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37
Necessary and sufficient graphical conditions for formation control of unicycles
, 2005
"... The feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control. The directed graph defined by the information flow plays a key role. It is proved that formation stabilization to a point is feasible if and only if the sensor d ..."
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Cited by 126 (5 self)
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The feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control. The directed graph defined by the information flow plays a key role. It is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node. A similar result is given for formation stabilization to a line and to more general geometric arrangements.
Natural frames and interacting particles in three dimensions
, 2005
"... Abstract — Motivated by the problem of formation control for vehicles moving at unit speed in threedimensional space, we are led to models of gyroscopically interacting particles, which require the machinery of curves and frames to describe and analyze. A Lie group formulation arises naturally, and ..."
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Cited by 43 (11 self)
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Abstract — Motivated by the problem of formation control for vehicles moving at unit speed in threedimensional space, we are led to models of gyroscopically interacting particles, which require the machinery of curves and frames to describe and analyze. A Lie group formulation arises naturally, and we discuss the general problem of determining (relative) equilibria for arbitrary Ginvariant controls (where G = SE(3) is a symmetry group for the control law). We then present global convergence (and noncollision) results for specific twovehicle interaction laws in three dimensions, which lead to specific formations (i.e., relative equilibria). Generalizations of the interaction laws to n vehicles is also discussed, and simulation results presented. I.
Steering laws for motion camouflage
, 2006
"... Motion camouflage is a stealth strategy observed in nature. We formulate the problem as a feedback system for particles moving at constant speed, and define what it means for the system to be in a state of motion camouflage. (Here, we focus on the planar setting, although the results can be generali ..."
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Cited by 28 (11 self)
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Motion camouflage is a stealth strategy observed in nature. We formulate the problem as a feedback system for particles moving at constant speed, and define what it means for the system to be in a state of motion camouflage. (Here, we focus on the planar setting, although the results can be generalized to threedimensional motion.) We propose a biologically plausible feedback law, and use a highgain limit to prove the accessibility of a motioncamouflage state in finite time. We discuss connections to work in missile guidance. We also present simulation results to explore the performance of the motioncamouflage feedback law for a variety of settings.
Collective Motion: Bistability and Trajectory Tracking
 in Proc. 43rd IEEE Conf. Decision and Control
, 2004
"... Abstract — This paper presents analysis and application of steering control laws for a network of selfpropelled, planar particles. We explore together the two stably controlled group motions, parallel motion and circular motion, for modeling and design purposes. We show that a previously considered ..."
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Cited by 27 (9 self)
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Abstract — This paper presents analysis and application of steering control laws for a network of selfpropelled, planar particles. We explore together the two stably controlled group motions, parallel motion and circular motion, for modeling and design purposes. We show that a previously considered control law simultaneously stabilizes both parallel and circular group motion, leading to bistability and hysteresis. We also present behavior primitives that enable piecewiselinear network trajectory tracking. I.
Coordinated patterns of unit speed particles on a closed curve
 Syst. Control Lett
, 2007
"... We present methods to stabilize a class of motion patterns for unit speed particles in the plane. From their initial positions within a compact set in the plane, all particles converge to travel along a closed curve. The relative distance between each pair of particles along the curve is measured us ..."
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Cited by 24 (8 self)
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We present methods to stabilize a class of motion patterns for unit speed particles in the plane. From their initial positions within a compact set in the plane, all particles converge to travel along a closed curve. The relative distance between each pair of particles along the curve is measured using the relative arclength between the particles. These distances are controlled to converge to constant values.
Group coordination and cooperative control of steered particles
 in the plane,” Lecture Notes in control and Information Sciences
, 2006
"... Summary. The paper overviews recent and ongoing efforts by the authors to develop a design methodology to stabilize isolated relative equilibria in a kinematic model of identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all p ..."
