DOCSLIB.ORG

ICLOCS2: Solve Your Optimal Control Problems with Less Pain

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
ICLOCS2: Solve Your Optimal Control Problems with Less Pain ICLOCS2: Solve your optimal control problems with less pain Yuanbo Nie ∗ Omar Faqir ∗∗ Eric C. Kerrigan ∗;∗∗ ∗ Department of Aeronautics, Imperial College London, UK (e-mail: [email protected]). ∗∗ Department of Electrical and Electronic Engineering, Imperial College London, UK (e-mails: [email protected], [email protected]) Abstract: ICLOCS2 is the new version of ICLOCS (pronounced `eye-clocks') and is a comprehensive software suite for solving nonlinear optimal control problems (OCPs) in Matlab and Simulink. The toolbox builds on a wide selection of numerical methods and automated tools to assist the design and implementation of OCPs. The aim is to reduce the requirements on the experience of the user, by providing a first port of call to solve a variety of OCPs. ICLOCS2 may not be the fastest solver for some problems, but it might work where other solvers fail. Keywords: Optimal control, trajectory optimization, direct transcription, orthogonal collocation, nonlinear model predictive control EXTENDED ABSTRACT Overview To enable the level of flexibility required, ICLOCS2 is Development Background equipped with state-of-the-art transcription methods and discretization methods (h/p/hp-adaptive) to transform the OCPs into large NLP problems with sparsity patterns Many existing OCP software packages are designed for off- that can be exploited. The users can then choose their line trajectory optimization, thus they pursue the most favourite NLP solver for robustly solving ill=conditioned accurate result at a high computational cost. Instead, problems as well as benefiting from faster warm starts. ICLOCS2 is designed to enable flexible trade-offs be- ICLOCS2 also allows various ways of supplying derivative tween accuracy and computational effort, aiming at bridg- information via analytical and numerical means. Addition- ing the gap between solving OCPs off-line and real-time ally, there are various built-in tools that can be used to optimization-based control methods, such as nonlinear improve the efficiency of the algorithms. See Table 1 for model predictive control (NMPC). an overview of the methods available in ICLOCS2. For practical optimal control problems, it is often difficult Results to anticipate beforehand which discretization scheme and which family of nonlinear programming (NLP) solvers are The capabilities and efficiency of ICLOCS2 have been better suited. The choice hinges on the required level tested and verified on various classical and modern ap- of accuracy, computational time and resources available, plications in the aerospace, automotive, robotics and com- and inherent characteristics of the solution (continuity, munication domains. As for efficiently solving OCPs, for differentiability, etc.). Inappropriate selection of the un- example, ICLOCS2 is able to solve the classical supersonic derlying solution method may result in poor accuracy and aircraft minimum-time-to-climb problem (Betts, 2010) to computational efficiency. a pre-defined accuracy level at least 20 times faster than The future trend is to implement optimal control problems the previous version of ICLOCS. in real-time in closed-loop. This further exacerbates the In many problems, time-optimal solutions exhibit a dis- challenges associated with the selection of methods. With continuity, often in the form of a \bang-bang" input. Con- the states and controls evolving under the influence of ventionally, accurately capturing this switching behaviour uncertainties, it becomes very difficult to test all possible requires mesh refinement iterations, by adding mesh points problem formulations beforehand. Therefore, the capabil- and/or changing the polynomial orders. With the new flex- ity to quickly identify and implement a good strategy ible mesh method in ICLOCS2, the placement of intervals becomes essential in efficiently solving the OCP. Existing can be automatically adjusted during the optimization OCP solvers, e.g. GPOPS-II (Patterson and Rao, 2014) process to accommodate this discontinuity. and ACADO (Houska et al., 2011), often