K-robots clustering of moving sensors using coresets

• Main Authors: Feldman, Dan (Contributor), Gil, Stephanie (Contributor), Knepper, Ross A. (Contributor), Julian, Brian John (Contributor), Rus, Daniela L. (Contributor)
• Other Authors: Lincoln Laboratory (Contributor), Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory (Contributor), Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor), Massachusetts Institute of Technology. School of Engineering (Contributor)
• Format: Article
• Language: English
• Published: Institute of Electrical and Electronics Engineers (IEEE), 2014-10-07T18:19:28Z.
• Subjects: Article
• Online Access: Get fulltext

 We present an approach to position k servers (e.g. mobile robots) to provide a service to n independently moving clients; for example, in mobile ad-hoc networking applications where inter-agent distances need to be minimized, connectivity constraints exist between servers, and no a priori knowledge of the clients' motion can be assumed. Our primary contribution is an algorithm to compute and maintain a small representative set, called a kinematic coreset, of the n moving clients.We prove that, in any given moment, the maximum distance between the clients and any set of k servers is approximated by the coreset up to a factor of (1 ± ε), where ε > 0 is an arbitrarily small constant. We prove that both the size of our coreset and its update time is polynomial in k log(n)/ε. Although our optimization problem is NP-hard (i.e., takes time exponential in the number of servers to solve), solving it on the small coreset instead of the original clients results in a tractable controller. The approach is validated in a small scale hardware experiment using robot servers and human clients, and in a large scale numerical simulation using thousands of clients.