Probabilistic Occupancy via Forward Stochastic Reachability for Markov Jump Affine Systems

• 成果类型: Article
• 署名作者: Vinod, Abraham P.; Oishi, Meeko M. K.
• 署名单位: University of New Mexico; University of Texas System; University of Texas Austin; University of New Mexico
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3014127
• 发表日期: 2021
• 页码: 3068-3083
• 关键词: Probabilistic logic; Markov processes; Collision avoidance; PLANNING; Robot kinematics; Convex Optimization; obstacle avoidance; robotic navigation; stochastic optimal control; stochastic reachability

摘要

Probabilistic occupancy, the likelihood that the state at a known future time lies in a given set, is important in a variety of stochastic motion planning problems. We provide efficient computational techniques, based in Fourier transforms, to characterize the stochasticity of the future state for Markov jump affine systems. This class of systems captures a variety of important dynamics in planning problems, including the Dubins' vehicle. We employ convex optimization to compute outer approximations of the superlevel sets of the probabilistic occupancy function, which is a key for preserving the safety guarantees sought in collision-avoidance problems. In contrast to traditional approaches, our approach does not rely on gridding, recursion, or sampling, accommodates non-Gaussian perturbed dynamics, and affords outer-approximation guarantees. We demonstrate our methods on the target pursuit problem with multiple robots pursuing a nonadversarial target with stochastic dynamics, and on the problem of computing keep-out regions for stochastic collision avoidance of a Dubins' vehicle.