require commit- ments to certain discretization schemes and NLP solvers As a simple example, Figure 1 shows the solution to at an early stage, making subsequent changes expensive the double-integrator minimum-time repositioning prob- and time-consuming. lem. This has the same problem formulation as in Betts Table 1. Methods available in ICLOCS2 Transcription Direct multiple shooting Direct collocation Method Discretization Euler Trapezoidal Hermite-Simpson Legendre-Gauss-Radau∗ Method NLP Solver IPOPT fmincon WORHP∗ Supported (W¨achter and Biegler, 2006) (MathWorks, 2017) (B¨uskens and Wassel, 2013) Jacobian Algorithmic differentiation (forward) User defined Finite difference Calculation with Adigator*(Weinstein and Rao, 2017) Algorithmic differentiation (forward) User defined Finite difference Hessian with Adigator*(Weinstein and Rao, 2017) Approximation Limited memory BFGS Limited-Memory Damped-BFGS with IPOPT with built-in SQP* Automatic scaling* Solution reconstruction* Mesh refinement* Flexible hp mesh* Tools Efficient implementation of rate Automatic meshing Available constraints*(Nie and Kerrigan, 2018b) (h/p/hp-adaptive)* Closed-loop simulations (Matlab & Simulink)* * New functionalities compared to the previous version. 300 1 Edition. Advances in Design and Control. Society for Position [m] Industrial and Applied Mathematics. Velocity [m/s] 200 0 B¨uskens, C. and Wassel, D. (2013). The esa nlp solver worhp. In G. Fasano and J. Pint´er(eds.), Modeling and Optimization in Space Engineering, volume 73, 85{110. 100 -1 hp mesh Springer New York. flexible hp mesh Houska, B., Ferreau, H., and Diehl, M. (2011). Acado 0 -2 0 10 20 30 0 10 20 30 toolkitan open-source framework for automatic control and dynamic optimization. Optimal Control Applica- (a) States (b) Input tions and Methods, 32(3), 298{312. MathWorks (2017). Find minimum of constrained nonlin- Fig. 1. Time-optimal solution for double integrator reposi- ear multivariable function - MATLAB fmincon. tioning problem obtained with a flexible mesh, using Nie, Y. and Kerrigan, E. (2018). How should rate con- an hp-adaptive method straints be implemented in nonlinear optimal control (2010, Ex. 4.11), but with different initial and terminal solvers? Submitted to 6th IFAC Conference on Non- conditions, and variable bounds. We start with five equally linear Model Predictive Control. spaced mesh points, each with a polynomial degree of six. Palma, V.G., Suardi, A., and Kerrigan, E.C. (2015). As the NLP converges, the mesh intervals and collocation Sensitivity-based multistep mpc for embedded systems. points start to gather around the control switching time IFAC-PapersOnLine, 48(23), 360{365. instance, accurately capturing this discontinuity in the Patterson, M. and Rao, A. (2014). GPOPS-II: A MAT- optimal solution at 20 s. LAB software for solving multiple-phase optimal con- trol problems using hp-adaptive gaussian quadrature For closed-loop design with Simulink, ICLOCS2 supports collocation methods and sparse nonlinear programming. classical NMPC implementations, as well as variants such ACM Transactions on Mathematical Software (TOMS), as multi-step MPC (Palma et al., 2015) and advanced- 41(1), 1. multi-step MPC (Yang and Biegler, 2013), where the op- W¨achter, A. and Biegler, L. (2006). On the implemen- timal control solution is updated at a lower rate compared tation of an interior-point filter line-search algorithm to control input updates. for large-scale nonlinear programming. Mathematical ACKNOWLEDGEMENTS Programming, 106(1), 25{57. doi:10.1007/s10107-004- 0559-y. Support of the EPSRC Centre for Doctoral Training in Weinstein, M. and Rao, A. (2017). Algorithm 984: Adi- High Performance Embedded and Distributed Systems gator, a toolbox for the algorithmic differentiation of (HiPEDS, Grant Reference EP/L016796/1) is gratefully mathematical functions in matlab using source trans- acknowledged. formation via operator overloading. ACM Transactions on Mathematical Software (TOMS), 44(2), 21. REFERENCES Yang, X. and Biegler, L.T. (2013). Advanced-multi-step Betts, J. (2010). Practical Methods for Optimal Control nonlinear model predictive control. Journal of process and Estimation Using Nonlinear Programming: Second control, 23(8), 1116{1128..
