System Identification for Safe Controllers using Inverse Optimization

Abstract

This paper presents algorithms for learning parameters of optimization-based controllers used in multiagent systems based on their position-velocity measurements. The motivation to learn these parameters stems from the need to infer an agent’s intent (human or robot) to facilitate accurate predictions of motion as well as efficient interactions in a multiagent system. In this work, we demonstrate how to perform inference using algorithms based on the theory of inverse optimization (IO). We propose QP-based reformulations of IO algorithms for faster processing of batch-data to facilitate quicker inference. In our prior work, we used persistency of excitation analysis for deriving conditions under which conventional estimators such as a Kalman filter can successfully perform such inference. In this work, we demonstrate that whenever these conditions are violated, inference of parameters will fail, be it using IO-based algorithms or a UKF. We provide numerical simulations to infer desired goal locations and controller gains of each robot in a multirobot system and compare performance of IO-based algorithms with a UKF and an adaptive observer. In addition to these, we also conduct experiments with Khepera-4 robots and demonstrate the power of IO-based algorithms in inferring goals in the presence of perception noise.