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A survey on coverage path planning for robotics

Linked: The New Science of Networks

We describe a simple yet general method to analyze networks of coupled identical nonlinear oscillators and study applications to fast synchronization, locomotion, and schooling. Specifically, we use nonlinear contraction theory to derive exact and global (rather than linearized) results on synchronization, antisynchronization, and oscillator death. The method can be applied to coupled networks of various structures and arbitrary size. For oscillators with positive definite diffusion coupling, it can be shown that synchronization always occurs globally for strong enough coupling strengths, and an explicit upper bound on the corresponding threshold can be computed through eigenvalue analysis. The discussion also extends to the case when network structure varies abruptly and asynchronously, as in "flocks" of oscillators or dynamic elements.

/pdf/on-partial-contraction-analysis-for-coupled-nonlinear-19bpk7wfyv.pdf

On partial contraction analysis for coupled nonlinear oscillators

This article describes the design of a linear robust dynamic output feedback control scheme for output reference trajectory tracking tasks in a leader-follower non-holonomic car formation problem using the cars' kinematic models. A simplification is proposed on the follower's exact open loop position tracking error dynamics, obtained by flatness considerations, resulting in a system described by an additively disturbed set of two, second order, integrators with non-linear velocity dependent control input matrix gain. The unknown disturbances are modeled as absolutely bounded, additive, unknown time signals which may be locally approximated by arbitrary elements of, a, fixed, sufficiently high degree family of Taylor polynomials. Linear Luenberger observers may be readily designed, which include the, self updating, internal model of the unknown disturbance input vector components as generic time-polynomial models. The proposed Generalized Proportional Integral (GPI) observers, which are the dual counterpart of GPI controllers ([11]), achieve a, simultaneous, disturbance estimation and tracking error phase variables estimation. This, on-line, gathered information is used to advantage on the follower's linear output feedback controller thus allowing for a simple, yet efficient, disturbance and control input gain cancelation effort. The results are applied to control the fixed time delayed trajectory tracking of the leader path on the part of the follower. Simulations are presented which illustrate the robustness of the proposed approach.

Trajectory tracking for non-holonomic cars: A linear approach to controlled leader-follower formation

In the world of living creatures, simple-minded animals often cooperate to achieve common goals with amazing performance. One can consider this idea in the context of robotics, and suggest models for programming goal-oriented behavior into the members of a group of simple robots lacking global supervision. This can be done by controlling the local interactions between the robot agents, to have them jointly carry out a given mission. As a test case we analyze the problem of many simple robots cooperating to clean the dirty floor of a non-convex region in Z2, using the dirt on the floor as the main means of inter-robot communication.

/pdf/cooperative-cleaners-a-study-in-ant-robotics-563mioi44r.pdf

Cooperative Cleaners: A Study in Ant Robotics

We consider the problem of patrolling—i.e. ongoing exploration of a network by a decentralized group of simple memoryless robotic agents. The model for the network is an undirected graph, and our goal, beyond complete exploration, is to achieve close to uniform frequency of traversal of the graph’s edges. A simple multi-agent exploration algorithm is presented and analyzed. It is shown that a single agent following this procedure enters, after a transient period, a periodic motion which is an extended Eulerian cycle, during which all edges are traversed an identical number of times. We further prove that if the network is Eulerian, a single agent goes into an Eulerian cycle within 2|E|D steps, |E| being the number of edges in the graph and D being its diameter. For a team of k agents, we show that after at most 2( 1 + 1/k) |E|D steps the numbers of edge visits in the network are balanced up to a factor of two. In addition, various aspects of the algorithm are demonstrated by simulations.

A Distributed Ant Algorithm for\protect Efficiently Patrolling a Network

Several recent works considered multi-a(ge)nt robotics in static environments. In this work we examine ways of operating in dynamic environments, where changes take place independently of the agents??? activity. The work focuses on a dynamic variant of the cooperative cleaners problem, a problem that requires several simple agents to clean a connected region of ???dirty??? pixels in Z2. A number of simple agents move in this dirty region, each having the ability to ???clean??? the place it is located in. Their goal is to jointly clean the given dirty region. The dynamic variant of the problem involves a deterministic expansion of dirt in the environment, simulating spreading of contamination or fire. Theoretical lower bounds for the problem are presented, as well as various impossibility results. A cleaning protocol for the problem is presented, and a wealth of experimental results testing its performance in comparison to the lower bounds. Several analytic upper bounds for the proposed protocol are also presented, accompanied with appropriate experimental results.

/pdf/multi-agent-cooperative-cleaning-of-expanding-domains-1w33aspzls.pdf

Multi-agent Cooperative Cleaning of Expanding Domains

We consider a problem of decentralized exploration of a faulty network by several simple, memoryless agents. The model we adopt for a network is a directed graph. We design an asynchronous algorithm that can cope with failures of network edges and nodes. The algorithm is self-stabilizing in the sense that it can be started with arbitrary initializations and scalable – new agents can be added while other agents are already running.

Vertex-Ant-Walk – A robust method for efficient exploration of faulty graphs

We present an algorithm for covering continuous domains by primitive robots whose only ability is to mark visited places with pheromone and to sense the level of the pheromone in their neighborhood. These pheromone marks can be sensed by all robots and thus provide a way for indirect communication between the robots. Apart from this, the robots have no means to communicate. Additionally they are memoryless, have no global information such as the domain map, own position, coverage percentage, etc. Despite the robots’ simplicity, we show that they are able to cover efficiently any connected domains, including non-planar ones.

Vladimir Yanovski

Papers

Cooperative Cleaners: A Study in Ant Robotics

A Distributed Ant Algorithm for\protect Efficiently Patrolling a Network

Multi-agent Cooperative Cleaning of Expanding Domains

Vertex-Ant-Walk – A robust method for efficient exploration of faulty graphs

Covering a continuous domain by distributed, limited robots