Parametric sensitivities for optimal control problems using automatic differentiation

Griesse, Roland; Walther, Andrea

doi:10.1002/oca.733

Cited by 16 publications

(9 citation statements)

References 23 publications

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“…For small systems, this computation can be done by hand [97]. For larger systems, formula manipulation programs such as MAPLE [123] or alternatively Automatic Differentiation procedures are proposed [66,67,68,69,87,91]. The effort is significantly increasing with system complexity and size [53].…”

Section: Equations Of Motion and Derivativesmentioning

confidence: 99%

“…This is because previously calculated quantities can be reused and the special structure of the derivatives can be exploited [37]. Remark 2.1 Currently Automatic Differentiation is receiving an increasing amount of attention in the optimization community, especially in combination with direct methods [62,66]. Therefore, the question arised whether Automatic Differentiation is preferable to the recursive techniques presented above in case of the manipulator systems discussed in this paper.…”

Section: Equations Of Motion and Derivativesmentioning

confidence: 99%

“…An upper limit of ≈ 852n 3 operations for the computation of the first-order derivatives of M (Θ) can be estimated by directly applying Automatic Differentiation. For the calculation of second-order derivatives two techniques are proposed in [66]. The first one uses an Automatic Differentiation tool which is based on operator overloading like ADOL-C [70].…”

Section: Equations Of Motion and Derivativesmentioning

confidence: 99%

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Optimal Control of Rigid‐Link Manipulators by Indirect Methods

Callies¹,

Rentrop

2008

GAMM-Mitteilungen

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The present paper is a survey and research paper on the treatment of optimal control problems of rigid-link manipulators by indirect methods. Maximum Principle based approaches provide an excellent tool to calculate optimal reference trajectories for multi-link manipulators with high accuracy. Their major drawback was the need to explicitly formulate the complicated system of adjoint differential equations and to apply the full apparatus of optimal control theory. This is necessary in order to convert the optimal control problem into a piecewise defined, nonlinear multi-point boundary value problem. An accurate and efficient access to first-and higher-order derivatives is crucial. The approach described in this paper allows it to generate all the derivative information recursively and simultaneously with the recursive formulation of the equations of motion. Nonlinear state and control constraints are treated without any simplifications by transforming them into sequences of systems of linear equations. By these means, the modeling of the complete optimal control problem and the accompanying boundary value problem is automated to a great extent. The fast numerical solution is by the advanced multiple shooting method JANUS.

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Section: Equations Of Motion and Derivativesmentioning

confidence: 99%

Section: Equations Of Motion and Derivativesmentioning

confidence: 99%

Section: Equations Of Motion and Derivativesmentioning

confidence: 99%

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Optimal Control of Rigid‐Link Manipulators by Indirect Methods

Callies¹,

Rentrop

2008

GAMM-Mitteilungen

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“…The complete equations of motion can be found in [10]. The robot's task to perform a turn-around maneuver is expressed by means of initial and terminal conditions as well as control constraints [7]. To compute an approximation of the corresponding trajectory, we apply the standard Runge-Kutta method of order 4 for the integration resulting in about 800 lines of code.…”

Section: Psfrag Replacementsmentioning

confidence: 99%

Efficient calculation of sensitivities for optimization problems

Kowarz

Walther

2007

Discuss. Math. Differential Inclusions, Control and Optimizatio

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Sensitivity information is required by numerous applications such as, for example, optimization algorithms, parameter estimations or real time control. Sensitivities can be computed with working accuracy using the forward mode of automatic differentiation (AD). ADOL-C is an AD-tool for programs written in C or C++. Originally, when applying ADOL-C, tapes for values, operations and locations are written during the function evaluation to generate an internal function representation. Subsequently, these tapes are evaluated to compute the derivatives, sparsity patterns etc., using the forward or reverse mode of AD. The generation of the tapes can be completely avoided by applying the recently implemented tapeless variant of the forward mode for scalar and vector calculations. The tapeless forward mode enables the joint computation of function and derivative values directly from main memory within one sweep. Compared to the original approach shorter runtimes are achieved due to the avoidance of tape handling and a more effective, joint optimization for function and derivative code. Advantages and disadvantages of the tapeless forward mode provided by ADOL-C will be discussed. Furthermore, runtime comparisons for two implemented variants of the tapeless forward mode are presented. The results are based on two numerical examples that require the computation of sensitivity information.

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“…The complete equations of motion can be found in [9]. The robot's task to perform a turn-around maneuver is expressed by means of initial and terminal conditions as well as control constraints [6]. However, for illustrating the run-time effects of the checkpointing facility integrated in ADOL-C we consider only the gradient computation of J(q, u) with respect to u.…”

Section: Numerical Examplementioning

confidence: 99%

Optimal Checkpointing for Time-Stepping Procedures in ADOL-C

Kowarz

Walther

2006

Computational Science – ICCS 2006

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Using the basic reverse mode of automatic differentiation, the memory needed for the computation of discrete adjoints is proportional to the number of operations performed. This behavior is frequently not acceptable, especially for large-scale problems that involve a kind of time-stepping procedure. Therefore, we integrate a checkpointing mechanism into ADOL-C, a tool for the automatic differentiation of C and C++ programs. This checkpointing procedure is optimal for a given number of checkpoints in the sense that it yields the minimal number of recomputations. The resulting effects on the run-time behavior are illustrated by means of the derivative computation for an ODE-based optimization problem.

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Parametric sensitivities for optimal control problems using automatic differentiation

Cited by 16 publications

References 23 publications

Optimal Control of Rigid‐Link Manipulators by Indirect Methods

Optimal Control of Rigid‐Link Manipulators by Indirect Methods

Efficient calculation of sensitivities for optimization problems

Optimal Checkpointing for Time-Stepping Procedures in ADOL-C

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