Abstract-This paper describes how a network of interacting timed automata can be used to model, analyze, and verify motion planning problems in a scenario with multiple robotic vehicles. The method presupposes an infra-structure of robots with feedback controllers obeying simple restriction on a planar grid. The automata formalism merely presents a high-level model of environment, robots and control, but allows composition and formal symbolic reasoning about coordinated solutions. Composition is achieved through synchronization, and the verification software UPPAAL is used for a symbolic verification against specification requirements formulated in computational tree logic (CTL). In this way, all feasible trajectories that satisfy specifications and which moves the robots from a set of initial positions to a set of desired goal positions may be algorithmically analyzed. The trajectories can then subsequently be used as a high-level motion plan for the robots. This paper reports on the timed automata framework, results of two verification experiments, promise of the approach, and gives a perspective for future research.
We propose a framework for the coordination of a network of robots with respect to formal requirement specifications expressed in temporal logics. A regular tessellation is used to partition the space of interest into a union of disjoint regular and equal cells with finite facets, and each cell can only be occupied by a robot or an obstacle. Each robot is assumed to be equipped with a finite collection of continuous-time nonlinear closed-loop dynamics to be operated in. The robot is then modeled as a hybrid automaton for capturing the finitely many modes of operation for either staying within the current cell or reaching an adjacent cell through the corresponding facet. By taking the motion capabilities into account, a bisimilar discrete abstraction of the hybrid automaton can be constructed. Having the two systems bisimilar, all properties that are expressible in temporal logics such as Linear-time Temporal Logic, Computation Tree Logic, and µ-calculus can be preserved. Motion planning can then be performed at a discrete level by considering the parallel composition of discrete abstractions of the robots with a requirement specification given in a suitable temporal logic. The bisimilarity ensures that the discrete planning solutions are executable by the robots. For demonstration purpose, a finite automaton is used as the abstraction and the requirement specification is expressed in Computation Tree Logic. The model checker Cadence SMV is used to generate coordinated verified motion planning solutions. Two autonomous aerial robots are used to demonstrate how the proposed framework may be applied to solve coordinated motion planning problems.
This paper suggests nonlinear attitude control of the Danish satellite Rømer. This satellite will be designed to fulfil two scientific objectives: The observation of stellar oscillations and the detection and localisation of gamma-ray bursts. The satellite will be equipped with a tetrahedron configuration of Wide Angle Telescopes for Cosmic Hard x-rays (WATCH), that serves the dual purpose of X-ray detectors and momentum wheels. By employing passivity theory it is shown, that the satellite is a passive system. This paper shows, that global asymptotic stability can be obtained with a passive and an input and output strictly passive system in a feedback interconnection. It is demonstrated in a simulation study that the resultant controller has a potential for on-board implementation in the acquisition phase, where global stability of the control law is vital.
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