Robust multi-agent collision avoidance through scheduling

We propose a class of computationally efficient algorithms for conflict resolution in the presence of modeling and measurement uncertainties. Specifically, we address a scenario where a number of agents, whose dynamics are possibly nonlinear, must cross an intersection avoiding collisions. We obtain an exact solution and an approximate one with quantified error bound whose complexity scales polynomially with the number of agents.National Science Foundation (U.S.) (Award CNS 0930081)Roberto Rocca Foundatio

Robot planning based on boolean specifications using petri net models

In this paper, we propose an automated method for planning a team of mobile robots such that a Boolean-based mission is accomplished. The task consists of logical requirements over some regions of interest for the agents'' trajectories and for their final states. In other words, we allow combinatorial specifications defining desired final states whose attainment includes visits to, avoidance of, and ending in certain regions. The path planning approach should select such final states that optimize a certain global cost function. In particular, we consider minimum expected traveling distance of the team and reduce congestions. A Petri net (PN) with outputs models the movement capabilities of the team and the regions of interest. The imposed specification is translated to a set of linear restrictions for some binary variables, the robot movement capabilities are formulated as linear constraints on PN markings, and the evaluations of the binary variables are linked with PN markings via linear inequalities. This allows us to solve an integer linear programming problem whose solution yields robotic trajectories satisfying the task

Supervisory control for collision avoidance in vehicular networks using discrete event abstractions

We consider the problem of collision avoidance at vehicular intersections for a set of controlled and uncontrolled vehicles that are linked by wireless communication. Each vehicle is modeled by a first order system. We use a disturbance to account for bounded model uncertainty. We construct a discrete event system abstraction and formulate the problem in the context of supervisory control for discrete event systems with uncontrollable events. This allows us to mitigate computational limitations related to the presence of continuous dynamics and infinite state spaces. For solving the resulting supervisory control problem at the discrete event level, we develop an algorithm that exploits the structure of the transition map to compute the supremal controllable sublanguage more efficiently than standard algorithms. We present implementation results on an intersection with several vehicles.National Science Foundation (U.S.) (Grant CNS-0930081

Discrete Event System Methods for Control Problems Arising in Cyber-physical Systems.

We consider two problems in cyber-physical systems. The first is that of dynamic fault diagnosis. Specifically, we assume that a plant model is available in the form of a discrete event system (DES) containing special fault events whose occurrences are to be diagnosed. Furthermore, it is assumed that there exist sensors that can be turned on or off and are capable of detecting some subset of the system’s non-faulty events. The problem to be solved consists of constructing a compact structure, called the most permissive observer (MPO), containing the set of all sequences of sensor activations that ensure the timely diagnosis of any fault event’s occurrence. We solve this problem by defining an appropriate notion of information state summarizing the information obtained from the past sequence of observations and sensor activations. The resulting MPO has a better space complexity than that of the previous approach in the literature. The second problem considered in this thesis is that of controlling vehicles through an intersection. Specifically, we wish to obtain a supervisor for the vehicles that is safe, non-deadlocking, and maximally permissive. Furthermore, we solve this problem in the presence of uncontrolled vehicles, bounded disturbances in the dynamics, and measurement uncertainty. Our approach consists of discretizing the system in time and space, obtaining a DES abstraction, solving for maximally permissive supervisors in the abstracted domain, and refining the supervisor to one for the original, continuous, problem domain. We provide general results under which this approach yields maximally permissive memoryless supervisors for the original system and show that, under certain conditions, the resulting supervisor will be maximally permissive over the class of all supervisors, not merely memoryless ones. Our contributions are as follows. First, by constructing DES abstractions from continuous systems, we can leverage the supervisory control theory of DES, which is well-suited to finding maximally permissive supervisors under safety and non-blocking constraints. Second, we define different types of relations between transition systems and their abstractions and, for each relation, characterize the class of supervisors over which the supervisors obtained under our approach are maximally permissive.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108720/1/edallal_1.pd