Rendezvous Algorithm Research Articles

Multi-Batch Carrier-Based UAV Formation Rendezvous Method Based on Improved Sequential Convex Programming

The limitations of the existing catapults necessitate multiple batches of take-offs for carrier-based unmanned aerial vehicles (UAVs) to form a formation. Because of the differences in takeoff time and location of each batch of UAVs, ensuring the temporal and spatial consistency and rendezvous efficiency of the formation becomes crucial. Concerning the challenges mentioned above, a multi-batch formation rendezvous method based on improved sequential convex programming (SCP) is proposed. A reverse solution approach based on the multi-batch rendezvous process is developed. On this basis, a non-convex optimization problem is formulated considering the following constraints: UAV dynamics, collision avoidance, obstacle avoidance, and formation consistency. An SCP method that makes use of the trust region strategy is introduced to solve the problem efficiently. Due to the spatiotemporal coupling characteristics of the rendezvous process, an inappropriate initial solution for SCP will inevitably reduce the rendezvous efficiency. Thus, an initial solution tolerance mechanism is introduced to improve the SCP. This mechanism follows the idea of simulated annealing, allowing the SCP to search for better reference solutions in a wider space. By utilizing the initial solution tolerance SCP (IST-SCP), the multi-batch formation rendezvous algorithm is developed correspondingly. Simulation results are obtained to verify the effectiveness and adaptability of the proposed method. IST-SCP reduces the rendezvous time from poor initial solutions without significantly increasing the computing time.

A composite channel hopping algorithm for blind rendezvous in heterogeneous cognitive radio networks

A composite channel hopping algorithm for blind rendezvous in heterogeneous cognitive radio networks

Deterministic rendezvous in infinite trees

The rendezvous task calls for two mobile agents, starting from different nodes of a network modeled as a graph to meet at the same node. Agents have different labels which are integers from a set {1,…,L}. They wake up at possibly different times and move in synchronous rounds. In each round, an agent can either stay idle or move to an adjacent node. We consider deterministic rendezvous algorithms. The time of such an algorithm is the number of rounds since the wakeup of the earlier agent till the meeting. In most of the literature concerning rendezvous in graphs, the graph is finite and the time of rendezvous depends on its size. This approach is impractical for very large graphs and impossible for infinite graphs. For such graphs it is natural to design rendezvous algorithms whose time depends on the initial distance D between the agents. In this paper we adopt this approach and consider rendezvous in infinite trees. All our algorithms work in finite trees as well. Our main goal is to study the impact of orientation of a tree on the time of rendezvous.We first design a rendezvous algorithm working for unoriented regular trees, whose time is in O(z(D)log⁡L), where z(D) is the size of the ball of radius D, i.e., the number of nodes at distance at most D from a given node. The algorithm works for arbitrary delay between waking times of agents and does not require any initial information about parameters L or D. Its disadvantage is its complexity: z(D) is exponential in D for any degree d>2 of the tree. We prove that this high complexity is inevitable: Ω(z(D)) turns out to be a lower bound on rendezvous time in unoriented regular trees, even for simultaneous start and even when agents know L and D. Then we turn attention to oriented trees. While for arbitrary delay between waking times of agents the lower bound Ω(z(D)) still holds, for simultaneous start the time of rendezvous can be dramatically shortened. We show that if agents know either a polynomial upper bound on L or a linear upper bound on D, then rendezvous can be accomplished in oriented trees in time O(Dlog⁡L), which is optimal. If no such extra knowledge is available, a significant speedup is still possible: in this case we design an algorithm working in time O(D2+log2⁡L).

Deterministic treasure hunt and rendezvous in arbitrary connected graphs

Treasure hunt and rendezvous are fundamental tasks performed by mobile agents in graphs. In treasure hunt, an agent has to find an inert target (called treasure) situated at an unknown node of the graph. In rendezvous, two agents, initially located at distinct nodes of the graph, traverse its edges in synchronous rounds and have to meet at some node. We assume that the graph is connected (otherwise none of these tasks is feasible) and consider deterministic treasure hunt and rendezvous algorithms. The time of a treasure hunt algorithm is the worst-case number of edge traversals performed by the agent until the treasure is found. The time of a rendezvous algorithm is the worst-case number of rounds since the wakeup of the earlier agent until the meeting.To the best of our knowledge, all known treasure hunt and rendezvous algorithms rely on the assumption that degrees of all nodes are finite, even when the graph itself may be infinite. In the present paper we remove this assumption for the first time, and consider both above tasks in arbitrary connected graphs whose nodes can have either finite or countably infinite degrees. Our main result is the first universal treasure hunt algorithm working for arbitrary connected graphs. We prove that the time of this algorithm has optimal order of magnitude among all possible treasure hunt algorithms working for arbitrary connected graphs. As a consequence of this result we obtain the first universal rendezvous algorithm working for arbitrary connected graphs. The time of this algorithm is polynomial in a lower bound holding in many graphs, in particular in the tree all of whose degrees are infinite.

