Risk-Perception-Aware Control Design Under Dynamic Spatial Risks

This letter 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. Using these sets, we define novel notions of “inclusiveness” and “versatility” which can be employed to compare and evaluate any risk models in the context of RPA safety-critical controls. We then prove that CPT is the most “inclusive” and “versatile” model w.r.t. Conditional Value at Risk (CVaR) and Expected Risk (ER). Given a RPM, we construct a class of Control Barrier Functions (CBFs) and generate perceived-safety-critical controls using a Quadratic Program (QP) to guide an agent safely to a goal. For a class of truncated-Gaussian costs, we provide sufficient geometric conditions for the above QP to be feasible. We also prove that CPT-equipped RPA controller has both a larger feasible control set and more accurate stabilization w.r.t CVaR and ER models. We present simulations in a 2D environment to illustrate the proposed controller.