A parametrization of the solutions of the finite-horizon LQ problem with general cost and boundary conditions

Ferrante, Augusto; Marro, G.; Ntogramatzidis, Lorenzo

doi:10.1016/j.automatica.2005.01.018

Cited by 39 publications

(39 citation statements)

References 11 publications

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“…[28] and [31] investigate methods of determining the appropriate level of smoothing by analyzing properties of the input data. LQ problems with various types of boundary conditions are studied in [7] and [23] but to the extent of our knowledge, little work has been done on the type of periodic boundary conditions studied in this paper.…”

Section: D2 Related Work and Contributionsmentioning

confidence: 99%

Contour reconstruction using recursive smoothing splines - Algorithms and experimental validation

Karasalo

Piccolo

Kragić

et al. 2009

Robotics and Autonomous Systems

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In this paper, a recursive smoothing spline approach for contour reconstruction is studied and evaluated. Periodic smoothing splines are used by a robot to approximate the contour of encountered obstacles in the environment. The splines are generated through minimizing a cost function subject to constraints imposed by a linear control system and accuracy is improved iteratively using a recursive spline algorithm. The filtering effect of the smoothing splines allows for usage of noisy sensor data and the method is robust with respect to odometry drift. The algorithm is extensively evaluated in simulations for various contours and in experiments using a SICK laser scanner mounted on a PowerBot from ActivMedia Robotics.Keywords: mapping, optimal control, recursive smoothing splines, implementation D.1 IntroductionToday robots are expected to operate in at least partially unknown, open-ended environments, detecting and moving around obstacles, building maps of the environment and localizing their position. The area of autonomous mapping has during the past few years matured and there has been a significant amount of work reported using both visual and laser sensors, [8], [26]. However, most methods are still concerned with detecting and maintaining a dense set of discrete features of the environment that are suitable for navigation and localization without retrieving any specific knowledge about the detailed shape of the encountered objects.In this paper, we consider the problem of estimating representations of objects using a type of continuous closed curves, the recursive periodic smoothing splines. The splines are retrieved from noisy measurements of the true contour. Intended applications include mapping, identification and path planning. It is well known that interpolating splines from noisy measurement data will give a poor result, as the resulting curve will go through every measurement point. Data smoothing has been a classical problem in system and control history [1], [13], [18]. The theory of regular smoothing splines is thoroughly treated in [29] and [30]. It has been further shown in [35] that control theoretic smoothing splines, where the curve is found through minimizing a cost function, act as filters and are better suited for noisy measurements. It is also noted in [27] that smoothing 89

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Section: D2 Related Work and Contributionsmentioning

confidence: 99%

Contour reconstruction using recursive smoothing splines - Algorithms and experimental validation

Karasalo

Piccolo

Kragić

et al. 2009

Robotics and Autonomous Systems

View full text Add to dashboard Cite

show abstract

“…[23] and [26] investigate methods of determining the appropriate level of smoothing by analyzing properties of the input data. LQ problems with various types of boundary conditions are studied in [18] and [4] but to the extent of our knowledge, little work has been done on the type of periodic boundary conditions studied in this paper.…”

Section: Related Work and Contributionsmentioning

confidence: 99%

Contour reconstruction using recursive smoothing splines - experimental validation

Piccolo

Karasalo

Kragić

et al. 2007

2007 IEEE/RSJ International Conference on Intelligent Robots and Systems

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“…Future investigations will also focus on examining how the use of generalised Riccati equations in the continuous time can be used to parameterise the trajectories that solve the Hamiltonian differential equation, to the end of addressing LQ problems with constraints at the end-points and biased performance indexes along the lines of [3], [12], [4], [5].…”

Section: A Infinite-horizon Lq Problem and Stabilisabilitymentioning

confidence: 99%

The role of the generalised continuous algebraic Riccati equation in impulse-free continuous-time singular LQ optimal control

Ferrante

Ntogramatzidis

2013

52nd IEEE Conference on Decision and Control

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A parametrization of the solutions of the finite-horizon LQ problem with general cost and boundary conditions

Cited by 39 publications

References 11 publications

Contour reconstruction using recursive smoothing splines - Algorithms and experimental validation

Contour reconstruction using recursive smoothing splines - Algorithms and experimental validation

Contour reconstruction using recursive smoothing splines - experimental validation

The role of the generalised continuous algebraic Riccati equation in impulse-free continuous-time singular LQ optimal control

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