Motion Coordination with Noisy Measurement in Natural and Artificial Swarms
Abstract
We consider the problem of controlling a group of mobile agents toward a formation defined by the desired relative positions between the agents. Each agent has available for control noisy measurements of its relative position with respect to a small set of neighbors. The motion of the group as a whole is due to a leader who moves independently of the other agents. We show that there are intrinsic limitations on the size of the group group determined by the underlying network structure imposed by the requirement of local interaction, which determine how low a tracking error can be achieved. It is shown that the tracking error covariance is given by the matrix-valued effective resistance introduced by the authors in Barooah and Hespanha (2005). We show how the effective resistance of a node in the multi-agent graph scales with the distance of that node from the leader for a large class of graphs. These scaling laws ultimately dictate on what kind of graphs scalable motion coordination can be achieved. Apart from providing design guidelines for robotic swarms, these results shed light on the dynamics of collective motion of certain animal groups.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 2006
- Accession Number
- ADA481531
Entities
People
- João P. Hespanha
- Prabir Barooah
Organizations
- University of California, Santa Barbara