报告题目：Attitude control of multi-rigid-body systems: from synchronization to intrinsic formation
报告人：Xiaoming Hu
报告人单位：Department of Mathematics KTH Royal Institute of Technology
报告时间：7月23日（周一）下午4:30-5:30
报告地点：数学学院西303报告厅
邀请人：张旭
Abstract:
Attitude control has attracted great research attention both due to its practical
implication and mathematical challenges. In this talk we will present our study on
attitude control of multi-rigid-body systems for which a key assumption is that only
relative attitude errors are available for feedback control design. We will first
consider systems that are modeled by the so-called unicycles, namely they have one
degree of freedom in orientation and two degrees of freedom in translation. Under the
assumption that the neighborhood for communication is defined by translational
distance, we study the minimal proportion of “leaders” needed such that all the
“followers” can be synchronized in orientation. We then move on to discuss the full
attitude synchronization problem for which a simple and intuitive linear control design
based on the axis-angle representation is presented, which also makes the maximal open
(geodesically) convex ball of initial attitudes invariant. When only relative attitude
information is used for feedback design, for any distributed attitude formation problem
the synchronized states are always equilibria of the closed-loop system regardless
of the topology of the inter-agent graph for communication, as long as the control law
is Lipschitz continuous. However, due to the fact that the involved manifolds are
compact and without boundary, continuous time-invariant feedback control will also
yield some other closed-loop equilibria that may vary with the graph topology. These
equilibria represent different attitude configurations of the system, which may include
a desired (intrinsic) formation depending on the application. Then a natural and
interesting question arises: is it possible to achieve a desired formation by imposing
some proper inter-agent graph to the system and then making that formation
asymptotically stable? In the last part of the talk, we will use the case of reduced
attitudes to answer this question affirmatively. We will show that all regular
polyhedra on the unit sphere can be achieved this way.
来源链接：http://math.scu.edu.cn/info/1062/3575.htm
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