A Channel Rendezvous Algorithm for Multi-Unmanned Aerial Vehicle Networks Based on Average Consensus.

Realizing the distributed adaptive network construction of multi-UAV networks is an urgent challenge, as they lack a reliable common control channel and can only maintain a limited sensing range in crowded electromagnetic environments. Multi-unmanned aerial vehicle (UAV) networks are gaining popularity in many fields. In order to address these issues, this paper proposes a multi-UAV network channel rendezvous algorithm based on average consistency. The goal of the algorithm is to adjust the communication channels of each UAV to converge on the same channel, since the communication link of the multi-UAV network is broken due to interference. The proposed memory-based average consistency (MAC) algorithm utilizes the network adjacency matrix as prior information. Furthermore, for the case where the adjacency matrix is unknown, this paper also proposes the Multi-Radio Average Consensus (MRAC) algorithm, which achieves a beneficial trade-off between rendezvous performance and hardware cost. Simulation results demonstrate that the proposed MAC and MRAC algorithms provide superior network convergence time and scalability in networks of different densities. Finally, a hardware simulation platform based on a multi-UAV network was designed using a software-defined radio platform, and experimental simulations were performed to prove the effectiveness of the MAC algorithm in a real environment.

An efficient coprime integer sets based rendezvous algorithm for distributed cognitive radio networks

AbstractMultichannel blind rendezvous problem is a fundamental problem in cognitive radio networks (CRNs). It refers to how to ensure that any two secondary users can meet on a common available channel at the same time. In this paper, an efficient channel hopping algorithm, called CISR (Coprime Integer Sets based Rendezvous), is designed for asymmetric role model (i.e. users can be divided into two types of roles, say, sender/leader and receiver/follower) in distributed CRNs. CISR can guarantee the rendezvous of the leader and follower and lowers the upper bound of both the maximum time to rendezvous and expected time to rendezvous by carefully constructing two coprime integer sets. The simulation results show that CISR has the near‐optimal performance.

Efficient distributed broadcasting algorithms for cognitive radio networks-enabled smart agriculture

Smart agriculture has a broad prospect with the fast development of information technologies, such as Internet of Things, big data, edge computing and artificial intelligence. As more intelligent devices are deployed for agricultural scenarios, such as quality monitoring and information aggregation, the communication channels among these devices will be crowded and the performance can be greatly affected. Cognitive Radio Networks (CRNs) are promising in promoting better spectrum utilization, where unlicensed users can opportunistically use the vacant spectrum assigned to licensed users. On the basis of CRNs, many agricultural scenarios can be empowered with efficient communication capabilities. However, the broadcasting problem, which handles the information dissemination, has not been thoroughly studied in CRNs. Existing works are either centralized solutions performing broadcast on single/multiple channels, or distributed algorithms without performance guarantee for general networks. In this paper, we propose efficient distributed algorithms with short broadcast delay and high success ratio. The difficulties lie in the non-uniform channel availability, which entails broadcasting on multiple channels even for single-hop neighbors, and the distributed behaviors, where the users are only aware of the local information. Our contributions are threefold. First, we propose an efficient distributed rendezvous algorithm which spurs the neighbors to find the common channels in a short time. Second, we handle the single-hop broadcast by presenting two distributed algorithms and they guarantee a successful broadcast in O(Δ2loglogN) and Δ time slots respectively, where N is the number of channels and Δ is the maximum number of neighbors. Finally, we extend these algorithms to multi-hop broadcast and the broadcast delay is only up to D times the delay of single-hop, where D is the network diameter. We also conduct extensive simulations and the results corroborate our theoretical analyses.

