Planning under non-rational perception of uncertain spatial costs

This work investigates the design of risk-perception-aware motion-planning strategies that incorporate non-rational perception of risks associated with uncertain spatial costs. Our proposed method employs the Cumulative Prospect Theory (CPT) to generate a perceived risk map over a given environment. CPT-like perceived risks and path-length metrics are then combined to define a cost function that is compliant with the requirements of asymptotic optimality of sampling-based motion planners (RRT). The modeling power of CPT is illustrated in theory and in simulation, along with a comparison to other risk perception models like Conditional Value at Risk (CVaR). Theoretically, we define a notion of expressiveness for a risk perception model and show that CPT's is higher than that of CVaR and expected risk. We then show that this expressiveness translates to our path planning setting, where we observe that a planner equipped with CPT together with a simultaneous perturbation stochastic approximation (SPSA) method can better approximate arbitrary paths in an environment. Additionally, we show in simulation that our planner captures a rich set of meaningful paths, representative of different risk perceptions in a custom environment. We then compare the performance of our planner with T-RRT (a planner for continuous cost spaces) and Risk-RRT* (a risk-aware planner for dynamic human obstacles) through simulations in cluttered and dynamic environments respectively, showing the advantage of our proposed planner.