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Hamilton-Jacobi (HJ) reachability is a method that provides rigorous analyses of the safety properties of dynamical systems. These guarantees can be provided by the computation of a backward reachable set (BRS), which represents the set of states from which the system may be driven into violating safety properties despite the system's best effort to remain safe. Unfortunately, the complexity of the...
Multi-UAV systems are safety-critical, and guarantees must be made to ensure no unsafe configurations occur. Hamilton-Jacobi (HJ) reachability is ideal for analyzing such safety-critical systems; however, its direct application is limited to small-scale systems of no more than two vehicles due to an exponentially-scaling computational complexity. Previously, the sequential path planning (SPP) method,...
Objective: Movements made by healthy individuals can be characterized as superpositions of smooth bell-shaped velocity curves. Decomposing complex movements into these simpler “submovement” building blocks is useful for studying the neural control of movement as well as measuring motor impairment due to neurological injury. Approach: One prevalent strategy to submovement decomposition is to formulate...
We consider the problem of planning trajectories for a group of N vehicles, each aiming to reach its own target set while avoiding danger zones of other vehicles. The analysis of problems like this is extremely important practically, especially given the growing interest in utilizing unmanned aircraft systems for civil purposes. The direct solution of this problem by solving a single-obstacle Hamilton-Jacobi-Isaacs...
In recent years, there has been a growing need for location-based services (LBS), ranging from resource tracking to personal life assistance. The Moving k Nearest Neighbor (MkNN) query is a main problem in the LBS area, which retrieves the top k nearest neighbors while the query consumer moves. Considerable attention is attracted to this query type and a large number of studies are proposed recently...
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