Mireille E. Broucke

Stabilisation of infinitesimally rigid formations of multi-robot networks

This article considers the design of a formation control for multivehicle systems that uses only local information. The control is derived from a potential function based on an undirected infinitesimally rigid graph that specifies the target formation. A potential function is obtained from the graph, from which a gradient control is derived. Under this controller the target formation becomes a manifold of equilibria for the multivehicle system. It is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold. A complete study of the stability of the regular polygon formation is presented and results for directed graphs are presented as well. Finally, the controller is validated experimentally.

Local control strategies for groups of mobile autonomous agents

The problem is studied of achieving a specified formation among a group of mobile autonomous agents by distributed control. If convergence to a point is feasible, then more general formations are achievable too, so the focus is on convergence to a point (the agreement problem). Three formation strategies are studied and convergence is proved under certain conditions. Also, motivated by the question of whether collisions occur, formation evolution is studied.

Pursuit formations of unicycles

In this paper, the stability of equilibrium formations for multiple unicycle systems in cyclic pursuit is studied in detail. The cyclic pursuit setup is particularly simple in that each unicycle i pursues only one other unicycle, unicycle i+1 (modulo n), where n is the number of unicycles. This research is principally motivated by the historical development of pursuit problems found in the mathematics and science literature, which dates as far back as 1732 and yet continues to be of current interest. On the other hand, it is anticipated that the analytical techniques and solutions pertaining to these problems will prove relevant to the study of multiagent systems and in cooperative control engineering.

Brief A hierarchical cyclic pursuit scheme for vehicle networks

The agreement problem is studied whereby a group of mobile agents achieves convergence to a common point. A hierarchical cyclic pursuit scheme is introduced, and it is shown that this scheme yields a very significant increase in the rate of convergence to a common point when compared to traditional cyclic pursuit. A second scheme is introduced in which there are more communication links between vehicles. It is shown that this scheme produces a rate of convergence greater than the traditional scheme but significantly less than the hierarchical scheme.

Necessary and sufficient conditions for reachability on a simplex

The reachability problem has received significant attention in the hybrid control literature with many questions still left unanswered. In this paper we solve the general problem of reaching a set of facets of an n-dimensional simplex in finite time, for a system evolving with linear affine dynamics. Necessary and sufficient conditions are presented in the form of inequalities on the vertices of the simplex, and a linear affine controller is constructed that solves the reachability problem.

A fault tolerant control architecture for automated highway systems

A hierarchical controller for dealing with faults and adverse environmental conditions on an automated highway system is proposed. The controller extends a previous control hierarchy designed to work under normal conditions of operation. The faults are classified according to the capabilities remaining on the vehicle or roadside after the fault has occurred. Information about these capabilities is used by supervisors in each of the layers of the hierarchy to select appropriate fault handling strategies. We outline the strategies needed by the supervisors and give examples of their detailed operation.

Curve Shortening and the Rendezvous Problem for Mobile Autonomous Robots

If a smooth, closed, and embedded curve is deformed along its normal vector field at a rate proportional to its curvature, it shrinks to a circular point. This curve evolution is called Euclidean curve shortening and the result is known as the Gage-Hamilton-Grayson theorem. Motivated by the rendezvous problem for mobile autonomous robots, we address the problem of creating a polygon shortening flow. A linear scheme is proposed that exhibits several analogues to Euclidean curve shortening: The polygon shrinks to an elliptical point, convex polygons remain convex, and the perimeter of the polygon is monotonically decreasing.

Reach Control on Simplices by Continuous State Feedback

This paper studies a theoretical problem of whether continuous state feedback and affine feedback are equivalent from the point of view of making an affine system defined on a simplex reach a prespecified facet in finite time. We show that the two classes of feedbacks are equivalent. As a byproduct, new necessary and sufficient conditions for solvability based more directly on the problem data are obtained.

Experiments in Multirobot Coordination

Abstract Consequent to previously published theoretical work by Marshall, Broucke, and Francis, this paper summarizes the apparatus and results of multirobot coordination experiments conducted at the University of Toronto Institute for Aerospace Studies. These experiments successfully demonstrate the practicality of cyclic pursuit as a distributed control strategy for multiple wheeled-robot systems. The pursuit-based coordination algorithm was found to be surprisingly robust in the presence of unmodelled dynamics and delays due to sensing and information processing. Moreover, the findings of this research not only bode well for continuing research on pursuit-based coordination strategies, but also for other cooperative multirobot control techniques employing similar local interactions.

A geometric approach to bisimulation and verification of hybrid systems

The paper opens up avenues for applying model checking algorithms to the verification of safety problems for hybrid systems consisting of coordinating autonomous agents, and especially hybrid systems where the continuous level is a model of the kinematic dynamics. There are some limitations and obstacles to be overcome. First, it is likely that model checking will still be a computationally expensive tool. Initially, the number of autonomous agents will be small and the continuous dynamics will be low-dimensional, at least until further breakthroughs appear on this frontier. The approach becomes more interesting when more of the burden of control can be placed at the logic level, for the performance of model checking is relatively unaffected by the number of states of the automaton. Some work that remains to be done is obtaining the approximate automaton automatically, given the analytical representation of its bisimulation, and to characterize the robustness of the reach set to model variations.