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This paper presents a real-time trajectory planning framework for Urban Air Mobility (UAM) that is both safe and scalable. The proposed framework employs a decentralized, free-flight concept of operation in which each aircraft independently performs separation assurance and conflict resolution, generating safe trajectories by accounting for the future states of nearby aircraft. The framework consists of two main components: a data-driven reachability analysis tool and an efficient Markov Decision Process (MDP) based decision maker. The reachability analysis over-approximates the reachable set of each aircraft through a discrepancy function learned online from simulated trajectories. The decision maker, on the other hand, uses a 6-degrees-of-freedom guidance model of fixed-wing aircraft to ensure collision-free trajectory planning. Additionally, the proposed framework incorporates reward shaping and action shielding techniques to enhance safety performance. The proposed framework is evaluated through simulation experiments involving up to 32 aircraft in a UAM setting, with performance measured by the number of Near Mid Air Collisions (NMAC) and computational time. The results demonstrate the safety and scalability of the proposed framework.

Ensuring nominal asymptotic stability of the Nonlinear Model Predictive Control controller is not trivial. Stabilizing ingredients such as terminal penalty term and terminal region are crucial in establishing the asymptotic stability. Current work presents alternate approaches namely arbitrary controller based approach and linear quadratic regulator based approach, which provide larger degrees of freedom for enlarging the terminal region as against conservative approaches from the literature. Efficacy of the proposed approaches is demonstrated using benchmark two state continuous stirrer tank reactor system around an unstable operating point. Terminal regions obtained using the arbitrary controller based approach and linear quadratic regulator based approach are approximately 45 and 412 times larger by area measure when compared to the largest terminal region obtained using the approach from the literature. As a result, there is significant reduction in the prediction and control horizon time., Comment: 19 pages, 6 figures, 4 tables. arXiv admin note: substantial text overlap with arXiv:2107.09267

Ensuring nominal asymptotic stability of the Non-linear Model Predictive Control (NMPC) controller is not trivial. Stabilizing ingredients such as terminal penalty term and terminal region are crucial in establishing the asymptotic stability. Approaches available in the literature provide limited degrees of freedom for the characterization of the terminal region for the discrete time Quasi Infinite Horizon NMPC (QIH-NMPC) formulation. Current work presents alternate approaches namely arbitrary controller based approach and LQR based approach, which provide large degrees of freedom for enlarging the terminal region. Both the approaches are scalable to system of any state and input dimension. Approach from the literature provides a scalar whereas proposed approaches provide a linear controller and two additive matrices as tuning parameters for shaping of the terminal region. Proposed approaches involve solving modified Lyapunov equations to compute terminal penalty term, followed by explicit characterization of the terminal region. Efficacy of the proposed approaches is demonstrated using benchmark two state system. Terminal region obtained using the arbitrary controller based approach and LQR based approach are approximately 10.4723 and 9.5055 times larger by area measure when compared to the largest terminal region obtained using the approach from the literature., Comment: 6 pages, 1 figure, 6 tables