Three-Dimensional Rendezvous Controls of Multiple Robots with Amplitude-Only Measurements in Cluttered Underwater Environments

This study addresses multi-robot distributed rendezvous controls in cluttered underwater environments with many unknown obstacles. In underwater environments, a Unmanned Underwater Vehicle (UUV) cannot localize itself, since a Global Positioning System (GPS) is not available. Assume that each UUV has multiple signal intensity sensors surrounding it. Multiple intensity sensors on a UUV can only measure the amplitude of signals generated from its neighbor UUVs. We prove that multiple UUVs with bounded speed converge to a designated rendezvous point, while maintaining the connectivity of the communication network. This study further discusses a fault detection method, which detects faulty UUVs based on local sensing measurements. In addition, the proposed rendezvous control is adaptive to communication link failure or invisible UUVs. Note that communication link failure or invisible UUVs can happen due to unknown obstacles in the workspace. As far as we know, our study is novel in developing 3D coordinate-free distributed rendezvous control, considering underwater robots that can only measure the amplitude of signals emitted from neighboring robots. The proposed rendezvous algorithms are provably complete, and the effectiveness of the proposed rendezvous algorithms is demonstrated under MATLAB simulations.

Using model checking to formally verify rendezvous algorithms for robots with lights in Euclidean space

The paper details the first successful attempt at using model checking techniques to verify the correctness of distributed algorithms for robots evolving in a continuous environment. The study focuses on the problem of rendezvous of two robots with lights.There exist many different rendezvous algorithms that aim at finding the minimal number of colors needed to solve rendezvous in various synchrony models (e.g., FSYNC, SSYNC, ASYNC). While these rendezvous algorithms are typically very simple, their analysis and proof of correctness tend to be extremely complex, tedious, and error-prone as impossibility results are based on subtle interactions between the activation schedules of the robots.The paper presents a generic verification model that can be concretely expressed in available software model-checkers. In particular, we explain the subtle design decisions that allow to keep the search space finite and tractable, as well as prove several important theorems that support them. As a sanity check, we use the model to verify several known rendezvous algorithms in six different models of synchrony. In each case, we find that the results obtained from the model checker are consistent with the results known in the literature. The model checker outputs a counter-example execution in every case that is known to fail.In the course of developing and proving the validity of the model, we identified several fundamental theorems, including the ability for a well chosen algorithm and ASYNC scheduler to produce an emerging property of memory in a system of oblivious mobile robots, and why it is not a problem when robots executing the gathering algorithms are equipped with lights.

Deterministic Collision-Resilient Channel Rendezvous: Theory and Algorithm

We formulate and investigate the problem of distributed channel rendezvous in collision-prone wireless networks. Existing researches on this topic are mainly devoted to designing channel hopping sequences, each pair of which can overlap on a common channel within bounded delay. However, this overlap-based canonical rendezvous design does not take into account channel collision, which may render existing rendezvous algorithms fail to achieve bounded delay in collision-prone environment. Motivated by this observation, we formulate and investigate the collision-aware channel rendezvous problem in a generic scenario, where a collision occurs if more than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> packets overlap in time on a same channel. Our generic formulation allows to model both the baseline single packet reception model with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C=1$ </tex-math></inline-formula> and the more sophisticated multiple packet reception model with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C &gt; 1$ </tex-math></inline-formula> . We further abstract the collision-aware rendezvous problem as the problem of constructing a robust rendezvous system. We establish the theoretical limit of the problem, guided by which we design a collision-resilient distributed rendezvous algorithm with truly bounded rendezvous delay. We then demonstrate the performance of our rendezvous algorithm both analytically and numerically.

Continuous Rendezvous Algorithm for Memoryless Agents with Limited Visibility in the Euclidean Space

A continuous-in-time rendezvous algorithm for memoryless agents with limited visibility on the Euclidean plane was proposed in [N. Gordon, I. A. Wagner, and A. M. Bruckstein in Ant Colony Optimization and Swarm Intelligence, Springer, Berlin, 2004, pp. 142--153] and was formulated as a system of differential equations in [L. I. Bellaiche and A. Bruckstein, Swarm Intell., 11 (2017), pp. 271--293]. We generalize this algorithm by letting the agents move in the Euclidean space of arbitrary dimension. And we provide a rigorous existence theory for this algorithm, which was not done before this work, even for the original algorithm for agents on a plane. Finally, for dimension not greater than three, we show that rendezvous is achieved in finite time, which is robust with respect to the number of the agents.

