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Direct multiple shooting and direct collocation perform similarly in biomechanical predictive simulations
[article]
2023
arXiv
pre-print
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Direct multiple shooting (DMS) and direct collocation (DC) are two common transcription methods for solving optimal control problems (OCP) in biomechanics and robotics. ...
Through five examples of predictive simulations solved using five transcription methods and 100 initial guesses in the Bioptim software, we showed that not a single method outperformed systematically better ...
Transcriptions of the optimal control problems Five OCP transcriptions were compared, three of them belonging to direct multiple shooting schemes: • explicit 4th-order Runge-Kutta with five intermediate ...
arXiv:2302.07645v2
fatcat:tdcmvdvzobh3zj4h6fpvi2uj74
Quadratic Integral Penalty Methods for Numerical Trajectory Optimization
[article]
2022
arXiv
pre-print
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The second method is a modified augmented Lagrangian method that leverages ideas from augmented Lagrangian methods for the solution of optimization problems with large quadratic penalty terms, such as ...
This thesis presents new mathematical algorithms for the numerical solution of a mathematical problem class called dynamic optimization problems. ...
Due to these developments, the most widely used class of numerical methods for solving optimal control problems today is direct transcription. ...
arXiv:2208.09264v1
fatcat:qu3vszoxgvbm5ecoewl7jacozq
Direct Numerical Computation of Periodic Orbits and Their Stability
2006
Journal of Spacecraft and Rockets
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Direct transcription methods are popularly used for trajectory optimization and optimal control because of the ease and speed with which they can be applied to complex systems. ...
M., Kang, W
Pseudospecti al
and Fahroo, F., “Convergence of
and
on
, and Fahroo, F., “Dual Convergence of the Method for Nonlinear Constrained Optimal Control Problems,” Proceedings of the Intelligent ...
doi:10.2514/1.20930
fatcat:sapjs2t7unhjfddojmdutwact4
An Integral Penalty-Barrier Direct Transcription Method for Optimal Control
[article]
2020
arXiv
pre-print
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We recently introduced a convergent direct transcription method for optimal control problems, called the penalty-barrier finite element method (PBF). ...
We highlight conceptual differences between collocation- and penalty-type direct transcription methods. Theoretical convergence results for both types of methods are reviewed and compared. ...
Motivation Direct transcription is a popular method for the numerical solution of optimal control, estimation and system identification problems. ...
arXiv:2009.06217v1
fatcat:xw6xb5dgyzeo5dqgw7pngslosu
Transcription Methods for Trajectory Optimization: a beginners tutorial
[article]
2017
arXiv
pre-print
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The first few sections describe the two classes of transcription methods (shooting \& simultaneous) that are used to convert the trajectory optimization problem into a general constrained optimization ...
This report is an introduction to transcription methods for trajectory optimization techniques. ...
For the remainder of this paper we will restrict focus to direct methods for transcribing and solving the optimal control problem. ...
arXiv:1707.00284v1
fatcat:uorhnp4wdnfm5beqkxxvtnhiou
Direct Transcription of Optimal Control Problems with Finite Elements on Bernstein Basis
2019
Journal of Guidance Control and Dynamics
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The paper introduces the use of Bernstein polynomials as a basis for the direct transcription of optimal control problems with Finite Elements in Time. ...
A simple but representative example is used to illustrate these properties and compare the new scheme against a more common way to transcribe optimal control problems with Finite Elements in Time. ...
., Applied optimal control: optimization, estimation and control, CRC Press, 1975. ...
doi:10.2514/1.g003753
fatcat:h5mfwj5pobbyxkkoy2nrxzspxy
Different optimization strategies for the optimal control of tumor growth
2019
Archives of Cancer Science and Therapy
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In this article different numerical techniques for solving optimal control problems is introduced, the aim of this paper is to achieve the best accuracy for the Optimal Control Problem (OCP) which has ...
Results show that the direct methods achieved better control than indirect methods. Different optimization strategies for the optimal control of tumor growth ...
(resting) T-cells.
1 × 10 −5 /day
d
Per capita decay rate of active (hunting) CTL cells.
0.0412/day
16 ] as a direct transcription for solving optimal control problems. ...
doi:10.29328/journal.acst.1001010
fatcat:f3cfnh3porhfvb36fbsa62l6ea
Simultaneous dynamic optimization strategies: Recent advances and challenges
2006
Computers and Chemical Engineering
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Simultaneous dynamic optimization strategies, also known as direct transcription methods, have been applied in a wide number of domains. ...