Load more

Recommended publications
  • Treball (1.484Mb)
    Treball Final de Màster MÀSTER EN ENGINYERIA INFORMÀTICA Escola Politècnica Superior Universitat de Lleida Mòdul d’Optimització per a Recursos del Transport Adrià Vall-llaura Salas Tutors: Antonio Llubes, Josep Lluís Lérida Data: Juny 2017 Pròleg Aquest projecte s’ha desenvolupat per donar solució a un problema de l’ordre del dia d’una empresa de transports. Es basa en el disseny i implementació d’un model matemàtic que ha de permetre optimitzar i automatitzar el sistema de planificació de viatges de l’empresa. Per tal de poder implementar l’algoritme s’han hagut de crear diversos mòduls que extreuen les dades del sistema ERP, les tracten, les envien a un servei web (REST) i aquest retorna un emparellament òptim entre els vehicles de l’empresa i les ordres dels clients. La primera fase del projecte, la teòrica, ha estat llarga en comparació amb les altres. En aquesta fase s’ha estudiat l’estat de l’art en la matèria i s’han repassat molts dels models més importants relacionats amb el transport per comprendre’n les seves particularitats. Amb els conceptes ben estudiats, s’ha procedit a desenvolupar un nou model matemàtic adaptat a les necessitats de la lògica de negoci de l’empresa de transports objecte d’aquest treball. Posteriorment s’ha passat a la fase d’implementació dels mòduls. En aquesta fase m’he trobat amb diferents limitacions tecnològiques degudes a l’antiguitat de l’ERP i a l’ús del sistema operatiu Windows. També han sorgit diferents problemes de rendiment que m’han fet redissenyar l’extracció de dades de l’ERP, el càlcul de distàncies i el mòdul d’optimització.
    [Show full text]
  • OPTIMAL CONTROL of NONHOLONOMIC MECHANICAL SYSTEMS By
    OPTIMAL CONTROL OF NONHOLONOMIC MECHANICAL SYSTEMS by Stuart Marcus Rogers A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Applied Mathematics Department of Mathematical and Statistical Sciences University of Alberta ⃝c Stuart Marcus Rogers, 2017 Abstract This thesis investigates the optimal control of two nonholonomic mechanical systems, Suslov's problem and the rolling ball. Suslov's problem is a nonholonomic variation of the classical rotating free rigid body problem, in which the body angular velocity Ω(t) must always be orthogonal to a prescribed, time-varying body frame vector ξ(t), i.e. hΩ(t); ξ(t)i = 0. The motion of the rigid body in Suslov's problem is actuated via ξ(t), while the motion of the rolling ball is actuated via internal point masses that move along rails fixed within the ball. First, by applying Lagrange-d'Alembert's principle with Euler-Poincar´e'smethod, the uncontrolled equations of motion are derived. Then, by applying Pontryagin's minimum principle, the controlled equations of motion are derived, a solution of which obeys the uncontrolled equations of motion, satisfies prescribed initial and final conditions, and minimizes a prescribed performance index. Finally, the controlled equations of motion are solved numerically by a continuation method, starting from an initial solution obtained analytically (in the case of Suslov's problem) or via a direct method (in the case of the rolling ball). ii Preface This thesis contains material that has appeared in a pair of papers, one on Suslov's problem and the other on rolling ball robots, co-authored with my supervisor, Vakhtang Putkaradze.
    [Show full text]
  • Clean Sky – Awacs Final Report
    Clean Sky Joint Undertaking AWACs – Adaptation of WORHP to Avionics Constraints Clean Sky – AWACs Final Report Table of Contents 1 Executive Summary ......................................................................................................................... 2 2 Summary Description of Project Context and Objectives ............................................................... 3 3 Description of the main S&T results/foregrounds .......................................................................... 5 3.1 Analysis of Optimisation Environment .................................................................................... 5 3.1.1 Problem sparsity .............................................................................................................. 6 3.1.2 Certification aspects ........................................................................................................ 6 3.2 New solver interfaces .............................................................................................................. 6 3.3 Conservative iteration mode ................................................................................................... 6 3.4 Robustness to erroneous inputs ............................................................................................. 7 3.5 Direct multiple shooting .......................................................................................................... 7 3.6 Grid refinement ......................................................................................................................
