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This paper considers the problem of parameter identification for a multirobotsystem. We wish to understand when is it feasible for an adversarial observerto reverse-engineer the parameters of tasks being performed by a team of robotsby simply observing their positions. We address this question by using theconcept of persistency of excitation from system identification. Each robot inthe team uses optimization-based controllers for mediating between tasksatisfaction and collision avoidance. These controllers exhibit an implicitdependence on the task's parameters which poses a hurdle for deriving necessaryconditions for parameter identification, since such conditions usually requirean explicit relation. We address this bottleneck by using duality theory andSVD of active collision avoidance constraints and derive an explicit relationbetween each robot's task parameters and its control inputs. This allows us toderive the main necessary conditions for successful identification which agreewith our intuition. We demonstrate the importance of these conditions throughnumerical simulations by using (a) an adaptive observer and (b) an unscentedKalman filter for goal estimation in various geometric settings. Thesesimulations show that under circumstances where parameter inference is supposedto be infeasible per our conditions, both these estimators fail and likewisewhen it is feasible, both converge to the true parameters. Videos of theseresults are available at https://bit.ly/3kQYj5J.

Parameter Identification for Multirobot Systems Using Optimization Based Controllers (Extended Version)