A linear control approach to distributed multi-agent formations in d-dimensional space

Zhiyun Lin, Zhiyong Chen, Minyue Fu
2013 52nd IEEE Conference on Decision and Control  
The paper presents a linear approach for formation control of multiple autonomous agents in d-dimensional space. The generalized notion of graph Laplacian, associated to a graph with possibly negative weights on the edges, is introduced aiming to solve the formation problem of controlling a network of point agents to form a given pattern (including rotation, translation, and scaling). By assuming the number of agents is larger than d + 1, we derive that a linear distributed control law exists
more » ... ontrol law exists for this purpose if and only if certain algebraic conditions hold (or equivalently, the graph is globally rigid). Next, it is shown that the generalized graph Laplacian used to stabilize the formations can be obtained by solving a convex optimization problem. Further results are also provided to reveal the conditions under which the attained formations are congruent to or just translations of the desired one. 52nd IEEE Conference on Decision and Control December 10-13, 2013. Florence, Italy 978-1-4673-5717-3/13/$31.00 ©2013 IEEE 6049
doi:10.1109/cdc.2013.6760845 dblp:conf/cdc/LinCF13 fatcat:c4nyfbxfnzehhlganz3vewrroy