Rendezvous Task Research Articles

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).

Co-Evolutionary Algorithm-Based Multi-Unmanned Aerial Vehicle Cooperative Path Planning

Multi-UAV cooperative path planning is a key technology to carry out multi-UAV tasks, and its research has important practical significance. A multi-UAV cooperative path is a combination of single-UAV paths, so the idea of problem decomposition is effective to deal with multi-UAV cooperative path planning. With this analysis, a multi-UAV cooperative path planning algorithm based on co-evolution optimization was proposed in this paper. Firstly, by analyzing the meaning of multi-UAV cooperative flight, the optimization model of multi-UAV cooperative path planning was given. Secondly, we designed the cost function of multiple UAVs with the penalty function method to deal with multiple constraints and designed two information-sharing strategies to deal with the combination path search between multiple UAVs. The two information-sharing strategies were called the optimal individual selection strategy and the mixed selection strategy. The new cooperative path planning algorithm was presented by combining the above designation and co-evolution algorithm. Finally, the proposed algorithm is applied to a rendezvous task in complex environments and compared with two evolutionary algorithms. The experimental results show that the proposed algorithm can effectively cope with the multi-UAV cooperative path planning problem in complex environments.

Dynamic Route Planning for a USV-UAV Multi-Robot System in the Rendezvous Task with Obstacles

Dynamic Route Planning for a USV-UAV Multi-Robot System in the Rendezvous Task with Obstacles

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.

Non-line-of-sight error mitigating algorithms for transmitter localization based on hybrid TOA/RSSI measurements

Rendezvous control of multiple robots without losing network connectivity has important implications in multi-robot system including formation control, coordinated task assignments, and cooperative robotic missions. This paper introduces a new coordinate-free, bearing-based algorithm to enable rendezvous of distributed mobile robots at any designated leader robot node using hierarchical tracking of wireless network topology. An assumption is made that the robot can only sense and communicate with their neighbors (i.e., local sensing). The proposed approach preserves connectivity during the rendezvous task, adapts to dynamic changes in the network topology (e.g., losing or re-gaining a communication link), and is tolerant of mobility faults in the robots. We theoretically analyze the proposed algorithm and experimentally demonstrate the approach through simulations and extensive field experiments. The results indicate that the method is effective in a variety of realistic scenarios in which the robots are distributed in a cluttered environment.

Single-Bit Consensus With Finite-Time Convergence: Theory and Applications

In this article, a new consensus protocol based on the sign of innovations is proposed. Based on this protocol, each agent requires only a single-bit of information about its relative state to its neighboring agents. This is significant in real-time applications, since it requires less computation and/or communication load on agents. Using Lyapunov stability theorem, the convergence is proved for networks having a spanning tree. Furthermore, the convergence is shown to be in finite time, which is significant as compared to most asymptotic protocols in the literature. Time-variant network topologies are also considered in this article, and final consensus value is derived for undirected networks. Applications of the proposed consensus protocol in two-dimensional (2-D)/3-D rendezvous task, distributed estimation distributed optimization, and formation control are considered and the significance of applying this protocol is discussed. Numerical simulations are provided to compare the protocol with those existing in the literature.

Navigation and Control Scheme for Space Rendezvous and Docking With Maneuvering Noncooperative Target Based on Dynamic Compensation

Rendezvous and docking with noncooperative targets is one of the key technologies for on-orbit service such as satellite maintenance, space supply and space debris cleaning, etc. For the rendezvous and docking with maneuvering noncooperative targets, a relative measurement scheme based on one monocular camera and one distance sensor is designed. A dynamic compensation filter (DCF) is also proposed to estimate the relative state and the unknow maneuver of the noncooperative target. Meanwhile, the control scheme to fulfill the rendezvous and docking mission is given. Compared with the extended Kalman filter (EKF) and variable state dimension estimator (VSDE), the numerical simulation results demonstrate that the proposed estimator has better performance in estimating the relative state and target maneuver. The control scheme based on DCF can accomplish the rendezvous and docking task when the noncooperative target performs time-varying maneuvers.

Integrated Robotic and Network Simulation Method.

The increasing use of mobile cooperative robots in a variety of applications also implies an increasing research effort on cooperative strategies solutions, typically involving communications and control. For such research, simulation is a powerful tool to quickly test algorithms, allowing to do more exhaustive tests before implementation in a real application. However, the transition from an initial simulation environment to a real application may imply substantial rework if early implementation results do not match the ones obtained by simulation, meaning the simulation was not accurate enough. One way to improve accuracy is to incorporate network and control strategies in the same simulation and to use a systematic procedure to assess how different techniques perform. In this paper, we propose a set of procedures called Integrated Robotic and Network Simulation Method (IRoNS Method), which guide developers in building a simulation study for cooperative robots and communication networks applications. We exemplify the use of the improved methodology in a case-study of cooperative control comparison with and without message losses. This case is simulated with the OMNET++/INET framework, using a group of robots in a rendezvous task with topology control. The methodology led to more realistic simulations while improving the results presentation and analysis.

