Feasible Region-based Identification Using Duality (Extended Version)

TL;DR

This paper introduces a novel method for estimating bounds on robot task parameters using duality and optimization conditions, especially when traditional methods like UKF fail, leading to faster convergence.

Contribution

It extends previous work by deriving explicit bounds on task parameters through KKT conditions and SVD, enabling feasible region-based identification in complex multirobot systems.

Findings

Proposed method generates feasible parameter regions where UKF fails.

The approach produces contracting sets that converge faster to true parameters.

Numerical simulations validate the effectiveness of the region-based identification.

Abstract

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