Book Chapter10.1007/978-3-0348-7539-4_9
Trajectory Optimization Using Sparse Sequential Quadratic Programming
John T. Betts
- 01 Jan 1993
- pp 115-128
18
TL;DR: A nonlinear programming algorithm is described which exploits the matrix sparsity produced by the transcription formulation which is characterized by matrices which are large and sparse.
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Abstract: One of the most effective numerical techniques for the solution of trajectory optimization and optimal control problems is the direct transcription method. This approach combines a nonlinear programming algorithm with a discretization of the trajectory dynamics. The resulting mathematical programming problem is characterized by matrices which are large and sparse. Constraints on the path of the trajectory are then treated as algebraic inequalities to be satisfied by the nonlinear program. This paper describes a nonlinear programming algorithm which exploits the matrix sparsity produced by the transcription formulation. Numerical experience is reported for trajectories with both state and control variable equality and inequality path constraints.
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Citations
Mesh refinement in direct transcription methods for optimal control
John T. Betts,William P. Huffman +1 more
TL;DR: In this article, a technique for changing the discretization in order to improve the accuracy of the approximation is described, and an integer programming technique is used to minimize the maximum error during the refinement iterations.
170
Optimal Low Thrust Trajectories to the Moon
John T. Betts,Sven O. Erb +1 more
TL;DR: The application of the transcription method is described to compute an optimal low thrust transfer from an Earth orbit using a sparse nonlinear programming algorithm with a discretization of the trajectory dynamics.
154
•Dissertation
Mixed-integer convex optimization for planning aggressive motions of legged robots over rough terrain
Andres Valenzuela
- 01 Jan 2016
TL;DR: In this article, the authors proposed a method to solve a set of problems in the field of Mechanical Engineering using a two-dimensional laser scanner, and demonstrated that it works well.
51
Compensating for order variation in mesh refinement for direct transcription methods
TL;DR: This paper discusses how this numerical theory for Implicit Runge–Kutta methods can be utilized in direct transcription trajectory optimization by modifying a currently used mesh refinement strategy.
37
References
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Numerical solution of boundary value problems for ordinary differential equations
Uri M. Ascher,R.M.M. Mattheij,Robert D. Russell +2 more
- 01 Jan 1985
TL;DR: This book discusses Consistency, Stability, and Convergence higher-Order One-Step Schemes Collocation Theory Acceleration Techniques Higher-Order ODEs Finite Element Methods and Initial Value Methods.
1.4K
Direct trajectory optimization using nonlinear programming and collocation
C. R. Hargraves,Stephen W. Paris +1 more
TL;DR: In this article, an algorithm for the direct numerical solution of an optimal control problem is given, which employs cubic polynomials to represent state variables, linearly interpolates control variables, and uses collocation to satisfy the differential equations.
1.2K
Energy-state approximation in performance optimization of supersonic aircraft
A. E. Bryson,M. N. Desai,W. C. Hoffman +2 more
- 01 Aug 1968
TL;DR: Energy state approximation for supersonic aircraft performance optimization with extension to maximum range problems was studied in this paper, where the authors compared the complexity of complex dynamic models with simple dynamic models.
248
Path-constrained trajectory optimization using sparse sequential quadratic programming
John T. Betts,William P. Huffman +1 more
TL;DR: In this paper, a nonlinear programming algorithm for trajectory optimization and optimal control problems is presented, which is based on the direct transcription method. But it is subject to a number of difficulties: the adjoint equations are often very nonlinear and cumbersome to obtain for complex vehicle dynamics.
156