  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.