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Cited by 15 (7 self)
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Summary. The paper overviews recent and ongoing efforts by the authors to develop a design methodology to stabilize isolated relative equilibria in a kinematic model of identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles about the same center with fixed relative headings. 1
Graph Laplacian and Lyapunov design of collective planar motions
 in Proc. Int. Symp. NOLTA
, 2005
"... Abstract—In recent work, the authors have proposed a Lyapunov design to stabilize isolated relative equilibria in a kinematic model of identical alltoall coupled particles moving in the plane at unit speed. This note presents an extension of these results to arbitrary connected topologies by consi ..."
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Cited by 8 (4 self)
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Abstract—In recent work, the authors have proposed a Lyapunov design to stabilize isolated relative equilibria in a kinematic model of identical alltoall coupled particles moving in the plane at unit speed. This note presents an extension of these results to arbitrary connected topologies by considering a general family of quadratic Lyapunov functions induced by the Laplacian matrix of the communication graph. 1.
Distributed Control of Spacecraft Formation via Cyclic Pursuit: Theory and Experiments
"... Abstract — In this paper we study distributed control policies for spacecraft formations that draw inspiration from the simple idea of cyclic pursuit. First, we extend existing cyclicpursuit control laws devised for singleintegrator models in two dimensions to the case of doubleintegrator models i ..."
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Cited by 7 (0 self)
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Abstract — In this paper we study distributed control policies for spacecraft formations that draw inspiration from the simple idea of cyclic pursuit. First, we extend existing cyclicpursuit control laws devised for singleintegrator models in two dimensions to the case of doubleintegrator models in three dimensions. In particular, we develop control laws that only require relative measurements of position and velocity with respect to the two leading neighbors in the ring topology of cyclic pursuit, and allow the spacecraft to converge to a variety of symmetric formations, including evenly spaced circular formations and evenly spaced Archimedes ’ spirals. Second, we discuss potential applications, including spacecraft coordination for interferometric imaging and convergence to zeroeffort orbits. Finally, we present and discuss experimental results obtained by implementing the aforementioned control laws on three nanospacecraft on board the International Space Station. I.
Lyapunov vector fields for autonomous uav flight control
, 2008
"... General techniques for constructing vector fields for UAV guidance are provided that incorporate Lyapunov stability properties to produce simple, globally stable vector fields in 3D. Use of these fields in circular loiter patterns is illustrated, along with simple switching algorithms for circular l ..."
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Cited by 5 (1 self)
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General techniques for constructing vector fields for UAV guidance are provided that incorporate Lyapunov stability properties to produce simple, globally stable vector fields in 3D. Use of these fields in circular loiter patterns is illustrated, along with simple switching algorithms for circular loiter vector fields to enable following of arbitrary way point paths or loops. Another variation is also developed, where a simple circular loiter is warped into other shapes, preserving global stability guarantees and accurate path tracking. An example of this technique is provided that produces a “racetrack ” loiter pattern, and three different variations in the warping technique are compared. Finally, tracking of the vector field is considered, using Lyapunov techniques to show global stability of heading and path position for several types of tracking control laws that are compatible with low cost UAV avionics. Nomenclature r = UAV position vector relative to an inertial reference frame ()z,y,x = Inertial frame coordinates of r ()ooo zyx,, = Loiter circle center
Symmetry and Reduction for Coordinated Rigid Bodies
"... Motivated by interest in the collective behavior of autonomous agents, we lay foundations for a study of networks of rigid bodies and, specifically, the problem of aligning orientation and controlling relative position across the group. Our main result is the reduction of the (networked) system in t ..."
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Cited by 3 (0 self)
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Motivated by interest in the collective behavior of autonomous agents, we lay foundations for a study of networks of rigid bodies and, specifically, the problem of aligning orientation and controlling relative position across the group. Our main result is the reduction of the (networked) system in the case that two individuals are coupled by control inputs that depend only on relative configuration. We use reduction theory based on semidirect products, yielding Poisson spaces that enable efficient formulation of control laws. We apply these reduction results to satellite and underwater vehicle dynamics, proving stability of coordinated behaviors such as the case of two underwater vehicles moving at constant speed with their orientations stably aligned. 1