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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
URN: urn:nbn:se:kth:diva-175429OAI: diva2:860934
51st IEEE Conference on Decision and Control, Maui, HI, USA, 2012
The Royal Swedish Academy of SciencesSwedish Foundation for Strategic Research

NQC 2015

Available from: 2015-10-14 Created: 2015-10-14 Last updated: 2015-10-15Bibliographically 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.
TRITA-MAT-A, 2015:10
National Category
Control Engineering
Research subject
Applied and Computational Mathematics
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)
Swedish Foundation for Strategic Research

QC 20151015

Available from: 2015-10-15 Created: 2015-10-14 Last updated: 2015-10-15Bibliographically approved

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Markdahl, JohanHoppe, JensHu, Xiaoming
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