In particular, we show properties of solutions generated by Simultaneous Approaches to those of classical variational methods for a variety of problem classes. ...
Moreover, rates of convergence will be shown in the next section for a class of optimal control problems. ...
doi:10.1016/j.compchemeng.2006.05.034
fatcat:5lha2pwtgzec7jhgzfcud26rmq
A Hybrid Optimization Technique Applied to the Intermediate-Target Optimal Control Problem
2016
Global Journal of Technology and Optimization
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Optimal control techniques have been proposed as a method for rapidly solving the intermediate-target (mid-point constraint) optimal control problem. ...
re-solved using a hybrid approach in which the results of the particle swarm optimization algorithm are used as the initial guess for the gradient-based direct orthogonal collocation method. ...
Acknowledgments The authors would like to thank the Air Force Research Laboratory, Power and Controls Division for their funding and support of this project. ...
doi:10.4172/2229-8711.1000200
fatcat:iw64xyrefrecroseah7nyenjny
An Introduction to Trajectory Optimization: How to Do Your Own Direct Collocation
2017
SIAM Review
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For this problem, a shorter solution can be obtained since the control u is simply the second derivative of the position x. ...
Direct collocation method. Most methods for solving trajectory optimization problems can be classified as either direct or indirect. ...
doi:10.1137/16m1062569
fatcat:q6llm5sg3bhzhl2whz5y5gqe4a
Path Tracking Algorithms for Non-Convex Waiter Motion Problem
2018
Periodica Polytechnica Electrical Engineering and Computer Science
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The presented method uses the direct transcription approach for the waiter problem, which means a optimization problem is formed in order to obtain a time-optimal control for the robot. ...
The paper presents a time-optimal approach for robotic manipulators. ...
Direct transcription is the third velocity profile generation method. The optimal control problem can be cast as a convex optimization problem [5, 13] . ...
doi:10.3311/ppee.11606
fatcat:r5mis6m7hvejrif6bdyt3lk33m
dymos: A Python package for optimal control of multidisciplinary systems
2021
Journal of Open Source Software
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Difference between optimal-control and co-design Optimal-control and co-design problems deal with dynamic systems. ...
To optimize a dynamic system we also need to account for the objective function (J): (x, t,ū,d) ...
The most efficient approach is to use a pair of analytic derivative approaches called the direct and adjoint methods, which were generalized in a single unified derivative equation (UDE) by Hwang and ...
doi:10.21105/joss.02809
fatcat:jwy5qsa7m5cennnjlluxvtyk6e
Application of Direct Transcription to Commercial Aircraft Trajectory Optimization
1995
Journal of Guidance Control and Dynamics
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In the next section we begin with a brief discussion of the optimal control problem and its formulation using direct transcription. ...
Cramer’ Boeing Computer Services, Seattle, Washington 98124-0346
One of the most effective numerical techniques for the solution of trajectory optimization and optimal control problems is the direct transcription ...
doi:10.2514/3.56670
fatcat:42xmeys5yjg4tcbpv3zzgxpmka
Optimizing static thermodynamic models of transcriptional regulation
2009
Computer applications in the biosciences : CABIOS
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We show that the optimization landscape has numerous local optima, resulting in poor performance for the GD methods. ...
Results: In this study, we evaluate the 'optimization landscape' of a class of static, quantitative models of regulation and explore the efficiency of a range of optimization methods. ...
ACKNOWLEDGEMENTS The authors wish to acknowledge John Reinitz for providing the code for the benchmark optimization and Lachlan Dufton for providing the initial implementation of SA. ...
doi:10.1093/bioinformatics/btp283
pmid:19398449
pmcid:PMC2732318
fatcat:ickz4mcfsnhlffkstfhvh563aq
A Unified Perspective on Multiple Shooting In Differential Dynamic Programming
[article]
2023
arXiv
pre-print
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Differential Dynamic Programming (DDP) is an efficient computational tool for solving nonlinear optimal control problems. ...
A penalty method is introduced to strategically control the step size, further improving the convergence performance. ...
A direct method parameterizes the state and control using a finite number of variables, and transcribes the original OCP (1) into a nonlinear optimization problem. ...
arXiv:2309.07872v2
fatcat:soy6gkcoc5ethfuvwbgasagrlq
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