Gradient methods for iterative distributed control synthesis

Mårtensson, Karl; Rantzer, Anders

doi:10.1109/cdc.2009.5400233

Cited by 42 publications

(49 citation statements)

References 15 publications

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“…In case a negative value is obtained nothing can be said about the suboptimality with this method. Though, as we get closer to the optimal feedback matrix, the adjoint trajectory will approach the optimal (with respect to (12)) and the inequalities in the proof of Theorem 2 will almost be equal implying that we can expect a positive value from (10). When positive, the suboptimality bound is always larger than 1 which is natural.…”

Section: Examplementioning

confidence: 98%

“…A first remark is that in the first iteration we get a negative value of the suboptimality bound. This is due to the fact that the minimization program in (10) is not guaranteed to give a positive value. In case a negative value is obtained nothing can be said about the suboptimality with this method.…”

Section: Examplementioning

confidence: 99%

“…The methods hinge on the solutions of Lyapunov equation and the solution of the centralized problem, thus not applicable to large-scale systems. In [10] an iterative distributed control synthesis scheme for discrete-time systems is considered. We will follow a similar approach when developing the theory in this paper.…”

Section: Introductionmentioning

confidence: 99%

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A scalable method for continuous-time distributed control synthesis

Mårtensson

Rantzer

2012

2012 American Control Conference (ACC)

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Abstract-In this paper a synthesis method for distributed controllers for continuous time distributed systems, is discussed. The systems considered consists of subsystems interconnected in a graph structure. This graph represents a communication structure of the system and hence governs the structure of the admissible controller, meaning that distributed controllers are considered. The objective of the synthesis is to obtain such admissible controllers that optimize a given performance. The method is scalable with respect to the size of the system and is therefore suitable for large-scale systems.Distributed controllers are suboptimal with respect to centralized ones and it is desirable to measure the amount of performance degradation. Using the variables of the synthesis scheme, it is shown how to determine such a measure of suboptimality.

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Section: Examplementioning

confidence: 98%

Section: Examplementioning

confidence: 99%

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A scalable method for continuous-time distributed control synthesis

Mårtensson

Rantzer

2012

2012 American Control Conference (ACC)

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“…However, because of the specific form of the cost functional, standard LQR methods are not applicable. Hence, we present two iterative algorithms to determine the feedback matrix, inspired by results in [9], [10]. These iterative algorithms are based on the simulation of trajectories of the system state and an adjoint state.…”

Section: Introductionmentioning

confidence: 99%

Iterative optimal feedback control design under relaxed rigidity constraints for multi-robot cooperative manipulation

Sieber

Deroo

Hirche

2013

52nd IEEE Conference on Decision and Control

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Abstract-Cooperative manipulation of multiple robots presents an interesting control application scenario of coupled dynamical systems with a common goal. Here, we treat the problem of moving a formation of physically interconnected robots to a desired goal while maintaining the formation. This control problen is for example relevant in cooperative transport of an object from an initial to a final configuration by mobile robotic manipulators. To achieve the control goal we formulate an LQR-like optimal control problem that, in addition to goal regulation and minimization of input energy, includes the formation rigidity constraint in a relaxed form expressed as a biquadratic penalty term. The control problem is solved by two different iterative algorithms, a gradient descent using adjoint states and a quasi-Newton method, that determine a static linear state-feedback matrix. The proposed control design and the iterative algorithms are validated and compared in numerical simulations showing the efficacy of both approaches.

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“…This relaxed rigidity constraint is justified by the use of impedance control, by which minor deviations from the rigidity constraint result in tolerable object stress. Because of the biquadratic term the LQR problem cannot be solved using standard methods, we propose an iterative descent method inspired by [8] and [9]. As an intermediate step in the controller design, we introduce an approximated state-space model for physically cooperating multi-robotteams.…”

Section: Introductionmentioning

confidence: 99%

Formation-based approach for multi-robot cooperative manipulation based on optimal control design

Sieber

Deroo

Hirche

2013

2013 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-Cooperative manipulation, where several robots collaboratively transport an object, poses a great challenge in robotics. In order to avoid object deformations in cooperative manipulation, formation rigidity of the robots is desired. This work proposes a novel linear state feedback controller that combines both optimal goal regulation and a relaxed form of the formation rigidity constraint, exploiting an underlying distributed impedance control scheme. Since the presented control design problem is in a biquadratic LQR-like form, we present an iterative design algorithm to compute the controller. As an intermediate result, an approximated state-space model of an interconnected robot system is derived. The controller design approach is evaluated in a full-scale multi-robot experiment.

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Gradient methods for iterative distributed control synthesis

Cited by 42 publications

References 15 publications

A scalable method for continuous-time distributed control synthesis

A scalable method for continuous-time distributed control synthesis

Iterative optimal feedback control design under relaxed rigidity constraints for multi-robot cooperative manipulation

Formation-based approach for multi-robot cooperative manipulation based on optimal control design

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