Direct trajectory optimization using nonlinear programming and collocation

Hargraves, C. R.; Paris, Stephen

doi:10.2514/3.20223

Cited by 944 publications

(331 citation statements)

References 14 publications

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“…To solve the resulting optimal control problem, Eqs. (7-12), a Hermite-Simpson collocation method [21] has been used. The so-called collocation methods are based on interpolating both control and state variables by means of some piecewise continuous functions.…”

Section: Resultsmentioning

confidence: 99%

Framework for Aircraft Trajectory Planning Toward an Efficient Air Traffic Management

Soler

Olivares

Staffetti

et al. 2012

Journal of Aircraft

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Section: Resultsmentioning

confidence: 99%

Framework for Aircraft Trajectory Planning Toward an Efficient Air Traffic Management

Soler

Olivares

Staffetti

et al. 2012

Journal of Aircraft

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“…In this way, we do not need to connect adjacent phases with linkage constraints. The resulting optimal control problem is then solved using a Simpson collocation method [15,16].…”

Section: Hybrid Optimal Control Approach To Commercial Aircraft Trajementioning

confidence: 99%

“…To solve the optimal control problem (10-15) a Simpson collocation method [15,16] has been used. The resulting sparse nonlinear programming problem (NLP), has been solved using IPOPT [21].…”

Section: Case Studymentioning

confidence: 99%

Hybrid Optimal Control Approach to Commercial Aircraft Trajectory Planning

Soler

Olivares

Staffetti

2010

Journal of Guidance, Control, and Dynamics

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“…The number of terms in the infinite series is related to the order of the polynomial: a higher-order polynomial approximation will be more accurate. There are many papers that cover the detailed mathematics of orthogonal polynomials [26,44,4,33,58,28] and their use in trajectory optimization [29,62,18,30,19,53,3,57,23,24,15,21]. Here we will focus on the practical implementation details and on gaining a qualitative understanding of how orthogonal collocation works.…”

Section: B1 Full Solutionmentioning

confidence: 99%

An Introduction to Trajectory Optimization: How to Do Your Own Direct Collocation

Kelly¹

2017

SIAM Rev.

431

262

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Abstract. This paper is an introductory tutorial for numerical trajectory optimization with a focus on direct collocation methods. These methods are relatively simple to understand and effectively solve a wide variety of trajectory optimization problems. Throughout the paper we illustrate each new set of concepts by working through a sequence of four example problems. We start by using trapezoidal collocation to solve a simple one-dimensional toy problem and work up to using Hermite-Simpson collocation to compute the optimal gait for a bipedal walking robot. Along the way, we cover basic debugging strategies and guidelines for posing well-behaved optimization problems. The paper concludes with a short overview of other methods for trajectory optimization. We also provide an electronic supplement that contains well-documented MATLAB code for all examples and methods presented. Our primary goal is to provide the reader with the resources necessary to understand and successfully implement their own direct collocation methods.

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Direct trajectory optimization using nonlinear programming and collocation

Cited by 944 publications

References 14 publications

Framework for Aircraft Trajectory Planning Toward an Efficient Air Traffic Management

Framework for Aircraft Trajectory Planning Toward an Efficient Air Traffic Management

Hybrid Optimal Control Approach to Commercial Aircraft Trajectory Planning

An Introduction to Trajectory Optimization: How to Do Your Own Direct Collocation

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