Risk-perception-aware control design under dynamic spatial risks

TL;DR

This paper introduces a risk-perception-aware control framework using Cumulative Prospect Theory to model dynamic spatial risks, ensuring safety through perceived risk-based control barrier functions and quadratic programming.

Contribution

It develops a novel CPT-based risk perception model for control design, proving its superiority in inclusiveness and versatility over existing models, and constructs perceived risk control barrier functions for safety guarantees.

Findings

CPT model is most inclusive and versatile for risk perception.

Safety guarantees are achieved for truncated-Gaussian costs.

Simulations demonstrate effective perceived safety control.

Abstract

This work proposes a novel risk-perception-aware (RPA) control design using non-rational perception of risks associated with uncertain dynamic spatial costs. We use Cumulative Prospect Theory (CPT) to model the risk perception of a decision maker (DM) and use it to construct perceived risk functions that transform the uncertain dynamic spatial cost to deterministic perceived risks of a DM. These risks are then used to build safety sets which can represent risk-averse to risk-insensitive perception. We define a notions of "inclusiveness" and "versatility" based on safety sets and use it to compare with other models such as Conditional value at Risk (CVaR) and Expected risk (ER). We theoretically prove that CPT is the most "inclusive" and "versatile" model of the lot in the context of risk-perception-aware controls. We further use the perceived risk function along with ideas from control barrier functions (CBF) to construct a class of perceived risk CBFs. For a class of truncated-Gaussian costs, we find sufficient geometric conditions for the validity of this class of CBFs, thus guaranteeing safety. Then, we generate perceived-safety-critical controls using a Quadratic program (QP) to guide an agent safely according to a given perceived risk model. We present simulations in a 2D environment to illustrate the performance of the proposed controller.