Kyoung-Dae Kim

Kyoung-Dae Kim, Sayan Mitra, P. R. Kumar

We define a special class of hybrid automata, called Deterministic and Transversal Linear Hybrid Automata (DTLHA), whose continuous dynamics in each location are linear time-invariant (LTI) with a constant input, and for which every discrete transition up to a given bounded time is deterministic and, importantly, transversal. For such a DTLHA starting from an initial state, we show that it is possible to compute an approximation of the reach set of a DTLHA over a finite time interval that is arbitrarily close to the exact reach set, called a bounded epsilon-reach set, through sampling and polyhedral over-approximation of sampled states. We propose an algorithm and an attendant architecture for the overall bounded epsilon-reach set computation process.

Qiang Lu, Kyoung-Dae Kim

In this paper, we address a problem of safe and efficient intersection crossing traffic management of autonomous and connected ground traffic. Toward this objective, we propose an algorithm that is called the Discrete-time occupancies trajectory based Intersection traffic Coordination Algorithm (DICA). We first prove that the basic DICA is deadlock free and also starvation free. Then, we show that the basic DICA has a computational complexity of $\mathcal{O}(n^2 L_m^3)$ where $n$ is the number of vehicles granted to cross an intersection and $L_m$ is the maximum length of intersection crossing routes. To improve the overall computational efficiency of the algorithm, the basic DICA is enhanced by several computational approaches that are proposed in this paper. The enhanced algorithm has the computational complexity of $\mathcal{O}(n^2 L_m \log_2 L_m)$. The improved computational efficiency of the enhanced algorithm is validated through simulation using an open source traffic simulator, called the Simulation of Urban MObility (SUMO). The overall throughput as well as the computational efficiency of the enhanced algorithm are also compared with those of an optimized traffic light control.