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Online trajectory planning and observer based control
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2006 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

The main body of this thesis consists of four appended papers. The first two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.

The first paper addresses the problem of designing a real time, high performance trajectory planner for aerial vehicles. The main contribution is two-fold. Firstly, by augmenting a novel safety maneuver at the end of the planned trajectory, this paper extends previous results by having provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method is shown to have finite time task completion. Moreover, in the second part of the paper, the problem of simultaneous arrival of multiple aerial vehicles is considered. By using a time-scale separation principle, one is able to adopt standard Laplacian control to this consensus problem, which is neither unconstrained, nor first order.

Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In the second paper, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for online trajectory optimization are illustrated by a missile guidance example.

In the third paper, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotics systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors.

Finally, in the fourth paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contraction is infinitely thin. However, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature.

Place, publisher, year, edition, pages
Stockholm: KTH , 2006. , x, 37 p.
Series
Trita-MAT. OS, ISSN 1401-2294 ; 06:04
Keyword [en]
Computational Optimal Control, Receding Horizon Control, Mission Uncertainty, Safety, Task Completion, Consensus Problem, Simultaneous Arrival, Adaptive Grid Methods, Missile Guidance, Nonlinear Observer Design, Active Observers, Non--uniformly Observable Systems, Mobile Robotic Systems, Intrinsic Observers, Differential Geometric Methods, Euler-Lagrange Systems, Contraction Analysis.
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-4153ISBN: 91-7178-469-1 (print)OAI: oai:DiVA.org:kth-4153DiVA: diva2:10938
Presentation
2006-11-10, 3721, KTH, Lindstedtsvägen 25, 100 44 Stockholm, 10:00
Opponent
Supervisors
Note
QC 20101108Available from: 2006-10-15 Created: 2006-10-15 Last updated: 2010-11-08Bibliographically approved
List of papers
1. Online Trajectory Planning for Aerial Vehicle: A Safe Approach with Guaranteed Task Completion
Open this publication in new window or tab >>Online Trajectory Planning for Aerial Vehicle: A Safe Approach with Guaranteed Task Completion
(English)Manuscript (Other academic)
Abstract [en]

On-line trajectory optimization in three dimensional space is the main topic of the paper at hand. The high-level framework augments on-line receding horizon control with an off-line computed terminal cost that captures the global characteristics of the environment, as well as any possible mission objectives. The first part of the paper is devoted to the single vehicle case while the second part considers the problem of simultaneous arrival of multiple aerial vehicles. The main contribution of the first part is two-fold. Firstly, by augmenting a so called safety maneuver at the end of the planned trajectory, this paper extends previous results by addressing provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method presented is shown to have finite time task completion. Moreover, a quantitative comparison between the two competing objectives of optimality and computational tractability is made. Finally, some other key characteristics of the trajectory planner, such as ability to minimize threat exposure and robustness, are highlighted through simulations. As for the simultaneous arrival problem considered in the second part, by using a time-scale separation principle, we are able to adopt standard Laplacian control to a consensus problem which is neither unconstrained, nor first order. 

National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-6264 (URN)
Note
QC 20100622Available from: 2006-10-15 Created: 2006-10-15 Last updated: 2011-11-21Bibliographically approved
2. Adaptive Node Distribution for Online Trajectory Planning
Open this publication in new window or tab >>Adaptive Node Distribution for Online Trajectory Planning
(English)Manuscript (Other academic)
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-6265 (URN)
Note
QC 20100622Available from: 2006-10-15 Created: 2006-10-15 Last updated: 2010-07-19Bibliographically approved
3. Active Observers for Mobile Robotic Systems
Open this publication in new window or tab >>Active Observers for Mobile Robotic Systems
(English)Manuscript (Other academic)
Abstract [en]

An important class of non-uniformly observable systems come from applications in mobile robotics. In this paper, the problem of active observer design for such systems is considered. The set of feasible configurations and the set of output flow equivalent states is defined. It is shown that the inter-relation between these two sets serves as the basis for design of active observers. The proposed observer design method is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors.

National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-6266 (URN)
Note
QC 20100622Available from: 2006-10-15 Created: 2006-10-15 Last updated: 2010-07-19Bibliographically approved
4. Riemannian Observers for Euler-Lagrange Systems
Open this publication in new window or tab >>Riemannian Observers for Euler-Lagrange Systems
2005 (English)In: Proceedings of the 16th IFAC World Congress: Prague, Czech Republic, July 3-8, 2005, 2005, 115-120 p.Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analysed. This observer is an generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contractivity is infinitely thin. However, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature. The convergence properties of the observer are illustrated by an example where the configuration manifold is the three-dimensional sphere, S3.

Series
IFAC Proceedings Volumes (IFAC-PapersOnline), ISSN 1474-6670 ; 16
Keyword
Contraction, Differential geometric methods, Euler-lagrange systems, Intrinsic observers, Nonlinear observers, Nonlinear systems theory
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-6267 (URN)2-s2.0-79960723494 (Scopus ID)008045108X (ISBN)9780080451084 (ISBN)
Conference
16th Triennial World Congress of International Federation of Automatic Control, IFAC 2005; Prague; Czech Republic; 3 July 2005 through 8 July 2005
Note

QC 20100622. Updated from manuscript to conference paper.

Available from: 2006-10-15 Created: 2006-10-15 Last updated: 2014-11-27Bibliographically approved

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