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Controlling a rigid formation from a triangle
- Source :
- CDC
- Publication Year :
- 2016
- Publisher :
- IEEE, 2016.
-
Abstract
- Consider a formation control problem in which agents in Euclidean space are tasked with stabilizing their positions at prescribed target distances from each other, and for which these distances are described by a rigid graph. There is a mismatch in target distances if there is a pair of neighboring agents i and j such that agent i aims to stabilize from agent j at a distance d ij , but agent j from agent i at a slightly different distance d′ ij . A mismatch in target distances results in a mismatch in the associated interaction laws. It was shown in a recent paper [1] that when there is a small mismatch in the interaction laws, the entire formation undergoes a constant rigid motion. In this work, we build on this observation to establish a controllability result. Specifically, given that there is a selected subset of agents that can control the mismatches in interactions among them, we show that if these agents are fully connected and form a nondegenerate triangle (or more generally, a nondegenerate k-simplex in the k-dimensional case), then it is possible to control an arbitrary rigid motion of the entire formation.
- Subjects :
- 0209 industrial biotechnology
Euclidean space
010102 general mathematics
Geometry
02 engineering and technology
Topology
01 natural sciences
Graph
Computer Science::Multiagent Systems
Controllability
020901 industrial engineering & automation
Aerospace electronics
Rigid motion
0101 mathematics
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- 2016 IEEE 55th Conference on Decision and Control (CDC)
- Accession number :
- edsair.doi...........97a8eccce545752899835d11756cbf99