  We consider the problem of estimating bounds on parameters representing tasks
being performed by individual robots in a multirobot system. In our previous
work, we derived necessary conditions based on persistency of excitation
analysis for the exact identification of these parameters. We concluded that
depending on the robot's task, the dynamics of individual robots may fail to
satisfy these conditions, thereby preventing exact inference. As an extension
to that work, this paper focuses on estimating bounds on task parameters when
such conditions are not satisfied. Each robot in the team uses
optimization-based controllers for mediating between task satisfaction and
collision avoidance. We use KKT conditions of this optimization and SVD of
active collision avoidance constraints to derive explicit relations between
Lagrange multipliers, robot dynamics, and task parameters. Using these
relations, we are able to derive bounds on each robot's task parameters.
Through numerical simulations, we show how our proposed region based
identification approach generates feasible regions for parameters when a
conventional estimator such as a UKF fails. Additionally, empirical evidence
shows that this approach generates contracting sets which converge to the true
parameters much faster than the rate at which a UKF based estimate converges.
Videos of these results are available at https://bit.ly/2JDMgeJ
