Analysis of robot navigation schemes using Rantzer's Dual Lyapunov Theorem

被引:10
作者
Dimarogonas, Dimos V. [1 ]
Johansson, Karl H. [1 ]
机构
[1] Royal Inst Technol, Sch Elect Engn, ACCESS Linnaeus Ctr, SE-10044 Stockholm, Sweden
来源
2008 AMERICAN CONTROL CONFERENCE, VOLS 1-12 | 2008年
关键词
AVOIDANCE;
D O I
10.1109/ACC.2008.4586491
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
When robots are driven by the negative gradient of a potential field that consists of the sum of an attractive and a repulsive term, convergence to the desired configuration cannot be guaranteed by traditional Lyapunov techniques. In this paper, sufficient conditions for convergence of such systems are provided instead with the use of Rantzer's Dual Lyaptinov Theorem. In particular, a condition that involves the trace of the Hessian matrix of the potential function is derived and then applied to the cases of navigation of a single robot and of multi-robot formation stabilization. The main result of the paper states that a sufficient condition for convergence to a desired configuration in both cases is that the attractive potential admits a sufficiently large gain. A lower bound on the attractive potential is computed. Computer simulations that support the new results are provided.
引用
收藏
页码:201 / 206
页数:6
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