    [Show full text]
  • Optimal Control for Constrained Hybrid System Computational Libraries and Applications
    FINAL REPORT: FEUP2013.LTPAIVA.01 Optimal Control for Constrained Hybrid System Computational Libraries and Applications L.T. Paiva 1 1 Department of Electrical and Computer Engineering University of Porto, Faculty of Engineering - Rua Dr. Roberto Frias, s/n, 4200–465 Porto, Portugal ) [email protected] % 22 508 1450 February 28, 2013 Abstract This final report briefly describes the work carried out under the project PTDC/EEA- CRO/116014/2009 – “Optimal Control for Constrained Hybrid System”. The aim was to build and maintain a software platform to test an illustrate the use of the conceptual tools developed during the overall project: not only in academic examples but also in case studies in the areas of robotics, medicine and exploitation of renewable resources. The grand holder developed a critical hands–on knowledge of the available optimal control solvers as well as package based on non–linear programming solvers. 1 2 Contents 1 OC & NLP Interfaces 7 1.1 Introduction . .7 1.2 AMPL . .7 1.3 ACADO – Automatic Control And Dynamic Optimization . .8 1.4 BOCOP – The optimal control solver . .9 1.5 DIDO – Automatic Control And Dynamic Optimization . 10 1.6 ICLOCS – Imperial College London Optimal Control Software . 12 1.7 TACO – Toolkit for AMPL Control Optimization . 12 1.8 Pseudospectral Methods in Optimal Control . 13 2 NLP Solvers 17 2.1 Introduction . 17 2.2 IPOPT – Interior Point OPTimizer . 17 2.3 KNITRO . 25 2.4 WORHP – WORHP Optimises Really Huge Problems . 31 2.5 Other Commercial Packages . 33 3 Project webpage 35 4 Optimal Control Toolbox 37 5 Applications 39 5.1 Car–Like .
    [Show full text]
  • Using SCIP to Solve Your Favorite Integer Optimization Problem
    Using SCIP to Solve Your Favorite Integer Optimization Problem Gregor Hendel, [email protected] Hiroshima University October 5, 2018 Gregor Hendel, [email protected] – Using SCIP 1/76 What is SCIP? SCIP (Solving Constraint Integer Programs) … • provides a full-scale MIP and MINLP solver, • is constraint based, • incorporates • MIP features (cutting planes, LP relaxation), and • MINLP features (spatial branch-and-bound, OBBT) • CP features (domain propagation), • SAT-solving features (conflict analysis, restarts), • is a branch-cut-and-price framework, • has a modular structure via plugins, • is free for academic purposes, • and is available in source-code under http://scip.zib.de ! Gregor Hendel, [email protected] – Using SCIP 2/76 Meet the SCIP Team 31 active developers • 7 running Bachelor and Master projects • 16 running PhD projects • 8 postdocs and professors 4 development centers in Germany • ZIB: SCIP, SoPlex, UG, ZIMPL • TU Darmstadt: SCIP and SCIP-SDP • FAU Erlangen-Nürnberg: SCIP • RWTH Aachen: GCG Many international contributors and users • more than 10 000 downloads per year from 100+ countries Careers • 10 awards for Masters and PhD theses: MOS, EURO, GOR, DMV • 7 former developers are now building commercial optimization sotware at CPLEX, FICO Xpress, Gurobi, MOSEK, and GAMS Gregor Hendel, [email protected] – Using SCIP 3/76 Outline SCIP – Solving Constraint Integer Programs http://scip.zib.de Gregor Hendel, [email protected] – Using SCIP 4/76 Outline SCIP – Solving Constraint Integer Programs http://scip.zib.de Gregor Hendel, [email protected] – Using SCIP 5/76 ZIMPL • model and generate LPs, MIPs, and MINLPs SCIP • MIP, MINLP and CIP solver, branch-cut-and-price framework SoPlex • revised primal and dual simplex algorithm GCG • generic branch-cut-and-price solver UG • framework for parallelization of MIP and MINLP solvers SCIP Optimization Suite • Toolbox for generating and solving constraint integer programs, in particular Mixed Integer (Non-)Linear Programs.
