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Exact Solutions to a Class of Feedback Systems on SO(n)
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0003-0177-1993
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.

Place, publisher, year, edition, pages
2016. Vol. 63, 138-147 p.
Keyword [en]
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: urn:nbn:se:kth:diva-175396DOI: 10.1016/j.automatica.2015.10.023ISI: 000367119300017Scopus ID: 2-s2.0-84949682088OAI: oai:DiVA.org:kth-175396DiVA: diva2:860809
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
In thesis
1. Rigid-Body Attitude Control and Related Topics
Open this publication in new window or tab >>Rigid-Body Attitude Control and Related Topics
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:nbn:se:kth:diva-175438 (URN)978-91-7595-716-6 (ISBN)
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

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Hu, Xiaoming

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