George J. Pappas

Flocking in Fixed and Switching Networks

This note analyzes the stability properties of a group of mobile agents that align their velocity vectors, and stabilize their inter-agent distances, using decentralized, nearest-neighbor interaction rules, exchanging information over networks that change arbitrarily (no dwell time between consecutive switches). These changes introduce discontinuities in the agent control laws. To accommodate for arbitrary switching in the topology of the network of agent interactions we employ nonsmooth analysis. The main result is that regardless of switching, convergence to a common velocity vector and stabilization of inter-agent distances is still guaranteed as long as the network remains connected at all times

Discrete abstractions of hybrid systems

A hybrid system is a dynamical system with both discrete and continuous state changes. For analysis purposes, it is often useful to abstract a system in a way that preserves the properties being analysed while hiding the details that are of no interest. We show that interesting classes of hybrid systems can be abstracted to purely discrete systems while preserving all properties that are definable in temporal logic. The classes that permit discrete abstractions fall into two categories. Either the continuous dynamics must be restricted, as is the case for timed and rectangular hybrid systems, or the discrete dynamics must be restricted, as is the case for o-minimal hybrid systems. In this paper, we survey and unify results from both areas.

Conflict resolution for air traffic management: a study in multiagent hybrid systems

Air traffic management (ATM) of the future allows for the possibility of free flight, in which aircraft choose their own optimal routes, altitudes, and velocities. The safe resolution of trajectory conflicts between aircraft is necessary to the success of such a distributed control system. In this paper, we present a method to synthesize provably safe conflict resolution manoeuvres. The method models the aircraft and the manoeuvre as a hybrid control system and calculates the maximal set of safe initial conditions for each aircraft so that separation is assured in the presence of uncertainties in the actions of the other aircraft. Examples of manoeuvres using both speed and heading changes are worked out in detail.

Leader-to-formation stability

The paper investigates the stability properties of mobile agent formations which are based on leader following. We derive nonlinear gain estimates that capture how leader behavior affects the interconnection errors observed in the formation. Leader-to-formation stability (LFS) gains quantify error amplification, relate interconnection topology to stability and performance, and offer safety bounds for different formation topologies. Analysis based on the LFS gains provides insight to error propagation and suggests ways to improve the safety, robustness, and performance characteristics of a formation.

Stable flocking of mobile agents, part I: fixed topology

This is the first of a two-part paper that investigates the stability properties of a system of multiple mobile agents with double integrator dynamics. In this first part we generate stable flocking motion for the group using a coordination control scheme which gives rise to smooth control laws for the agents. These control laws are a combination of attractive/repulsive and alignment forces, ensuring collision avoidance and cohesion of the group and an aggregate motion along a common heading direction. In this control scheme the topology of the control interconnections is fixed and time invariant. The control policy ensures that all agents eventually align with each other and have a common heading direction while at the same time avoid collisions and group into a tight formation.

Stable flocking of mobile agents part I: dynamic topology

This is the second of a two-part paper, investigating the stability properties of a system of multiple mobile agents with double integrator dynamics. In this second part, we allow the topology of the control inter-connections between the agents in the group to vary with time. Specifically, the control law of an agent depends on the state of a set of agents that are within a certain neighborhood around it. As the agents move around this set changes, giving rise to a dynamic control interconnection topology and a switching control law. This control law consists of a combination of attractive/repulsive and alignment forces. The former ensure collision avoidance and cohesion of the group and the latter result to all agents attaining a common heading angle, exhibiting flocking motion. Despite the use of only local information and the time varying nature of agent interaction which affects the local controllers, flocking motion is established, as long as connectivity in the neighboring graph is maintained.

Approximation Metrics for Discrete and Continuous Systems

Established system relationships for discrete systems, such as language inclusion, simulation, and bisimulation, require system observations to be identical. When interacting with the physical world, modeled by continuous or hybrid systems, exact relationships are restrictive and not robust. In this paper, we develop the first framework of system approximation that applies to both discrete and continuous systems by developing notions of approximate language inclusion, approximate simulation, and approximate bisimulation relations. We define a hierarchy of approximation pseudo-metrics between two systems that quantify the quality of the approximation, and capture the established exact relationships as zero sections. Our approximation framework is compositional for a synchronous composition operator. Algorithms are developed for computing the proposed pseudo-metrics, both exactly and approximately. The exact algorithms require the generalization of the fixed point algorithms for computing simulation and bisimulation relations, or dually, the solution of a static game whose cost is the so-called branching distance between the systems. Approximations for the pseudo-metrics can be obtained by considering Lyapunov-like functions called simulation and bisimulation functions. We illustrate our approximation framework in reducing the complexity of safety verification problems for both deterministic and nondeterministic continuous systems

Temporal-Logic-Based Reactive Mission and Motion Planning

This paper provides a framework to automatically generate a hybrid controller that guarantees that the robot can achieve its task when a robot model, a class of admissible environments, and a high-level task or behavior for the robot are provided. The desired task specifications, which are expressed in a fragment of linear temporal logic (LTL), can capture complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, which results in a novel paradigm for sensor-based temporal-logic-motion planning. As one robot is part of the environment of another robot, our sensor-based framework very naturally captures multirobot specifications in a decentralized manner. Our computational approach is based on first creating discrete controllers satisfying specific LTL formulas. If feasible, the discrete controller is then used to guide the sensor-based composition of continuous controllers, which results in a hybrid controller satisfying the high-level specification but only if the environment is admissible.

O-Minimal Hybrid Systems

Abstract. An important approach to decidability questions for verification algorithms of hybrid systems has been the construction of a bisimulation. Bisimulations are finite state quotients whose reachability properties are equivalent to those of the original infinite state hybrid system. In this paper we introduce the notion of o-minimal hybrid systems, which are initialized hybrid systems whose relevant sets and flows are definable in an o-minimal theory. We prove that o-minimal hybrid systems always admit finite bisimulations. We then present specific examples of hybrid systems with complex continuous dynamics for which finite bisimulations exist.

Symbolic planning and control of robot motion [Grand Challenges of Robotics]

In this paper, different research trends that use symbolic techniques for robot motion planning and control are illustrated. As it often happens in new research areas, contributions to this topic started at about the same time by different groups with different emphasis, approaches, and notation. This article tries to describe a framework in which many of the current methods and ideas can be placed and to provide a coherent picture of what the authors want to do, what have they got so far, and what the main missing pieces are. Generally speaking, the aim of symbolic control as is envisioned in this article is to enable the usage of methods of formal logic, languages, and automata theory for solving effectively complex planning problems for robots and teams of robots. The results presented in this article can be divided in two groups: top-down approaches, whereby formal logic tools are employed on rather abstract models of robots; and bottom up approaches, whose aim is to provide means by which such abstractions are possible and effective. The two ends do not quite tie as yet, and much work remains to be done in both directions to obtain generally applicable methods. However, the prospects of symbolic control of robots are definitely promising, and the challenging nature of problems to be solved warrants for the interest of a wide community of researchers