    [Show full text]
  • On Scaled Stopping Criteria for a Safeguarded Augmented Lagrangian Method with Theoretical Guarantees
    Noname manuscript No. (will be inserted by the editor) On scaled stopping criteria for a safeguarded augmented Lagrangian method with theoretical guarantees R. Andreani · G. Haeser · M. L. Schuverdt · L. D. Secchin · P. J. S. Silva Received: date / Accepted: date Abstract This paper discusses the use of a stopping criterion based on the scaling of the Karush-Kuhn-Tucker (KKT) conditions by the norm of the ap- proximate Lagrange multiplier in the ALGENCAN implementation of a safe- guarded augmented Lagrangian method. Such stopping criterion is already used in several nonlinear programming solvers, but it has not yet been con- sidered in ALGENCAN due to its firm commitment with finding a true KKT point even when the multiplier set is not bounded. In contrast with this view, we present a strong global convergence theory under the quasi-normality con- straint qualification, that allows for unbounded multiplier sets, accompanied by an extensive numerical test which shows that the scaled stopping criterion is more efficient in detecting convergence sooner. In particular, by scaling, ALGENCAN is able to recover a solution in some difficult problems where the original implementation fails, while the behavior of the algorithm in the easier instances is maintained. Furthermore, we show that, in some cases, a R. Andreani · P. J. S. Silva Department of Applied Mathematics, University of Campinas, Rua S´ergio Buarque de Holanda, 651, 13083-859, Campinas, SP, Brazil. E-mail: [email protected], [email protected] G. Haeser Department of Applied Mathematics, University of S~aoPaulo, Rua do Mat~ao, 1010, Cidade Universit´aria,05508-090, S~aoPaulo, SP, Brazil.
    [Show full text]
  • Technical Program
    TECHNICAL PROGRAM Wednesday, 9:00-10:30 Wednesday, 11:00-12:40 WA-01 WB-01 Wednesday, 9:00-10:30 - 1a. Europe a Wednesday, 11:00-12:40 - 1a. Europe a Opening session - Plenary I. Ljubic Planning and Operating Metropolitan Passenger Transport Networks Stream: Plenaries and Semi-Plenaries Invited session Stream: Traffic, Mobility and Passenger Transportation Chair: Bernard Fortz Invited session Chair: Oded Cats 1 - From Game Theory to Graph Theory: A Bilevel Jour- ney 1 - Frequency and Vehicle Capacity Determination using Ivana Ljubic a Dynamic Transit Assignment Model In bilevel optimization there are two decision makers, commonly de- Oded Cats noted as the leader and the follower, and decisions are made in a hier- The determination of frequencies and vehicle capacities is a crucial archical manner: the leader makes the first move, and then the follower tactical decision when planning public transport services. All meth- reacts optimally to the leader’s action. It is assumed that the leader can ods developed so far use static assignment approaches which assume anticipate the decisions of the follower, hence the leader optimization average and perfectly reliable supply conditions. The objective of this task is a nested optimization problem that takes into consideration the study is to determine frequency and vehicle capacity at the network- follower’s response. level while accounting for the impact of service variations on users In this talk we focus on new branch-and-cut (B&C) algorithms for and operator costs. To this end, we propose a simulation-based op- dealing with mixed-integer bilevel linear programs (MIBLPs).
