Feasible Region-Based System Identification Using Duality

We consider the problem of estimating bounds on parameters that represent tasks being performed by robots in a multirobot system. In our previous work, we derived necessary conditions based on persistency of excitation analysis for exact parameter inference to be possible. 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 control synthesis 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 the task parameters of each robot. 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