Error characterization in the vicinity of singularities in multi-robot cluster space control

The cluster space control technique promotes simplified specification and monitoring of the motion of mobile multi-robot systems of limited size. Previous work has established the conceptual foundation of this approach and has experimentally verified and validated its use for 2-robot, 3-robot and 4-robot systems, with varying implementations ranging from automated trajectory control to human-in-the-loop piloting. In this publication, we review the cluster space framework and its application to a 3-robot system and present the problem of robot space to cluster space error propagation and its impact on cluster position uncertainty and control performance. A theoretical formulation of cluster position error is presented. Using a 3-robot system testbed, the results are verified through experimental measurements. The cluster space Jacobian matrix condition number is proposed as a metric for acceptable cluster configuration errors.