    [Show full text]
  • Datascientist Manual
    DATASCIENTIST MANUAL . 2 « Approcherait le comportement de la réalité, celui qui aimerait s’epanouir dans l’holistique, l’intégratif et le multiniveaux, l’énactif, l’incarné et le situé, le probabiliste et le non linéaire, pris à la fois dans l’empirique, le théorique, le logique et le philosophique. » 4 (* = not yet mastered) THEORY OF La théorie des probabilités en mathématiques est l'étude des phénomènes caractérisés PROBABILITY par le hasard et l'incertitude. Elle consistue le socle des statistiques appliqué. Rubriques ↓ Back to top ↑_ Notations Formalisme de Kolmogorov Opération sur les ensembles Probabilités conditionnelles Espérences conditionnelles Densités & Fonctions de répartition Variables aleatoires Vecteurs aleatoires Lois de probabilités Convergences et théorèmes limites Divergences et dissimilarités entre les distributions Théorie générale de la mesure & Intégration ------------------------------------------------------------------------------------------------------------------------------------------ 6 Notations [pdf*] Formalisme de Kolmogorov Phé nomé né alé atoiré Expé riéncé alé atoiré L’univérs Ω Ré alisation éléméntairé (ω ∈ Ω) Evé némént Variablé aléatoiré → fonction dé l’univér Ω Opération sur les ensembles : Union / Intersection / Complémentaire …. Loi dé Augustus dé Morgan ? Independance & Probabilités conditionnelles (opération sur des ensembles) Espérences conditionnelles 8 Variables aleatoires (discret vs reel) … Vecteurs aleatoires : Multiplét dé variablés alé atoiré (discret vs reel) … Loi marginalés Loi
    [Show full text]
  • A Primal-Dual Augmented Lagrangian Penalty-Interior-Point Filter Line Search Algorithm
    Journal name manuscript No. (will be inserted by the editor) A Primal-Dual Augmented Lagrangian Penalty-Interior-Point Filter Line Search Algorithm Renke Kuhlmann · Christof B¨uskens Received: date / Accepted: date Abstract Interior-point methods have been shown to be very efficient for large-scale nonlinear programming. The combination with penalty methods increases their robustness due to the regularization of the constraints caused by the penalty term. In this paper a primal-dual penalty-interior-point algo- rithm is proposed, that is based on an augmented Lagrangian approach with an `2-exact penalty function. Global convergence is maintained by a combina- tion of a merit function and a filter approach. Unlike other filter methods no separate feasibility restoration phase is required. The algorithm has been im- plemented within the solver WORHP to study different penalty and line search options and to compare its numerical performance to two other state-of-the- art nonlinear programming algorithms, the interior-point method IPOPT and the sequential quadratic programming method of WORHP. Keywords Nonlinear Programming · Constrained Optimization · Augmented Lagrangian · Penalty-Interior-Point Algorithm · Primal-Dual Method Mathematics Subject Classification (2000) 49M05 · 49M15 · 49M29 · 49M37 · 90C06 · 90C26 · 90C30 · 90C51 Renke Kuhlmann Optimization and Optimal Control, Center for Industrial Mathematics (ZeTeM), Biblio- thekstr. 5, 28359 Bremen, Germany E-mail: [email protected] Christof B¨uskens E-mail: [email protected] 2 Renke Kuhlmann, Christof B¨uskens 1 Introduction In this paper we consider the nonlinear optimization problem min f(x) n x2R s.t. c(x) = 0 (1.1) x ≥ 0 with twice continuously differentiable functions f : Rn ! R and c : Rn ! Rm, but the methods can easily be extended to the general case with l ≤ x ≤ g and c(x) ≤ 0 (cf.
