This paper considers a reach-avoid game on a rectangular domain with two defenders and one attacker. The attacker aims to reach a specified edge of the game domain boundary, while the defenders strive to prevent that by capturing the attacker. First, we are concerned with the barrier, which is the boundary of the reach-avoid set, splitting the state space into two disjoint parts: 1) defender dominance region (DDR) and 2) attacker dominance region (ADR). For the initial states lying in the DDR, there exists a strategy for the defenders to intercept the attacker regardless of the attacker's best effort, while for the initial states lying in the ADR, the attacker can always find a successful attack strategy. We propose an attack region method to construct the barrier analytically by employing Voronoi diagram and Apollonius circle for two kinds of speed ratios. Then, by taking practical payoff functions into considerations, we present optimal strategies for the players when their initial states lie in their winning regions, and show that the ADR is divided into several parts corresponding to different strategies for the players. Numerical approaches, which suffer from inherent inaccuracy, have already been utilized for multiplayer reach-avoid games, but computational complexity complicates solving such games and consequently hinders efficient on-line applications. However, this method can obtain the exact formulation of the barrier and is applicable for real-time updates.
This work considers a multiplayer reach-avoid game between two adversarial teams in a general convex domain which consists of a target region and a play region. The evasion team, initially lying in the play region, aims to send as many its team members into the target region as possible, while the pursuit team with its team members initially distributed in both play region and target region, strives to prevent that by capturing the evaders. We aim at investigating a task assignment about the pursuer-evader matching, which can maximize the number of the evaders who can be captured before reaching the target region safely when both teams play optimally. To address this, two winning regions for a group of pursuers to intercept an evader are determined by constructing an analytical barrier which divides these two parts. Then, a task assignment to guarantee the most evaders intercepted is provided by solving a simplified 0-1 integer programming instead of a non-deterministic polynomial problem, easing the computation burden dramatically. It is worth noting that except the task assignment, the whole analysis is analytical. Finally, simulation results are also presented.
In this paper, a distributed velocity sensor fault diagnosis scheme is presented for a formation of a second-order multi-agent system with unknown constant communication time delays. An existing distributed proportion-derivation (DPD) formation control law is adopted and a delay-independent condition is proposed to guarantee the asymptotical formation stability of the formation system based on the Nyquist stability criterion. Then a distributed fault diagnosis scheme is developed. In each agent, a distributed fault detection residual generator (DFDRG) and a bank of distributed fault isolation residual generators (DFIRGs) are designed based on the closed-loop model of the whole system. Each DFIRG is built up on the basis of a reduced-order unknown input observer (UIO) which is robust to the fault of one neighboring agent. According to the robust relationship between DFIRGs and faults, distributed fault isolation can be achieved. Conditions are presented to guarantee that each agent is able to diagnose faults of itself and its neighbors despite the disturbance of time delays. Finally, outdoor experimental results illustrate the effectiveness of the proposed schemes.
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