Enclosing a moving target with an optimally rotated and scaled multiagent pattern

We propose a novel control method to enclose a moving target in a two-dimensional setting with a team of agents forming a prescribed geometric pattern. The approach optimises a measure of the overall agent motion costs, via the minimisation of a suitably defined cost function encapsulating the pattern rotation and scaling. We propose two control laws which use global information and make the agents exponentially converge to the prescribed formation with an optimal scale that remains constant, while the team's centroid tracks the target. One control law results in a multiagent pattern that keeps a constant orientation in the workspace; for the other, the pattern rotates with constant speed. These behaviours, whose optimality and steadiness are very relevant for the task addressed, occur independently from the target's velocity. Moreover, the methodology does not require distance measurements, common coordinate references, or communications. We also present formal guarantees of collision avoidance for the proposed approach. Illustrative simulation examples are provided

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

Clustering-Based Robot Navigation and Control

In robotics, it is essential to model and understand the topologies of configuration spaces in order to design provably correct motion planners. The common practice in motion planning for modelling configuration spaces requires either a global, explicit representation of a configuration space in terms of standard geometric and topological models, or an asymptotically dense collection of sample configurations connected by simple paths, capturing the connectivity of the underlying space. This dissertation introduces the use of clustering for closing the gap between these two complementary approaches. Traditionally an unsupervised learning method, clustering offers automated tools to discover hidden intrinsic structures in generally complex-shaped and high-dimensional configuration spaces of robotic systems. We demonstrate some potential applications of such clustering tools to the problem of feedback motion planning and control. The first part of the dissertation presents the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. We reinterpret this classical method for unsupervised learning as an abstract formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions, by relating the continuous space of configurations to the combinatorial space of trees. Based on this new abstraction and a careful topological characterization of the associated hierarchical structure, a provably correct, computationally efficient hierarchical navigation framework is proposed for collision-free coordinated motion design towards a designated multirobot configuration via a sequence of hierarchy-preserving local controllers. The second part of the dissertation introduces a new, robot-centric application of Voronoi diagrams to identify a collision-free neighborhood of a robot configuration that captures the local geometric structure of a configuration space around the robot’s instantaneous position. Based on robot-centric Voronoi diagrams, a provably correct, collision-free coverage and congestion control algorithm is proposed for distributed mobile sensing applications of heterogeneous disk-shaped robots; and a sensor-based reactive navigation algorithm is proposed for exact navigation of a disk-shaped robot in forest-like cluttered environments. These results strongly suggest that clustering is, indeed, an effective approach for automatically extracting intrinsic structures in configuration spaces and that it might play a key role in the design of computationally efficient, provably correct motion planners in complex, high-dimensional configuration spaces

Non-uniform circle formation algorithm for oblivious mobile robots with convergence toward uniformity

AbstractThis paper presents a distributed algorithm whereby a group of mobile robots self-organize and position themselves into forming a circle in a loosely synchronized environment. In spite of its apparent simplicity, the difficulty of the problem comes from the weak assumptions made on the system. In particular, robots are anonymous, oblivious (i.e., stateless), unable to communicate directly, and disoriented in the sense that they share no knowledge of a common coordinate system. Furthermore, robots’ activations are not synchronized. More specifically, the proposed algorithm ensures that robots deterministically form a non-uniform circle in a finite number of steps and converges to a situation in which all robots are located evenly on the boundary of the circle

Cooperative Label-Free Moving Target Fencing for Second-Order Multi-Agent Systems with Rigid Formation

This paper proposes a label-free controller for a second-order multi-agent system to cooperatively fence a moving target of variational velocity into a convex hull formed by the agents whereas maintaining a rigid formation. Therein, no label is predetermined for a specified agent. To attain a rigid formation with guaranteed collision avoidance, each controller consists of two terms: a dynamic regulator with an internal model to drive agents towards the moving target merely by position information feedback, and a repulsive force between each pair of adjacent agents. Significantly, sufficient conditions are derived to guarantee the asymptotic stability of the closed-loop systems governed by the proposed fencing controller. Rigorous analysis is provided to eliminate the strong nonlinear couplings induced by the label-free property. Finally, the effectiveness of the controller is substantiated by numerical simulations

Abstracting Multidimensional Concepts for Multilevel Decision Making in Multirobot Systems

Multirobot control architectures often require robotic tasks to be well defined before allocation. In complex missions, it is often difficult to decompose an objective into a set of well defined tasks; human operators generate a simplified representation based on experience and estimation. The result is a set of robot roles, which are not best suited to accomplishing those objectives. This thesis presents an alternative approach to generating multirobot control algorithms using task abstraction. By carefully analysing data recorded from similar systems a multidimensional and multilevel representation of the mission can be abstracted, which can be subsequently converted into a robotic controller. This work, which focuses on the control of a team of robots to play the complex game of football, is divided into three sections: In the first section we investigate the use of spatial structures in team games. Experimental results show that cooperative teams beat groups of individuals when competing for space and that controlling space is important in the game of robot football. In the second section, we generate a multilevel representation of robot football based on spatial structures measured in recorded matches. By differentiating between spatial configurations appearing in desirable and undesirable situations, we can abstract a strategy composed of the more desirable structures. In the third section, five partial strategies are generated, based on the abstracted structures, and a suitable controller is devised. A set of experiments shows the success of the method in reproducing those key structures in a multirobot system. Finally, we compile our methods into a formal architecture for task abstraction and control. The thesis concludes that generating multirobot control algorithms using task abstraction is appropriate for problems which are complex, weakly-defined, multilevel, dynamic, competitive, unpredictable, and which display emergent properties