Fast Neighborhood Rendezvous

In the rendezvous problem, two computing entities (called \emph{agents}) located at different vertices in a graph have to meet at the same vertex. In this paper, we consider the synchronous \emph{neighborhood rendezvous problem}, where the agents are initially located at two adjacent vertices. While this problem can be trivially solved in $O(\Delta)$ rounds ($\Delta$ is the maximum degree of the graph), it is highly challenging to reveal whether that problem can be solved in $o(\Delta)$ rounds, even assuming the rich computational capability of agents. The only known result is that the time complexity of $O(\sqrt{n})$ rounds is achievable if the graph is complete and agents are probabilistic, asymmetric, and can use whiteboards placed at vertices. Our main contribution is to clarify the situation (with respect to computational models and graph classes) admitting such a sublinear-time rendezvous algorithm. More precisely, we present two algorithms achieving fast rendezvous additionally assuming bounded minimum degree, unique vertex identifier, accessibility to neighborhood IDs, and randomization. The first algorithm runs within $\tilde{O}(\sqrt{n\Delta/\delta} + n/\delta)$ rounds for graphs of the minimum degree larger than $\sqrt{n}$, where $n$ is the number of vertices in the graph, and $\delta$ is the minimum degree of the graph. The second algorithm assumes that the largest vertex ID is $O(n)$, and achieves $\tilde{O}\left( \frac{n}{\sqrt{\delta}} \right)$-round time complexity without using whiteboards. These algorithms attain $o(\Delta)$-round complexity in the case of $\delta = {\omega}(\sqrt{n} \log n)$ and $\delta = \omega(n^{2/3} \log^{4/3} n)$ respectively.

Multiple Prime Expansion Channel Hopping for Blind Rendezvous in a Wireless Sensor Network

A channel rendezvous is a significant aspect of communication. In this context, blind rendezvous is the process of selecting a common available channel and establishing a communication link for wireless devices in a wireless sensor network. The rendezvous of asymmetric and heterogeneous wireless devices is a challenge. Thus, to improve speeds and stability of rendezvous, we analyze time slot overlap and channel determinism in the rendezvous algorithm and propose a rendezvous algorithm named Multiple Prime Expansion (MPE). In a final simulation study, we compare the performance of the MPE with other existing algorithms in an asymmetric and heterogeneous scenario. Results show that MPE has excellent performance for the ATTR and MTTR.

Multi-Robot Symmetric Rendezvous Search on the Line

We study the Symmetric Rendezvous Search Problem for a multi-robot system. There are $n>2$ robots arbitrarily located on a line. Their goal is to meet somewhere on the line as quickly as possible. The robots do not know the initial location of any of the other robots or their own positions on the line. The symmetric version of the problem requires the robots to execute the same search strategy to achieve rendezvous. Therefore, we solve the problem in an online fashion with a randomized strategy. In this paper, we present a symmetric rendezvous algorithm which achieves a constant competitive ratio for the total distance traveled by the robots. We validate our theoretical results through simulations.

Optimal rendezvous on a line by location-aware robots in the presence of spies*

A set of mobile robots is placed at arbitrary points of an infinite line. The robots are equipped with GPS devices and they may communicate their positions on the line to a central authority. The collection contains an unknown subset of “spies”, i.e., byzantine robots, which are indistinguishable from the non-faulty ones. The set of the non-faulty robots needs to rendezvous in the shortest possible time in order to perform some task, while the byzantine robots may try to delay their rendezvous for as long as possible. The problem facing a central authority is to determine trajectories for all robots so as to minimize the time until all the non-faulty robots have met. The trajectories must be determined without knowledge of which robots are faulty. Our goal is to minimize the competitive ratio between the time required to achieve the first rendezvous of the non-faulty robots and the time required for such a rendezvous to occur under the assumption that the faulty robots are known at the start. In this paper, we give rendezvous algorithms with bounded competitive ratio, where the central authority is informed only of the set of initial robot positions, without knowing which ones or how many of them are faulty. In general, regardless of the number of faults [Formula: see text] it can be shown that there is an algorithm with bounded competitive ratio. Further, we are able to give a rendezvous algorithm with optimal competitive ratio provided that the number [Formula: see text] of faults is strictly less than [Formula: see text]. Note, however, that in general this algorithm does not give an estimate on the actual value of the competitive ratio. However, when an upper bound on the number of byzantine robots is known to the central authority, we can provide algorithms with constant competitive ratios and in some instances we are able to show that these algorithms are optimal. Moreover, in the cases where the number of faults is either [Formula: see text] or [Formula: see text] we are able to compute the competitive ratio of an optimal rendezvous algorithm, for a small number of robots.

A survey on Rendezvous Algorithms in Cognitive Radio Networks Under Jamming Attacks

The problem of congestion in the licensed radio channels spectrum can be solved by Cognitive Radio Networks (CRN). Several algorithms exist to ensure the rendezvous between Secondary Users (SUs), they are increasingly efficient, allowing faster rendezvous under multiple scenarios. In parallel, several jamming algorithms are developed to counter rendezvous which are also improving. The goal in CRN is to ensure the rendezvous by warding such jammers with robust algorithms. In this paper, we classify various jamming techniques and analyze the performance of various well-known rendezvous algorithms under jamming attacks.

