector of the system center of mass with respect to the inertial frame aP=I = translational acceleration of the projectile center of mass with respect to the inertial frame aT=I = translational acceleration vector of the internal translating mass center of mass with respect to the inertial frame aT=P = translational acceleration of the internal translating mass with respect to the projectile reference frame B = point at center of internal translating mass cavity

Design of a Roll-Stabilized Mortar Projectile with Reciprocating Canards

The design of a canard-controlled mortar projectile using a bank-to-turn concept is presented. A unique feature of this smart mortar configuration is that it is equipped with a set of two reciprocating fixed-angle maneuver canards and a set of two reciprocating fixed-angle roll canards. An active control system is designed such that the roll canards set the body in the proper maneuver plane and the maneuver canards extend to perform trajectory corrections. Example results and Monte Carlo simulations demonstrate control system effectiveness in reducing dispersion error due to launch perturbations and winds. Comparison studies with a rolling airframe equipped with reciprocating maneuver canards show that the bank-to-turn approach offers more control authority, eliminates problematic angle-of-attack oscillations, and requires lower-bandwidth actuators.

Roll Orientation Estimator for Smart Projectiles Using Thermopile Sensors

The use of inexpensive, commercially available thermopiles sensors for roll orientation estimation of spinning bodies is explored. The sensors convert observed thermal gradients into an electrical signal well suited for onboard data acquisition and real-time signal processing. An environmental model emulating sensor stimulus for a six-degree-of-freedom body is generated given standard atmospheric and typical ground conditions. When sensor characteristics are included, the fully developed model can be used to generate accurate sensor output as a function of Euler angles and altitude. Outputs from the model are then shown to compare favorably with experimental flight data, capturing the predominant and nearly sinusoidal signal variation as the projectile rolls. An extended Kalman filter algorithm is offered, which enables real-time roll angle and roll rate estimation using solely thermopiles as feedback. Example results demonstrate that the algorithm yields reasonably accurate roll information. Finally, a trade study demonstrates that roll error is further mitigated as the number of thermopile sensors is increased. This research shows that thermopiles could be useful in a diverse multisensor constellation as a convenient absolute inertial roll reference.

Bézier Curve Path Planning for Parafoil Terminal Guidance

Autonomous parafoil terminal guidance plays a critical role in landing accuracy but is inherently difficult due to underactuation and path disturbances caused by winds. Terminal path planners must generate flight paths that deliver the parafoil as close as possible to the destination while landing into the wind. This paper presents a novel path-planning scheme capable of highly general trajectory shapes that enable successful path planning from a wide set of initial conditions in constrained three-dimensional environments. The path-planning approach parameterizes the two-point boundary value guidance solution in the form of one or more Bezier curves that connect the current parafoil location with a final approach point downwind of the target. Online nonlinear optimization of curve parameters allows for path regeneration given changing winds. Furthermore, generality of the trajectory shape provides a wide set of initial conditions at which terminal guidance may be initiated in obstacle-constrained scenario...

A variable stability projectile using an internal moving mass

Abstract Weapon designers have known for some time that projectiles with low static margin have proven to be more susceptible to launch perturbations than comparable projectiles with high static stability, and that low static margin allows greater control authority. The work reported here examines a mechanism for active static margin control in flight through mass centre modification, demonstrating that such a system has significant impact on required manoeuvre control force to achieve a given control authority. A system is developed wherein a mass translates aft during flight inside a cavity aligned with the projectile centre-line, thereby altering the mass centre. This in turn decreases the projectiles static margin after launch and allows greater control authority later in flight, while at the same time decreasing initial throw-off errors. A seven-degree-of-freedom flight dynamic model is used to predict the performance of the system. Results show that by decreasing static margin after launch the projectile is less susceptible to launch perturbations and has increased control authority through the remainder of flight, leading to a smart projectile that outperforms rigid projectiles that are highly stable or highly manoeuvrable. This smart weapon feature is particularly attractive when the maximum control force and moment are small, and therefore is developed specifically for controllable munitions rather than missiles, which often exhibit ample control authority.

