Distributed Autonomous Systems (Benchmark Proposal)

This benchmark suite consists of a number of examples of autonomous multi-agent systems where the agent number ranges from two to ten. The benchmarks are derived from the field of position-based formation control in autonomous robotics and vehicles. Their models are given as network of hybrid automata in the SpaceEx XML model format and can be transformed to other verification tools model formats using HyST, a model transformation tool. Safety of a small benchmark with two agents is analyzed using SpaceEx. Category: academic Difficulty: low through challenge 1 Context and Origins Intelligent autonomous systems have been a “hot” research topic for many years because of its rigorous application domains such as robotics, unmanned aerial vehicles (UAV), autonomous cars and sensors networks. The challenges in modeling, analysis, design and testing a such intelligent system have attracted researchers from different disciplines such as biology, computer, communication and control. In an early step, the intelligent behavior called “flocking behavior” of a group of animals such as bird, insect and fish has been investigated deeply over decades in the field of biology [1]. The behavior has been first modeled and simulated using computer in [2]. This work has inspired a new field of modeling, control and design for autonomous systems which is now considerably an important topic for the next generation of modern technology. Consensus and formation controls are two fundamental problems in designing an autonomous system that perform an intelligent behavior. Control scientists have proposed numerous protocols over last decades to drive the system to achieve some control objectives [3–9]. Generally, to perform a specific task, the agents need to exchange their information and cooperate with each other over communication channel. The communication topology of an autonomous system describes in detail how the information flow in the system. The communication topology can be static, i.e. does not change over times, or dynamics, i.e. may change over times. It can also be directed, i.e. information flows in one direction over a connection between two agents, or undirected, i.e. the information flows in both directions over a connection between two agents. The communication topology expresses the sensing and communicating capacities of the agents which affect significantly to the stability, controllability and the convergence of an autonomous system. Graph theory has been proved as an powerful tool to model the communication topology and analyze the controllability of autonomous systems [10]. G.Frehse and M.Althoff (eds.), ARCH17 (EPiC Series in Computing, vol. XXX), pp. 1–12 Autonomous Multi-Agent Systems H-D. Tran, L.V. Nguyen, Weiming Xiang and Taylor T. Johnson Formation control for autonomous systems [7–9] is seeking control laws to guarantee that the agents move to pre-determined positions while keeping the system formation in some specific shapes when moving. Depending on the sensing and communicating capacities of the agents, i.e. the communication topology, the formation control strategies can be categorized into positionbased, displacement-based and distance-based approaches [11]. One essential safety requirement for the system is that there is no collision when the agents are moving. These formation control strategies have shown informally the ability of the agents avoiding collision via simulation-based testing. To guarantee the safety of the system, its formal model need to be given and verified using formal verification techniques. Toward safety and liveness requirements of autonomous systems, some control algorithms have been proposed and verified using formal verification techniques recently [12, 13]. In this context, the formal model of an autonomous system is given based on discrete time intervals and to guarantee the safety of the system, the controller usually can perform some particular actions to resolve the potential risks coming. The whole system is modeled as a labeled transition system and the safety and liveness requirements are written in form of linear temporal logic (LTL). Inspired by above interesting works, in this paper, we obtain a set of autonomous systems benchmarks written in SpaceEx XML format. Each agent is modeled separately as a single hybrid automaton and the whole system is a network of hybrid automata which is basically a composition of all agents. Different from [12,13], these benchmarks have continuous dynamics. Therefore, their safety requirements can be verified using existing verification tools that support verifying continuous dynamics [14–17]. In addition, when the number of agents increases, the benchmark models become larger that makes them harder to be verified. Thus, our benchmark suite is also useful for testing the scalability of verification tools. The rest of the paper is organized as follows: Section 2 presents the description of an autonomous system including the communication topology, the motion dynamics of the agents and the position-based formation control strategies. Section 3 gives the safety analysis of some small autonomous systems using SpaceEx. Section 4 discusses some interesting issues for the future work and concludes the paper. 2 System descriptions 2.1 Communication topology Directed/undirected graphs are powerful tool for modeling the interaction between agents in an autonomous system. In this benchmark suite, the communication topologies of all autonomous systems are modeled using directed graphs. A digraph (directed graph) defined by a tuple (V, E), where V is a finite non-empty set of vertices and E ∈ V2 is a set of ordered pairs of vertices, called edges. It can be understood that vertice vi ∈ V represents for the i agent an autonomous system and ordered edge (i, j) represents for the interaction between the agent i and the agent j where the information flows from i to j, i.e. agent j receives the information from agent i. To model how much information flows in communication, we use a weighted digraph which can be defined by an adjacency matrix A = [aij ]n×n, where aii = 0, aij > 0 if (j, i) ∈ E and n = |V| is the number of agents in the system. Figure 2.1 illustrates an example of communication topology of an autonomous system with six agents [18]. From the communication topology, it can be seen that one agent only can collect some information from its neighbors, not from all other agents.