The evolution of non-degenerate and degenerate rendezvous tasks

In this paper, we weaken the nice condition of an n-dimensional rendezvous task defined in the work of X. Liu et al [11]. Then we introduce the definition of evolution of non-degenerate n-dimensional rendezvous task. A non-degenerate n-rendezvous task is said to be evolution if the q-th reduced homology group of its decision space is abelian group for q=n and trivial for the others. Well-known examples are set agreement, simplex agreement, and approximation agreement and so on. Each n-rendezvous task is assigned an algebraic signature, which consists of n-th homology group of the decision space, as well as a distinguished element in the group. We show that an evolution of non-degenerate n-dimensional rendezvous task implements another if and only if there is a homomorphism from its signature to the other. Hence the computational power of evolution of non-degenerate rendezvous task is completely characterized by its signature. Last, we talk about the degenerate n-dimensional rendezvous task in which the output values in any execution can construct at most an n-dimensional simplex.

Fixed-Time Maneuver Control of Spacecraft Autonomous Rendezvous With a Free-Tumbling Target

This paper considers the fixed-time translational operation control issue for the spacecraft rendezvous task with a free-tumbling target. The translation dynamics model of the rendezvous mission under actuator misalignments is first established in the line-of-sight coordinate frame. Then, a novel time-varying sliding mode surface is constructed and a control scheme with the sliding manifold is proposed to achieve the fixed-time convergence of relative parameters’ tracking errors. It is interesting that the preceding convergence time can be altered explicitly according to the specific rendezvous requirements. Meanwhile, a modified updating strategy is developed to ensure system's fixed-time convergence property in the presence of lumped uncertainties (external disturbance and actuator misalignments). The associated stability proof is constructive and accomplished by the development of a Lyapunov function candidate. Finally, numerical simulations on rendezvous missions are performed to demonstrate the effectiveness and the superiorities of the designed fixed-time control scheme.

6-DOF Multi-Constrained Adaptive Tracking Control for Noncooperative Space Target

This paper addresses the problem of six-degree-of-freedom (6-DOF) relative position and attitude-tracking control for noncooperative space targets subject to multiple constraints, including input and full-state constraints. First, a novel 6-DOF integrated relative motion dynamics with control command coupling is established for the final approaching stage of a rendezvous task. Second, a Barrier Lyapunov function (BLF)-based controller is developed to guarantee the relative position, attitude, and velocity constraints of the spacecraft at all times. The requirement of less restrictive initial conditions compared with the quadratic Lyapunov function is presented via a detailed theoretical analysis. Third, a novel 6-DOF integrated multi-constrained adaptive tracking control scheme is proposed to simultaneously deal with input constraints, full-state constraints, unknown disturbances, and uncertainties. In particular, a solution to the chattering phenomenon, arising from the existence of sign function, is explored in an adaptive manner. Detailed controller design procedures and rigorous theoretical proof of all related closed-loop uniform ultimate bounded (UUB) stability are provided. In addition, the numerical simulation results are also exhibited to demonstrate the effectiveness and superior control performance of the proposed control scheme.

Multi-robot rendezvous based on bearing-aided hierarchical tracking of network topology

Rendezvous control of multiple robots without losing network connectivity has important implications in multi-robot system including formation control, coordinated task assignments, and cooperative robotic missions. This paper introduces a new coordinate-free, bearing-based algorithm to enable rendezvous of distributed mobile robots at any designated leader robot node using hierarchical tracking of wireless network topology. An assumption is made that the robot can only sense and communicate with their neighbors (i.e., local sensing). The proposed approach preserves connectivity during the rendezvous task, adapts to dynamic changes in the network topology (e.g., losing or re-gaining a communication link), and is tolerant of mobility faults in the robots. We theoretically analyze the proposed algorithm and experimentally demonstrate the approach through simulations and extensive field experiments. The results indicate that the method is effective in a variety of realistic scenarios in which the robots are distributed in a cluttered environment.

Robust rendezvous for multi-robot system with random node failures: an optimization approach

In this paper, we consider the problem of designing distributed control algorithms to solve the rendezvous problem for multi-robot systems with limited sensing, for situations in which random nodes may fail during execution. We first formulate a distributed solution based upon averaging algorithms that have been reported in the consensus literature. In this case, at each stage of execution a one-step sequential optimal control (i.e., naive greedy algorithm) is used. We propose a distributed stochastic optimal control algorithm that minimizes a mean–variance cost function for each stage, given that the probability distribution for possible node failures is known a priori, as well as a minimax version of the problem when the prior probability distribution is not known. We demonstrate via extensive numerical simulations that our proposed algorithm provides statistically better rendezvous task performance than contemporary algorithms in cases for which failures occur.

