Distributed Geodesic Control Laws for Flocking of Nonholonomic Agents

We study the problem of flocking and velocity alignment in a group of kinematic nonholonomic agents in 2 and 3 dimensions. By analyzing the velocity vectors of agents on a circle (for planar motion) or sphere (for 3-D motion), we develop a geodesic control law that minimizes a misalignment potential and results in velocity alignment and flocking. The proposed control laws are distributed and will provably result in flocking when the underlying proximity graph which represents the neighborhood relation among agents is connected. We further show that flocking is possible even when the topology of the proximity graph changes over time, so long as a weaker notion of joint connectivity is preserved

Distributed Geodesic Control Laws for Flocking of Nonholonomic Agents

We study the problem of flocking and coordination of a group of kinematic nonholonomic agents in 2 and 3 dimensions. By analyzing the velocity vectors of agents on a circle (for planar motion) or sphere (for 3D motion), we develop geodesic control laws that minimize a misalignment potential based on graph Laplacians resulting in velocity alignment. The proposed control laws are distributed and will provably result in flocking when the underlying proximity graph which represents the neighborhood relation among agents is connected. Furthermore, we develop a vision based control law that does not rely on heading measurements, but only requires measurement of bearing, optical flow and time-to-collision, all of which can be efficiently measured

Hybrid Flocking Control Algorithm with Application to Coordination between Multiple Fixed-wing Aircraft

Flocking, as a collective behavior of a group, has been investigated in many areas, and in the recent decade, flocking algorithm design has gained a lot of attention due to its variety of potential applications. Although there are many applications exclusively related to fixed-wing aircraft, most of the theoretical works rarely consider these situations. The fixed-wing aircraft flocking is distinct from the general flocking problems by four practical concerns, which include the nonholonomic constraint, the limitation of speed, the collision avoidance and the efficient use of airspace. None of the existing works have addressed all these concerns. The major difficulty is to take into account the all four concerns simultaneously meanwhile having a relatively mild requirement on the initial states of aircraft. In this thesis, to solve the fixed-wing aircraft flocking problem, a supervisory decentralized control algorithm is proposed. The proposed control algorithm has a switching control structure, which basically includes three modes of control protocol and a state-dependent switching logic. Three modes of decentralized control protocol are designed based on the artificial potential field method, which helps to address the nonholonomic constraint, the limitation of speed and the collision avoidance for appropriate initial conditions. The switching logic is designed based on the invariance property induced by the control modes such that the desirable convergence properties of the flocking behavior and the efficient use of airspace are addressed. The proposed switching logic can avoid the fast mode switching, and the supervisor does not require to perform switchings frequently and respond to the aircraft immediately, which means the desired properties can still be guaranteed with the presence of the dwell time in the supervisor

Optimal strategies in the average consensus problem

We prove that for a set of communicating agents to compute the average of their initial positions (average consensus problem), the optimal topology of communication is given by a de Bruijn's graph. Consensus is then reached in a finitely many steps. A more general family of strategies, constructed by block Kronecker products, is investigated and compared to Cayley strategies.Comment: 9 pages; extended preprint with proofs of a CDC 2007 (Conference on decision and Control) pape

Analysis of multi-agent systems under varying degrees of trust, cooperation, and competition

Multi-agent systems rely heavily on coordination and cooperation to achieve a variety of tasks. It is often assumed that these agents will be fully cooperative, or have reliable and equal performance among group members. Instead, we consider cooperation as a spectrum of possible interactions, ranging from performance variations within the group to adversarial agents. This thesis examines several scenarios where cooperation and performance are not guaranteed. Potential applications include sensor coverage, emergency response, wildlife management, tracking, and surveillance. We use geometric methods, such as Voronoi tessellations, for design insight and Lyapunov-based stability theory to analyze our proposed controllers. Performance is verified through simulations and experiments on a variety of ground and aerial robotic platforms. First, we consider the problem of Voronoi-based coverage control, where a group of robots must spread out over an environment to provide coverage. Our approach adapts online to sensing and actuation performance variations with the group. The robots have no prior knowledge of their relative performance, and in a distributed fashion, compensate by assigning weaker robots a smaller portion of the environment. Next, we consider the problem of multi-agent herding, akin to shepherding. Here, a group of dog-like robots must drive a herd of non-cooperative sheep-like agents around the environment. Our key insight in designing the control laws for the herders is to enforce geometrical relationships that allow for the combined system dynamics to reduce to a single nonholonomic vehicle. We also investigate the cooperative pursuit of an evader by a group of quadrotors in an environment with no-fly zones. While the pursuers cannot enter the no-fly zones, the evader moves freely through the zones to avoid capture. Using tools for Voronoi-based coverage control, we provide an algorithm to distribute the pursuers around the zone's boundary and minimize capture time once the evader emerges. Finally, we present an algorithm for the guaranteed capture of multiple evaders by one or more pursuers in a bounded, convex environment. The pursuers utilize properties of the evader's Voronoi cell to choose a control strategy that minimizes the safe-reachable area of the evader, which in turn leads to the evader's capture

Steering laws for distributed motion coordination of kinematic agents in three dimensions

We develop a systematic approach to synthesize distributed control laws for motion coordination in a group of constant-speed kinematic rigid bodies. Parallel and balanced circular formations of mobile agents moving in a three dimensional space are studied, and provably correct steering laws are presented. The resulting steering laws have simple geometric intuitions which are based on the structure of each particular formation

An Overview of Recent Progress in the Study of Distributed Multi-agent Coordination

This article reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, task assignment, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations

Coordination of Multirobot Teams and Groups in Constrained Environments: Models, Abstractions, and Control Policies

Robots can augment and even replace humans in dangerous environments, such as search and rescue and reconnaissance missions, yet robots used in these situations are largely tele-operated. In most cases, the robots\u27 performance depends on the operator\u27s ability to control and coordinate the robots, resulting in increased response time and poor situational awareness, and hindering multirobot cooperation. Many factors impede extended autonomy in these situations, including the unique nature of individual tasks, the number of robots needed, the complexity of coordinating heterogeneous robot teams, and the need to operate safely. These factors can be partly addressed by having many inexpensive robots and by control policies that provide guarantees on convergence and safety. In this thesis, we address the problem of synthesizing control policies for navigating teams of robots in constrained environments while providing guarantees on convergence and safety. The approach is as follows. We first model the configuration space of the group (a space in which the robots cannot violate the constraints) as a set of polytopes. For a group with a common goal configuration, we reduce complexity by constructing a configuration space for an abstracted group state. We then construct a discrete representation of the configuration space, on which we search for a path to the goal. Based on this path, we synthesize feedback controllers, decentralized affine controllers for kinematic systems and nonlinear feedback controllers for dynamical systems, on the polytopes, sequentially composing controllers to drive the system to the goal. We demonstrate the use of this method in urban environments and on groups of dynamical systems such as quadrotors. We reduce the complexity of multirobot coordination by using an informed graph search to simultaneously build the configuration space and find a path in its discrete representation to the goal. Furthermore, by using an abstraction on groups of robots we dissociate complexity from the number of robots in the group. Although the controllers are designed for navigation in known environments, they are indeed more versatile, as we demonstrate in a concluding simulation of six robots in a partially unknown environment with evolving communication links, object manipulation, and stigmergic interactions