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Rigid-Body Attitude Control and Related Topics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This dissertation explores aspects of control in rigid-body and robotic systems. The first and second paper analyze the attitude stabilization problem and its generalization to n-dimensional rigid bodies. The third and fourth paper are on cooperative control design for systems that evolve on the n-sphere and related topics such as rigid-body reduced attitude synchronization. The fifth, and final, paper proposes a hybrid systems approach to task-priority based control for mobile manipulation.

he first and second paper concern the problem of attitude tracking by kinematic actuation for a class of almost globally asymptotically stabilizing feedback laws on SO(n). The closed-loop systems are solved exactly for the rotation matrices as functions of time. Exact solutions provide insight into both the transient and asymptotical behavior of a system. Applications of these results are found in model predictive control and in sampled systems. The second paper also solves the optimal control problem of geodesic reduced attitude stabilization subject to full attitude stabilization.

The third and fourth paper concern three cooperative control problems on the n-sphere with applications to reduced attitude synchronization and formation control. The global behavior of a consensus protocol is studied both forwards and backwards in time. The forward time stability properties of all equilibria are characterized for a non-trivial class of graph topologies. The reverse time behavior in the case of cyclic graph topologies results in two types of formations depending on the parity of the number of agents. A third control protocol renders the centroid of agent states constant.

The fifth, and final, paper proposes a hybrid control approach to task priority based planar mobile manipulation, i.e., control on the n-torus. The end-effector path following problem for a nonholonomic mobile manipulator is solved subject to constraints on the input norm, feasible joint configurations, and distance to singularities. The hybrid system is well-posed; there is no Zeno behavior or chattering. A continuous, time-independent feedback law is derived based on the hybrid control design.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. , ix, 21 p.
Series
TRITA-MAT-A, 2015:10
National Category
Control Engineering
Research subject
Applied and Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-175438ISBN: 978-91-7595-716-6 (print)OAI: oai:DiVA.org:kth-175438DiVA: diva2:860974
Public defence
2015-11-06, Kollegiesalen, Brinellvägen 8, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Foundation for Strategic Research
Note

QC 20151015

Available from: 2015-10-15 Created: 2015-10-14 Last updated: 2015-10-15Bibliographically approved
List of papers
1. Exact Solutions to a Class of Feedback Systems on SO(n)
Open this publication in new window or tab >>Exact Solutions to a Class of Feedback Systems on SO(n)
2016 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 63, 138-147 p.Article in journal (Refereed) Published
Abstract [en]

This paper provides a novel approach to the problem of attitude tracking for a class of almost globally asymptotically stable feedback laws on SO(n). The closed-loop systems are solved exactly for the rotation matrices as explicit functions of time, the initial conditions, and the gain parameters of the control laws. The exact solutions provide insight into the transient dynamics of the system and can be used to prove almost global attractiveness of the identity matrix. Applications of these results are found in model predictive control problems where detailed insight into the transient attitude dynamics is utilized to approximately complete a task of secondary importance. Knowledge of the future trajectory of the states can also be used as an alternative to the zero-order hold in systems where the attitude is sampled at discrete time instances.

Keyword
Attitude control, Global stability, Lie groups, Nonlinear systems, Predictive control, Sampled-data systems
National Category
Control Engineering
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-175396 (URN)10.1016/j.automatica.2015.10.023 (DOI)000367119300017 ()2-s2.0-84949682088 (Scopus ID)
Conference
19th IFAC World Congress, Cape Town, South Africa, 2014
Funder
Knut and Alice Wallenberg FoundationSwedish Foundation for Strategic Research
Note

QC 20160121

Available from: 2015-10-14 Created: 2015-10-14 Last updated: 2017-12-01Bibliographically approved
2. A Geodesic Feedback Law to Decouple the Full and Reduced Aitude
Open this publication in new window or tab >>A Geodesic Feedback Law to Decouple the Full and Reduced Aitude
(English)In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956Article in journal (Refereed) Submitted
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-175429 (URN)
Conference
51st IEEE Conference on Decision and Control, Maui, HI, USA, 2012
Funder
The Royal Swedish Academy of SciencesSwedish Foundation for Strategic Research
Note

NQC 2015

Available from: 2015-10-14 Created: 2015-10-14 Last updated: 2017-12-01Bibliographically approved
3. Global and Invariant Aspects of Consensus on the n-Sphere
Open this publication in new window or tab >>Global and Invariant Aspects of Consensus on the n-Sphere
(English)In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956Article in journal (Refereed) Submitted
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-175431 (URN)
Funder
Swedish Foundation for Strategic Research
Note

NQC 2015

Available from: 2015-10-14 Created: 2015-10-14 Last updated: 2017-12-01Bibliographically approved
4. Graph Based Formation Control on the Sphere
Open this publication in new window or tab >>Graph Based Formation Control on the Sphere
(English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836Article in journal (Refereed) Submitted
Place, publisher, year, edition, pages
Pergamon Press
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-175432 (URN)
Conference
54th IEEE Conference and Decision and Control, Osaka, Japan, 2015
Note

QC 20151102

Available from: 2015-10-14 Created: 2015-10-14 Last updated: 2017-12-01Bibliographically approved
5. A Hybrid Control Approach to Task-Priority Based Mobile Manipulation
Open this publication in new window or tab >>A Hybrid Control Approach to Task-Priority Based Mobile Manipulation
(English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523Article in journal (Refereed) Submitted
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-175436 (URN)
Conference
54th IEEE Conference on Decision and Control, Osaka, Japan, 2015
Funder
Swedish Foundation for Strategic Research
Note

NQC 2015

Available from: 2015-10-14 Created: 2015-10-14 Last updated: 2017-12-01Bibliographically approved

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