Mohamed I. El-Hawwary

Distributed Circular Formation Stabilization for Dynamic Unicycles

This paper investigates the problem of designing distributed control laws making a group of dynamic unicycles converge to a common circle of prespecified radius, whose center is stationary but dependent on the initial conditions, and travel around the circle in a desired direction. The vehicles are required to converge to a formation on the circle, expressed by desired separations and ordering of the unicycles. The information exchange between unicycles is modelled by a directed graph which is assumed to have a spanning tree. A hierarchical approach is proposed which simplifies the control design by decoupling the problem of making the unicycles converge to a common circle from the problem of stabilizing the formation.

Reduction Principles and the Stabilization of Closed Sets for Passive Systems

In this technical note, we explore the stabilization of closed invariant sets for passive systems, and present conditions under which a passivity-based feedback asymptotically stabilizes the goal set. Our results rely on novel reduction principles allowing one to extrapolate the properties of stability, attractivity, and asymptotic stability of a dynamical system from analogous properties of the system on an invariant subset of the state space.

Global path following for the unicycle and other results

We address the maneuver regulation of the kinematic unicycle to a circle. Our control approach is passivity-based, and we frame the control design objective as a set stabilization problem. We present two main results. First, we provide a smooth, time-invariant, static feedback that globally asymptotically stabilizes the motion on the circle in a desired direction and constant velocity. Second, we provide a smooth time-varying feedback that almost globally asymptotically stabilizes the set of configurations corresponding to the unicycle centre of mass on the circle with desired heading on the circle.

Case studies on passivity-based stabilisation of closed sets

We present a novel control design procedure for the passivity-based stabilisation of closed sets which leverages recent theoretical advances. The procedure involves using part of the control freedom in order to enforce a detectability property, while the remaining part is used for passivity-based stabilisation. The procedure is illustrated in four case studies of path following coordination for one or two kinematic unicycles, and variations of these problems. Among other things, we present a smooth global path following controller making the unicycle converge to an arbitrary closed and strictly convex curve, and a coordinated path following controller for two unicycles.

Passivity-based stabilization of non-compact sets

We investigate the stabilization of closed sets for passive nonlinear systems which are contained in the zero level set of the storage function.

A set stabilization approach for circular formations of rigid bodies

The paper presents a set stabilizing framework for distributed control design to achieve circular formations for rigid bodies in three-dimensional Euclidean space. Information exchange between the rigid bodies is modeled by a directed graph which is assumed to have a spanning tree. Actuation scenarios of fully actuated, degree-one underactuated, and degree-two underactuated rigid bodies are addressed. Control design is based on a hierarchical approach that relies on a reduction principle for asymptotic stability of closed sets.

Distributed circular formation stabilization of unicycles part I: Undirected information flow graph

We investigate the following problem: design a distributed control law making n kinematic unicycles converge to a common circle of prespecified radius, whose centre is stationary but dependent on the initial conditions, and traverse the circle in a desired direction. Moreover, the vehicles are required to converge to a formation on the circle, expressed by desired separations and ordering of the unicycles. We present a solution for the case when the information flow graph is undirected. In part II of this paper we generalize the solution to the case of arbitrary information flow graphs, and to the case of dynamic unicycles.

Distributed circular formation stabilization of unicycles part II: Arbitrary information flow graph

In part I of this paper we presented a solution to the circular formation stabilization problem of kinematic unicycles when the information flow graph is undirected. This paper extends the results of part I in two directions. First, we present a control law that solves the circular formation stabilization problem when the information flow is described by an arbitrary directed graph with a globally reachable node. Second, we generalize our results to the case when the unicycles are dynamic.

Stabilization of closed sets for passive systems, part II: Passivity-based control

In this paper we explore the stabilization of closed invariant sets for passive systems, and present conditions under which a passivity-based feedback makes the set stable, semi-attractive, or semi-asymptotically stable for the closed-loop system. Our results rely on novel reduction principles, presented in Part I of this work. As an application of the theory, we present a coordination problem for two unicycles.

Stabilization of closed sets for passive systems, part I: Reduction principles

Given an unforced nonlinear system and two nested closed and invariant sets ¿ ¿ O, we present reduction principles allowing one to extrapolate the properties of stability, attractivity, and asymptotic stability of ¿ from analogous properties of the system restricted to O. As a corollary to our reduction principles, we present a stability criterion for cascade-connected systems which generalizes well-known results in the literature. Using the reduction principles, in Part II of this paper we present a comprehensive theory for passivity-based stabilization of closed sets.