    [Show full text]
  • OSE4 Workshop, March 27Th
    OSE4 4th European Optimisation in Space Engineering Workshop March 27th - 30th 2017 Zentrum für Technomathematik Moin!1 The 4th workshop on Optimisation in Space Engineering (OSE) is organised by the European Space Agency and the University of Bremen. The goal of the OSE initiative is to provide a forum for space companies, universities, research institutes and organisations to discuss recent advances in space technology and further research in the area of optimisation in space engineering. Scientific Program The OSE4 consists of: • On Monday, March 27th, tutorials will be given for the ESA NLP solver WORHP and the optimal control library TransWORHP. This day addresses especially to PhD students and active researchers. However, anyone is invited to participate. • From Tuesday to Thursday, March 28th to March 30th, the workshop including presen- tations of the participants and round table discussion take place. Each presentation takes 30 minutes, including discussion. Venue The venue for the OSE4 is the building MZH on the campus of the University of Bremen. • Registration is in MZH 1450 (first floor) • The tutorials on Monday as well as the workshop from Tuesday to Thursday will be held in the lecture room MZH 1470. • Coffee will be served directly in front of these rooms. • Lunch can be taken at the Mensa of the university, or in some nearby restaurants. • Free WiFi is available at the university for eduroam users. We organize WiFi access also for non university participants. Social Events • The mathematical city tour starts on Monday at 17:30 on the Marktplatz (market square) in the city center near the statue of Roland in front of the Rathaus (town hall).
    [Show full text]
  • The Non-Linear Parallel Optimization Tool (Nlparopt): a Software Overview and Efficiency Analysis
    © 2015 Laura Richardson THE NON-LINEAR PARALLEL OPTIMIZATION TOOL (NLPAROPT): A SOFTWARE OVERVIEW AND EFFICIENCY ANALYSIS BY LAURA RICHARDSON THESIS Submitted in partial fulfillment of the requirements for the degree of Master of Science in Aerospace Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2015 Urbana, Illinois Adviser: Professor Victoria Coverstone ABSTRACT Modern spacecraft trajectory mission planning regularly involves some component of numerical optimization to provide a significant improvement in a solution, and in some instances is the only manner for finding an acceptable solution to a problem. One of the most useful constrained optimization formulations is the Non-Linear Programming (NLP) problem. NLP problem solvers have been used to analyze complex optimization problems by space mission designers as well as a wide variety of other fields such as economics and city planning. There are several state-of-the-art software packages that are currently used to solve NLPs in the aerospace industry, such as SNPOT, IPOPT, and WORHP. Most of the critical space trajectory design software tools in use today, such as OTIS, EMTG, and MALTO, are dependent on a drop-in NLP solver (typically SNOPT or IPOPT); this dependence is not unwarranted, as the existing solvers are especially adept at solving very large-scale, preferably sparse, non-linear programming problems. However, neither SNOPT nor any other NLP solver available exploits parallel programming techniques. Most trajectory design tools have already started to implement parallel techniques, and it is now the serial-execution nature of the existing packages that represents the largest bottleneck. A high-fidelity trajectory optimization NLP can take days, weeks, or even months before converging to a solution, resulting in a prohibitively expensive mission planning design tool, both in terms of time and cost.
    [Show full text]
  • Opty: Software for Trajectory Optimization and Parameter Identification Using Direct Collocation
    opty: Software for trajectory optimization and parameter identification using direct collocation Jason K. Moore1 and Antonie van den Bogert2 DOI: 10.21105/joss.00300 1 University of California, Davis 2 Cleveland State University Software • Review Summary • Repository • Archive opty is a tool for describing and solving trajectory optimization and parameter identi- Submitted: 04 June 2017 fication problems based on symbolic descriptions of ordinary differential equations and Published: 30 January 2018 differential algebriac equations that describe a dynamical system. The motivation for its development resides in the need to solve optimal control problems of biomechanical Licence Authors of JOSS papers retain systems. The target audience is engineers and scientists interested in solving nonlinear copyright and release the work un- optimal control and parameter identification problems with minimal computational over- der a Creative Commons Attri- head. bution 4.0 International License A user of opty is responsible for specifying the system’s dynamics (the ODE/DAEs), the (CC-BY). cost or fitness function, bounds on the solution, and the initial guess for the solution. opty uses this problem specification to derive the constraints needed to solve the optimization problem using the direct collocation method (Betts 2010). This method maps the problem to a non-linear programming problem and the result is then solved numerically with an interior point optimizer IPOPT (Wächter and Biegler 2006) which is wrapped by cyipopt (cyipopt Developers 2017) for use in Python. The software allows the user to describe the dynamical system of interest at a high level in symbolic form without needing to concern themselves with the numerical computation details.
    [Show full text]