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### Publications

### Issue Archive

# Algorithm Optimally Allocates Actuation of a Spacecraft

Monday, 02 July 2007

A report presents an algorithm that solves the following problem: Allocate the force and/or torque to be exerted by each thruster and reaction-wheel assembly on a spacecraft for best performance, defined as minimizing the error between (1) the total force and torque commanded by the spacecraft control system and (2) the total of forces and torques actually exerted by all the thrusters and reaction wheels. The algorithm incorporates the matrix⋅vector relationship between (1) the total applied force and torque and (2) the individual actuator force and torque values. It takes account of such constraints as lower and upper limits on the force or torque that can be applied by a given actuator. The algorithm divides the aforementioned problem into two optimization problems that it solves sequentially. These problems are of a type, known in the art as semi-definite programming problems, that involve linear matrix inequalities. The algorithm incorporates, as subalgorithms, prior algorithms that solve such optimization problems very efficiently. The algorithm affords the additional advantage that the solution requires the minimum rate of consumption of fuel for the given best performance.

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Posted in: Briefs

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# Efficient Optimization of Low-Thrust Spacecraft Trajectories

Friday, 29 June 2007

A paper describes a computationally efficient method of optimizing trajectories of spacecraft driven by propulsion systems that generate low thrusts and, hence, must be operated for long times. A common goal in trajectory-optimization problems is to find minimum-time, minimum-fuel, or Pareto-optimal trajectories (here, Pareto-optimality signifies that no other solutions are superior with respect to both flight time and fuel consumption). The present method utilizes genetic and simulated-annealing algorithms to search for globally Pareto-optimal solutions. These algorithms are implemented in parallel form to reduce computation time. These algorithms are coupled with either of two traditional trajectory- design approaches called “direct” and “indirect.” In the direct approach, thrust control is discretized in either arc time or arc length, and the resulting discrete thrust vectors are optimized. The indirect approach involves the primervector theory (introduced in 1963), in which the thrust control problem is transformed into a co-state control problem and the initial values of the co-state vector are optimized. In application to two example orbit-transfer problems, this method was found to generate solutions comparable to those of other state-of-theart trajectory-optimization methods while requiring much less computation time.

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Posted in: Briefs, TSP

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# Simulation of Heat Generation in Analyzing Thermoelastic Instability in Disk Brakes

Friday, 29 June 2007

Transient analysis of the thermoelastic contact problem for disk brakes with frictional heat
generation is accomplished using finite element analysis software.
During a vehicle’s braking
action, a wheel’s kinetic energy is
transformed into heat, which
doesn’t dissipate fast enough into
the air stream from the brake to
the brake disk. Thus, one of a disk
brake’s material properties —
thermal conductivity — plays a
critical role. In addition, thermal
judder results from non-uniform
contact cycles between the pad
and the disk brake rotor, which is
primarily an effect of the localized
thermoelastic instabilities (TEI) at
the disk brake’s rotor surface.
Localized TEI can generate intermittent
hot bands around the rubbing
path.

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Posted in: Briefs

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# Retaining Rings for Industrial Fastening Applications

Wednesday, 30 May 2007

Retaining rings are selected based on material, finish, and a variety of application parameters.
A discussion of retaining rings inevitably must begin with a debunking of myths; namely, that one style of retaining ring will function better than all other types in all instances. No one retaining ring style is better than another. Rather, the parameters of an application actually determine which retaining ring is best to use, and this can vary from assembly to assembly. Selecting the correct type of retaining ring based on variables such as installation/removal requirements, anticipated thrust load, and end-play take-up can ensure the retaining ring chosen will perform reliably, while significantly reducing fastener costs.

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Posted in: Briefs

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# Simulation and Testing of Maneuvering of a Planetary Rover

Wednesday, 30 May 2007

A report discusses the development of a computational model of a Mars Explorer Rover maneuvering across terrain under varying conditions. The model is used to increase understanding of the rover dynamics. Increased understanding is helpful in planning further tests and in extending the operational range of the rover to terrain conditions that would otherwise have to be avoided in a conservative approach. The model is implemented within MSC.ADAMS®, a commercial suite of computer programs for simulating a variety of automotive and aeronautical mechanical systems. Following its initial formulation, the model has been successively refined in an iterative process of simulation, testing on simulated terrain, correlation of simulation results with test results, and adjustment of model parameters to increase degrees of matching between simulation and test results. In particular, three aspects of the model have been refined, as follows:

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Posted in: Briefs, TSP

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# Update on Controlling Herds of Cooperative Robots

Wednesday, 30 May 2007

A document presents further information on the subject matter of “Controlling Herds of Cooperative Robots” (NPO-40723), NASA Tech Briefs, Vol. 30, No. 4 (April 2006), page 81. To recapitulate: A methodology for controlling a herd of cooperative and autonomous mobile robots exploring the surface of a remote planet or moon (specifically, Titan or Titan-like) is undergoing development. The proposed configuration of mobile robots consists of a blimp and a herd of surface sondes. The blimp is the leader of the herd, and it commands the other robots to move to locations on the surface or below the surface to conduct science operations. Once a target is chosen, the sondes cooperatively aim sensors at the target to maximize scientific return. This hierarchical and cooperative behavior is necessary in the face of such unpredictable factors as terrain obstacles and uncertainties in the model of the environment.

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Posted in: Briefs, TSP

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# Pseudo-Waypoint Guidance for Proximity Spacecraft Maneuvers

Wednesday, 30 May 2007

A paper describes algorithms for guidance and control (G&C) of a spacecraft maneuvering near a planet, moon, asteroid, comet, or other small astronomical body. The algorithms were developed following a model- predictive-control approach along with a convexification of the governing dynamical equations, control constraints, and trajectory and state constraints. The open-loop guidance problem is solved in advance or in real time by use of the pseudo-waypoint generation (PWG) method, which is a blend of classical waypoint and state-of-theart, real-time trajectory-generation methods. The PWG method includes satisfaction of required thruster silent times during maneuvers. Feedback control is implemented to track PWG trajectories in a manner that guarantees the resolvability of the open-loop-control problem, enabling updating of G&C in a provably robust, model-predictive manner. Thruster firing times and models of the gravitational field of the body are incorporated into discretized versions of the dynamical equations that are solved as part of an optimal-control problem to minimize consumption of fuel or energy. The optimal- control problem is cast as a linear matrix inequality (specifically a secondorder cone program), then solved through semi-definite-programming techniques in a computationally efficient manner that guarantees convergence and satisfaction of constraints.

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