Risk-aware UAV-UGV Rendezvous with Chance-Constrained Markov Decision Process

We study a chance-constrained variant of the cooperative aerial-ground vehicle routing problem, in which an Unmanned Aerial Vehicle (UAV) with limited battery capacity and an Unmanned Ground Vehicle (UGV) that can also act as a mobile recharging station need to jointly accomplish a mission such as monitoring a set of points. Due to the limited battery capacity of the UAV, two vehicles sometimes have to deviate from their task to rendezvous and recharge the UAV. Unlike prior work that has focused on the deterministic case, we address the challenge of stochastic energy consumption of the UAV. We are interested in finding the optimal policy that decides when and where to rendezvous such that the expected travel time of the UAV is minimized and the probability of running out of charge is less than a user-defined tolerance. We formulate this problem as a Chance Constrained Markov Decision Process (CCMDP), which can be equivalently transformed into a Constrained Markov Decision Process (CMDP). To the best knowledge of the authors, this is the first CMDP-based formulation for the UAVUGV routing problems under power consumption uncertainty. We adopt a Linear Programming (LP) based approach to solve the problem optimally. We demonstrate the effectiveness of our formulation in the context of an Intelligence Surveillance and Reconnaissance (ISR) mission.