We consider the problem of fault-tolerant parallel search on an infinite line by @math robots. Starting from the origin, the robots are required to find a target at an unknown location. The robots can move with maximum speed @math and can communicate in wireless mode among themselves. However, among the @math robots, there are @math robots that exhibit byzantine faults . A faulty robot can fail to report the target even after reaching it, or it can make malicious claims about having found the target when in fact it has not. Given the presence of such faulty robots, the search for the target can only be concluded when the non-faulty robots have sufficient verification that the target has been found. We aim to design algorithms that minimize the value of @math , the time to find a target at a distance @math from the origin by @math robots among which @math are faulty. We give several different algorithms whose running time depends on the ratio @math , the density of faulty robots, and also prove lower bounds. Our algorithms are optimal for some densities of faulty robots.
Fault tolerance was studied in distributed computing in various settings in the past (e.g., see @cite_27 @cite_2 @cite_3 ). However, the subject of unreliability was mainly for static components of the environment (e.g. network nodes or links), which was sometimes modelled by dynamically evolving environments (cf. @cite_28 @cite_7 ). The malfunctions arising to mobile robots were investigated for various problems of gathering or pattern forming @cite_1 @cite_25 @cite_0 @cite_4 or patrolling @cite_21 . Recently @cite_12 investigated crash faults of robots performing linear search, where the time of finding the target by the first reliable robot was optimized. However, dealing with Byzantine agents is in general more tricky, requiring to identify and to refute the most malicious adversarial behavior (e.g., see @cite_0 ).
@cite_4 @cite_7 @cite_28 @cite_21 @cite_1 @cite_3 @cite_0 @cite_27 @cite_2 @cite_25 @cite_12
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This paper studies fault-tolerant algorithms for the problem of gathering @math autonomous mobile robots. A gathering algorithm, executed independently by each robot, must ensure that all robots are gathered at one point within finite time. In a failure-prone system, a gathering algorithm is required to successfully gather the nonfaulty robots, independently of the behavior of the faulty ones. Both crash and Byzantine faults are considered. It is first observed that most existing algorithms fail to operate correctly in a setting allowing crash failures. Subsequently, an algorithm tolerant against one crash-faulty robot in a system of three or more robots is presented. It is then observed that all known algorithms fail to operate correctly in a system prone to Byzantine faults, even in the presence of a single fault. Moreover, it is shown that in an asynchronous environment it is impossible to perform a successful gathering in a @math -robot system, even if at most one of them might fail in a Byzantine manner. Thus, the problem is studied in a fully synchronous system. An algorithm is provided in this model for gathering @math robots with at most a single faulty robot, and a more general gathering algorithm is given in an @math -robot system with up to @math faults, where @math . This paper investigates the task solvability of mobile robot systems subject to Byzantine faults. We first consider the gathering problem, which requires all robots to meet in finite time at a non-predefined location. It is known that the solvability of Byzantine gathering strongly depends on a number of system attributes, such as synchrony, the number of Byzantine robots, scheduling strategy, obliviousness, orientation of local coordinate systems and so on. However, the complete characterization of the attributes making Byzantine gathering solvable still remains open. In this paper, we show strong impossibility results of Byzantine gathering. Namely, we prove that Byzantine gathering is impossible even if we assume one Byzantine fault, an atomic execution system, the n-bounded centralized scheduler, non-oblivious robots, instantaneous movements and a common orientation of local coordinate systems (where n denote the number of correct robots). Those hypotheses are much weaker than used in previous work, inducing a much stronger impossibility result. At the core of our impossibility result is a reduction from the distributed consensus problem in asynchronous shared-memory systems. In more details, we newly construct a generic reduction scheme based on the distributed BG-simulation. Interestingly, because of its versatility, we can easily extend our impossibility result for general pattern formation problems. Distributed algorithms for multi-robot systems rely on network communications to share information. However, the motion of the robots changes the network topology, which affects the information presented to the algorithm. For an algorithm to produce accurate output, robots need to communicate rapidly enough to keep the network topology correlated to their physical configuration. Infrequent communications will cause most multi-robot distributed algorithms to produce less accurate results, and cause some algorithms to stop working altogether. The central theme of this work is that algorithm accuracy, communications bandwidth, and physical robot speed are related. This thesis has three main contributions: First, I develop a prototypical multi-robot application and computational model, propose a set of complexity metrics to evaluate distributed algorithm performance on multi-robot systems, and introduce the idea of the robot speed ratio, a dimensionless measure of robot speed relative to message speed in networks that rely on multi-hop communication. The robot speed ratio captures key relationships between communications bandwidth, mobility, and algorithm accuracy, and can be used at design time to trade off between them. I use this speed ratio to evaluate the performance of existing distributed algorithms for multi-hop communication and navigation. Second, I present a definition of boundaries in multi-robot systems, and develop new distributed algorithms to detect and characterize them. Finally, I define the problem of dynamic task assignment, and present four distributed algorithms that solve this problem, each representing a different trade-off between accuracy, running time, and communication resources. All the algorithms presented in this work are provably correct under ideal conditions and produce verifiable real-world performance. They are self-stabilizing and robust to communications failures, population changes, and other errors. All the algorithms were tested on a swarm of 112 robots. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.) Abstract : In this report, we study tolerance of semantic faults, one of the crucial Issues In the Simplex(TM) architecture. In particular, we examine semantic faults that cause the controlled device to be unsafe (i.e., unable to carry out its normal operation) and eventually cause the device to become damaged. We also consider fault detection as a safety check. For the class of control systems operating around an equilibrium, the objective of maintaining the safety of the controlled device is formulated as a stabilization problem, and the safety of the controlled device is tested against the stability region of the device under the safety control. To establish the stability region, we apply the Lyapunov stability theory and linear matrix inequality (LMI) methodologies. It is shown that the stability region for a given safety controller as well as a safety control law can be systematically derived by LMI based approaches. We conclude the report with a summary of the procedure for deriving the safety check and safety controller for a given application.