Optimal byzantine resilient convergence in oblivious robot networks

Given a set of robots with arbitrary initial location and no agreement on a global coordinate system, convergence requires that all robots asymptotically approach the exact same, but unknown beforehand, location. Robots are oblivious-- they do not recall the past computations -- and are allowed to move in a one-dimensional space. Additionally, robots cannot communicate directly, instead they obtain system related information only via visual sensors. We draw a connection between the convergence problem in robot networks, and the distributed \emph{approximate agreement} problem (that requires correct processes to decide, for some constant $\epsilon$, values distance $\epsilon$ apart and within the range of initial proposed values). Surprisingly, even though specifications are similar, the convergence implementation in robot networks requires specific assumptions about synchrony and Byzantine resilience. In more details, we prove necessary and sufficient conditions for the convergence of mobile robots despite a subset of them being Byzantine (i.e. they can exhibit arbitrary behavior). Additionally, we propose a deterministic convergence algorithm for robot networks and analyze its correctness and complexity in various synchrony settings. The proposed algorithm tolerates f Byzantine robots for (2f+1)-sized robot networks in fully synchronous networks, (3f+1)-sized in semi-synchronous networks. These bounds are optimal for the class of cautious algorithms, which guarantee that correct robots always move inside the range of positions of the correct robots

Robust Environmental Mapping by Mobile Sensor Networks

Constructing a spatial map of environmental parameters is a crucial step to preventing hazardous chemical leakages, forest fires, or while estimating a spatially distributed physical quantities such as terrain elevation. Although prior methods can do such mapping tasks efficiently via dispatching a group of autonomous agents, they are unable to ensure satisfactory convergence to the underlying ground truth distribution in a decentralized manner when any of the agents fail. Since the types of agents utilized to perform such mapping are typically inexpensive and prone to failure, this results in poor overall mapping performance in real-world applications, which can in certain cases endanger human safety. This paper presents a Bayesian approach for robust spatial mapping of environmental parameters by deploying a group of mobile robots capable of ad-hoc communication equipped with short-range sensors in the presence of hardware failures. Our approach first utilizes a variant of the Voronoi diagram to partition the region to be mapped into disjoint regions that are each associated with at least one robot. These robots are then deployed in a decentralized manner to maximize the likelihood that at least one robot detects every target in their associated region despite a non-zero probability of failure. A suite of simulation results is presented to demonstrate the effectiveness and robustness of the proposed method when compared to existing techniques.Comment: accepted to icra 201

Certified Impossibility Results for Byzantine-Tolerant Mobile Robots

We propose a framework to build formal developments for robot networks using the COQ proof assistant, to state and to prove formally various properties. We focus in this paper on impossibility proofs, as it is natural to take advantage of the COQ higher order calculus to reason about algorithms as abstract objects. We present in particular formal proofs of two impossibility results forconvergence of oblivious mobile robots if respectively more than one half and more than one third of the robots exhibit Byzantine failures, starting from the original theorems by Bouzid et al.. Thanks to our formalization, the corresponding COQ developments are quite compact. To our knowledge, these are the first certified (in the sense of formally proved) impossibility results for robot networks

Distributed Fault-Tolerant Control for Networked Robots in the Presence of Recoverable/Unrecoverable Faults and Reactive Behaviors

The paper presents an architecture for distributed control of multi-robot systems with an integrated fault detection, isolation, and recovery strategy. The proposed solution is based on a distributed observer-controller schema where each robot, by communicating only with its direct neighbors, is able to estimate the overall state of the system; such an estimate is then used by the controllers of each robot to achieve global missions as, for example, centroid and formation tracking. The information exchanged among the observers is also used to compute residual vectors that allow each robot to detect failures on anyone of the teammates, even if not in direct communication. The proposed strategy considers both recoverable and unrecoverable actuator faults as well as it properly manages the possible activation of reactive local control behaviors of the robots (e.g., the activation of obstacle avoidance strategy), which generate control inputs different from those required by the global mission control. In particular, when the robots are subject to recoverable faults, those are managed at a local level by computing a proper compensating control action. On the other side, when the robots are subject to unrecoverable faults, the faults are isolated from anyone of the teammates by means of a distributed fault detection and isolation strategy; then, the faulty robots are removed from the team and the mission is rearranged. The proposed strategy is validated via numerical simulations where the system properly identifies and manages the different cases of recoverable and unrecoverable actuator faults, as well as it manages the activation of local reactive control in an integrated case study

Optimal Byzantine Resilient Convergence in Asynchronous Robot Networks

We propose the first deterministic algorithm that tolerates up to $f$ byzantine faults in $3f+1$-sized networks and performs in the asynchronous CORDA model. Our solution matches the previously established lower bound for the semi-synchronous ATOM model on the number of tolerated Byzantine robots. Our algorithm works under bounded scheduling assumptions for oblivious robots moving in a uni-dimensional space