Terminal Guidance for Complex Drop Zones Using Massively Parallel Processing

Existing precision airdrop strategies almost exclusively use impact error in a flat target plane as the criterion for optimality. Practical airdrop systems must also include other criteria such as constraints imposed by terrain and challenging drop zones. Designing robust guidance strategies for drop zones with complex terrain is further complicated by the probabilistic nature of winds. The work described here develops a guidance strategy that uses massively parallel Monte Carlo simulations performed on a graphics processing unit to rank candidate trajectories through minimization of a flexible cost function that penalizes impact error based on a provided terrain map. Strengths of the proposed algorithm include: flexibility in designing mission optimality conditions, statistically robust trajectory solutions, and the ability to accommodate complex digital terrain data in terminal guidance solutions. Through simulation it is shown that the proposed massively parallel algorithm can provide robust terminal guidance even in severe terrain.

A belief function distance metric for orderable sets

This paper describes a new metric for characterizing conflict between belief assignments. The new metric, specifically designed to quantify conflict on orderable sets, uses a Hausdorff-based measure to account for the distance between focal elements. This results in a distance metric that can accurately measure conflict between belief assignments without saturating simply because two assignments do not have common focal elements. The proposed metric is particularly attractive in sensor fusion applications in which belief is distributed on a continuous measurement space. Several example cases demonstrate the proposed metrics performance, and comparisons with other common measures of conflict show the significant benefit of using the proposed metric in cases where a sensors error and noise characteristics are not known precisely a priori.

Projectile Monte-Carlo Trajectory Analysis Using a Graphics Processing Unit

Monte Carlo trajectory simulation is a key element in the design and evaluation process for smart weapons development. Graphics processing units (GPU’s) are powerful massively parallel computing devices that are increasingly being used for general purpose computing. This paper explores the use of graphics processing units for Monte Carlo trajectory prediction with the goal of accelerating ballistic dispersion analysis. First, an overview of general purpose GPU computing is briefly presented. The six-degree-of-freedom projectile dynamic model is then described, and GPU implementation details are outlined. Runtime performance comparisons are performed between serial Monte Carlo simulations performed on a CPU and parallel simulations performed on a GPU. Results show that for large numbers of trajectories, significant runtime reductions are possible for Monte Carlo simulations performed on the GPU in comparison to simulations performed serially.

Airframe Performance Optimization of Guided Projectiles Using Design of Experiments

Performance optimization of guided, gun-launched projectiles is a difficult task due to nonlinear flight behavior, complex aerodynamic interactions, and unique engineering constraints. Historically, the design process for many smart weapons has been iterative in which a series of design improvements are made until performance requirements have been met. This paper presents an alternative formal methodology for smart weapons conceptual airframe design and optimization based on design of experiments. At the initial stage, a basic aerobody shape is defined along with candidate control actuators and associated design parameters. Based on a design of experiments, a kriging response surface is generated mapping design variables to performance criteria. Simultaneously, a neural network is trained to recognize unstable designs. Finally, a genetic algorithm determines the optimal projectile design with respect to a predefined cost function. By varying this cost function, a Pareto frontier of optimal designs can be...

Cantilever Beam Design for Projectile Internal Moving Mass Systems

Abstract : Internal masses that undergo controlled translation within a projectile have been shown to be effective control mechanisms for smart weapons. However, internal mass oscillation must occur at the projectile roll frequency to generate sufficient control force. This can lead to high power requirements and place a heavy burden on designers attempting to allocate volume within the projectile for internal mass actuators and power supplies. The work reported here outlines a conceptual design for an internal translating mass system using a cantilever beam and electromagnetic actuators. The cantilever beam acts as the moving mass, vibrating at the projectile roll frequency to generate control force. First, a dynamic model is developed to describe the system. Then, the natural frequency, damping ratio, and length of the beam are varied to study their effects on force required and total battery size. Trade studies also examine the effect on force required and total battery size of a roll-rate feedback system that actively changes beam elastic properties. Results show that with proper sizing and specifications, the cantilever beam control mechanism requires relatively small batteries and low actuator control forces, with minimum actuator complexity and space requirements.