CPI: Conservativeness, Permissiveness and Intervention Metrics for Shared Control Evaluation

This paper presents an approach to measure the ability of a shared control system to track user input while simultaneously ensuring safety. These CPI metrics, based on reachability theory, are used to measure the Conservativeness (C), Permissiveness (P) and the amount of Intervention (I) applied to a user nominal control. The metrics apply to arbitrary dynamic systems, state and control constraints, and unlike other existing metrics, they apply to non-differentiable shared controllers including controllers implemented in procedural code. Moreover, we propose a parallel algorithm based on Rapidly-exploring Random Trees (RRTs) for conducting the reachability analysis necessary for computing conservativeness and permissiveness metrics efficiently. We demonstrate how CPI metrics may be used to evaluate a Linear-Quadratic Regulator (LQR) and two different Model Predictive Controller (MPC) based safe shared controllers applied to the cartpole system, for different control parameters.