Fault Recovery in Swarm Robotics Systems using Learning Algorithms

When faults occur in swarm robotic systems they can have a detrimental effect on collective behaviours, to the point that failed individuals may jeopardise the swarm's ability to complete its task. Although fault tolerance is a desirable property of swarm robotic systems, fault recovery mechanisms have not yet been thoroughly explored. Individual robots may suffer a variety of faults, which will affect collective behaviours in different ways, therefore a recovery process is required that can cope with many different failure scenarios. In this thesis, we propose a novel approach for fault recovery in robot swarms that uses Reinforcement Learning and Self-Organising Maps to select the most appropriate recovery strategy for any given scenario. The learning process is evaluated in both centralised and distributed settings. Additionally, we experimentally evaluate the performance of this approach in comparison to random selection of fault recovery strategies, using simulated collective phototaxis, aggregation and foraging tasks as case studies. Our results show that this machine learning approach outperforms random selection, and allows swarm robotic systems to recover from faults that would otherwise prevent the swarm from completing its mission. This work builds upon existing research in fault detection and diagnosis in robot swarms, with the aim of creating a fully fault-tolerant swarm capable of long-term autonomy

Fault-tolerant control policies for multi-robot systems

Throughout the past decade, we have witnessed an active interest in distributed motion coordination algorithms for networked mobile autonomous robots. Often, in multi-robot systems, each robot executing a coordination task is a little cost, a disposable autonomous agent that has ad-hoc sensing or communication capability, and limited mobility. Coordination tasks that a group of multiple mobile robots might perform include formation control, rendezvous, distributed estimation, deployment, flocking, etc. Also, there are challenging tasks that are more suitable for a group of mobile robots than an individual robot, such as surveillance, exploration, or hazardous environmental monitoring. The field has been collectively investigated by many researchers in robotics, control, artificial intelligence, and distributed computing. However, relatively little work has been done on developing algorithms to provide resilience to failures that can occur. The problem is extremely difficult to handle in that any partial failure of a robot is not readily detectable. Some failures in robot resources can have an adverse effect on not only the performance of the robot itself, but also other robots, and the collective task performance as well. This study presents the development of fault-tolerant distributed control policies for multi-robot systems. We consider two problems: rendezvous and coverage. For the former, the goal is to bring all robots to a common location, while for the latter the goal is to deploy robots to achieve optimal coverage of an environment. We consider the case in which each robot is an autonomous decision maker that is anonymous (i.e., robots are indistinguishable to one another), memoryless (i.e., each robot makes decisions based upon only its current information), and dimensionless (i.e., collision checking is not considered). Each robot has a limited sensing range and can directly estimate the state of only those robots within that sensing range, which induces a network topology for the multi-robot system. We assume that it is not possible for the fault-free robots to identify the faulty robots (e.g., due to the anonymous property of the robots). For each problem, we provide an efficient computational framework and analysis of algorithms, all of which converge in the face of faulty robots under a few assumptions on the network topology and sensing abilities. A suite of experiments and simulations confirm our theoretical analysis and demonstrate that our proposed algorithms are useful in fault-prone multi-robot systems

Compatibility of convergence algorithms for autonomous mobile robots

We investigate autonomous mobile robots in the Euclidean plane. A robot has a function called target function to decide the destination from the robots' positions, and operates in Look-Compute-Move cycles, i.e., identifies the robots' positions, computes the destination by the target function, and then moves there. Robots may have different target functions. Let $\Phi$ and $\Pi$ be a set of target functions and a problem, respectively. If the robots whose target functions are chosen from $\Phi$ always solve $\Pi$, we say that $\Phi$ is compatible with respect to $\Pi$. If $\Phi$ is compatible with respect to $\Pi$, every target function $\phi \in \Phi$ is an algorithm for $\Pi$ (in the conventional sense). Note that even if both $\phi$ and $\phi'$ are algorithms for $\Pi$, $\{ \phi, \phi' \}$ may not be compatible with respect to $\Pi$. From the view point of compatibility, we investigate the convergence, the fault tolerant ($n,f$)-convergence (FC($f$)), the fault tolerant ($n,f$)-convergence to $f$ points (FC($f$)-PO), the fault tolerant ($n,f$)-convergence to a convex $f$-gon (FC($f$)-CP), and the gathering problems, assuming crash failures. As a result, we see that these problems are classified into three groups: The convergence, the FC(1), the FC(1)-PO, and the FC($f$)-CP compose the first group: Every set of target functions which always shrink the convex hull of a configuration is compatible. The second group is composed of the gathering and the FC($f$)-PO for $f \geq 2$: No set of target functions which always shrink the convex hull of a configuration is compatible. The third group, the FC($f$) for $f \geq 2$, is placed in between. Thus, the FC(1) and the FC(2), the FC(1)-PO and the FC(2)-PO, and the FC(2) and the FC(2)-PO are respectively in different groups, despite that the FC(1) and the FC(1)-PO are in the first group