SurveyofNumericalMethodsforTrajectoryOptimizationVIP专享VIP免费

JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICSVol. 21, No. 2, March–April 1998Survey of Numerical Methods for Trajectory OptimizationJohn T. BettsBoeing Information and Support Services, Seattle, Washington 98124-2207I.IntroductionI T isnotsurprisingthatthedevelopmentof numericalmethodsfortrajectory optimization have closely paralleled the explorationof space and the developmentof the digital computer. Space explo-ration provided the impetus by presenting scientists and engineerswith challengingtechnicalproblems.The digitalcomputerprovidedthe tool for solving these new problems.The goal of this paper is toreviewthe state of the art in the eld looselyreferredto as trajectoryoptimization.Presentinga surveyof a eld as diverseas trajectoryoptimizationis a daunting task. Perhaps the most difcult issue is restricting thescope of the survey to permit a meaningful discussion within alimited amount of space. To achieve this goal, I made a consciousdecision to focus on the two types of methods most widely usedtoday,namely,directand indirect.I begin the discussionwith a briefreview of the underlying mathematics in both direct and indirectmethods. I then discuss the complications that occur when pathand boundary constraints are imposed on the problem description.Finally, I describe unresolvedissues that are the subject of ongoingresearch.A number of recurrentthemes appearthroughoutthe paper. First,the aforementioned direct vs indirect is introduced as a means ofcategorizing an approach. Unfortunately, not every technique fallsneatly into one category or another. I will attempt to describe thebenets and deciencies in both approaches and then suggest thatthe techniquesmay ultimatelymerge.Second, I shall attempt to dis-criminatebetween method vs implementat...