A novel fast and fair asynchronous channel hopping rendezvous scheme in cognitive radio networks for internet of things

Recent years have witnessed significant growth in the area of Internet of things (IoT) and is further expected to increase manifolds in the foreseeable future. Such a massive usage of IoT comes with spectrum scarcity issues. In the last few years, Cognitive Radio Network (CRN) has been widely researched because of its potential to be an effective solution to the problem of spectrum scarcity. The unlicensed users in CRN need to rendezvous on a commonly available channel for the purpose of necessary information exchange. Channel hopping (CH) is one of the representative technique to achieve rendezvous in CRNs in which users hop among available channels according to a pre-defined sequence. Providing guaranteed rendezvous which is fair and having full rendezvous diversity in minimum possible time is a challenging issue in CRN. In this paper, we propose an asymmetric asynchronous CH algorithm that provides guaranteed, fair and full rendezvous diversity among the users. The idea is to construct sender and receiver matrices to generate CH sequences based on the number of available channels of sender and receiver. Analytical and simulation results verify that the proposed algorithm outperform some existing state of the art rendezvous algorithms in terms of maximum time to rendezvous (MTTR), provide full rendezvous diversity and rendezvous fairness among the users.

Aperiodic Communication for MPC in Autonomous Cooperative Landing

This paper investigates the rendezvous problem for the autonomous cooperative landing of an unmanned aerial vehicle (UAV) on an unmanned surface vehicle (USV). Such heterogeneous agents, with nonlinear dynamics, are dynamically decoupled but share a common cooperative rendezvous task. The underlying control scheme is based on distributed Model Predictive Control (MPC). The main contribution is a rendezvous algorithm with an online update rule of the rendezvous location. The algorithm only requires the agents to exchange information when they can not guarantee to rendezvous. Hence, the exchange of information occurs aperiodically, which reduces the necessary communication between the agents. Furthermore, we prove that the algorithm guarantees recursive feasibility. The simulation results illustrate the effectiveness of the proposed algorithm applied to the problem of autonomous cooperative landing.

Rendezvous algorithms for large-scale modeling and simulation

Rendezvous algorithms encode a communication pattern that is useful when processors sending data do not know who the receiving processors should be, or vice versa. The idea is to define an intermediate decomposition where datums from different sending processors can ”rendezvous” to perform a computation, in a manner that both the senders and eventual receivers of the results can identify the appropriate rendezvous processor.Originally designed for interpolating between overlaid grids with independent parallel decompositions (Plimpton et al., 2004), we have recently found rendezvous algorithms useful for a variety of operations in particle- or grid-based simulation codes when running large problems on large numbers of processors. In particular, we show they can perform well when a load-balanced intermediate decomposition is randomized and not spatial, requiring all-to-all communication to move data between processors. In this case rendezvous algorithms leverage the large bisection communication bandwidths which parallel machines provide.We describe how rendezvous algorithms work in a scientific computing context and give specific examples for molecular dynamics and Direct Simulation Monte Carlo codes which result in dramatic performance improvements versus simpler algorithms which do not scale as well. We explain how a generic rendezvous algorithm can be implemented, and also point out similarities with the MapReduce paradigm popularized by Google and Hadoop.

Distributed Rendezvous of Heterogeneous Robots with Motion-Based Power Level Estimation

This article introduces distributed rendezvous algorithms to make all heterogeneous robots (agents) rendezvous at a designated agent in environments with many obstacles. The proposed control laws are developed considering heterogeneous agents having distinct power level, sensing range, or communication range. It is assumed that each agent is initially distributed in a cluttered environment. An agent cannot utilize global positioning systems (GPS) to localize itself. Each agent can only sense neighboring agents and moves based on proximity interaction. This article presents distributed rendezvous algorithms so that heterogeneous agents rendezvous at a designated agent while maintaining (directed) network connectivity. The speed of each agent is set proportional to the remaining power level of the agent. This article then presents a method of estimating the power of each agent by measuring the movement of the agent. Then, we present a method of sharing power if an agent is lack of power. Under the proposed approach, we achieve distributed rendezvous as well as power recharging. It is proved that multiple heterogeneous agents rendezvous at the designated agent while maintaining (directed) network connectivity. Utilizing MATLAB simulations, the performance of the proposed distributed controls is verified in an environment with many obstacles.