Study on navigation and manual steering strategies in the fly-around phase of teleoperation rendezvous and docking

Teleoperation rendezvous and docking can be used as a supporting technology for unmanned spacecraft. An attempt to apply this technology to an unmanned spacecraft’s fly-around maneuver in a space station-based rendezvous and docking task is described in this paper; relative navigation (state determination) strategies and manual steering strategies are proposed sequentially. Parameters to delineate the relative motion states between spacecraft were specifically defined, and an estimation strategy for the parameter set was designed based on the configured relative measurement sensors. Then, manual steering strategies, characterized by decoupling control of the line-of-sight (LOS) orientation between the unmanned spacecraft and the relative orbit motion, were developed to ensure that the unmanned spacecraft, piloted by operators on the space station, flies with almost invariant radial velocity and angular velocity in the LOS axis. A human-in-the-loop simulation result demonstrated the feasibility and effectiveness of the strategies proposed.

Modeling human behavior in manual control Rendezvous and Docking task

Manual control rendezvous and docking (RVD) with human participation can be used when autonomous RVD is invalid under uncertain environment. Because of the particularity and complexity of the RVD task, it is necessary to understand human cognitive processes when evaluating human performance. A modeling approach, focusing on the information processing underlying the decisions process, is proposed to achieve real-time visualization of information processing and to generate human-like behavior of manual control RVD in this paper. It is implemented by combining the symbolic knowledge representations with queuing network mechanism. This computational model here can be used for describing and explaining how human cognition works. Furthermore, a quantitative validation of the model is conducted by comparing the performance results of the model with the results of people doing the same tasks, which reflects that this model can be applied as "replacements" for human participants to evaluate their cognition and performance in manual control RVD task.

Method for Design and Performance Evaluation of Ad Hoc Networked Mobile Robotic Systems using OMNET++

Abstract: Using a team of mobile robots connected through ad hoc networks is becoming increasingly attractive for a myriad of applications, including search, rescue and surveillance. In this paper, we present a method for the design and performance evaluation of complex wireless networked control systems, focusing on cooperative control strategy in robotic tasks. It is described a simulation architecture and specific developments that are required to simulate cooperative robotic systems over a mobile ad hoc network (MANET), regarding individual control, cooperative control, network model and topology control aspects. We assess the capabilities of the proposed method using OMNET++/INET simulator and a rendezvous task with topology control over a MANET. The rendez-vous task is implemented as a consensus problem and is solved by receding horizon control. The resulting simulation shows that not only it is possible to simulate this complex set of algorithms on OMNeT++, but if an organized simulation process is followed, it may allow a better planning of experimental cases to achieve more meaningful results.

Socialized Multi-Agent System Rendezvous via Networks of Networks

Networks of networks paradigm was introduced to explore the rendezvous problems of leader-follower multi-agent system, where the rendezvous actors were categorized into the target object, the leader agents, the informed follower agents and the isolated follower agents, respectively. Then, three humanized system inspired strategies were investigated. Results demonstrated that, the democracy strategy could fulfill the rendezvous task in expenses with a long convergent time and the autarchy democracy could come to the targeted object quickly with the risk of failing in rendezvous, while the mixed strategy cared about both of the convergent speed and the utmost task, would take autarchy strategy when the connections were available for the follower agents, while the democracy rules had to be used if the connections were not possible.

Time versus space trade-offs for rendezvous in trees

Two identical (anonymous) mobile agents start from arbitrary nodes of an unknown tree and have to meet at some node. Agents move in synchronous rounds: in each round an agent can either stay at the current node or move to one of its neighbors. We consider deterministic algorithms for this rendezvous task. The main result of this paper is a tight trade-off between the optimal time of completing rendezvous and the size of memory of the agents. For agents with $$k$$ memory bits, we show that optimal rendezvous time is $$\Theta (n+n^2/k)$$ in $$n$$ -node trees. More precisely, if $$k \ge c\log n$$ , for some constant $$c$$ , we design agents accomplishing rendezvous in arbitrary trees of size $$n$$ (unknown to the agents) in time $$O(n+n^2/k)$$ , starting with arbitrary delay. We also show that no pair of agents can accomplish rendezvous in time $$o(n+n^2/k)$$ , even in the class of lines of known length and even with simultaneous start. Finally, we prove that at least logarithmic memory is necessary for rendezvous, even for agents starting simultaneously in a $$n$$ -node line.

Preserving Multirobot Connectivity in Rendezvous Tasks in the Presence of Obstacles With Bounded Control Input

Maintaining the connectivity of an underlying robot network during a rendezvous task in the presence of obstacles is a challenge in control systems technology. In this brief, a navigation-function-based potential field approach is developed to address this challenging problem. A concept called connectivity constraint is used to establish a navigation function. A new potential field that simultaneously integrates rendezvous requirement, connectivity maintenance, and obstacle avoidance is also developed. On the basis of this potential field, we design a bounded control input for multirobot control. The proposed controller can drive multiple robots to an agreement state while maintaining connectivity of the underlying network provided that the initial configurations of the robots are connected. Simulations and experiments are performed to verify the effectiveness of the proposed approach.

Classifying rendezvous tasks of arbitrary dimension

The rendezvous is a type of distributed decision tasks including many well-known tasks such as set agreement, simplex agreement, and approximation agreement. An n -dimensional rendezvous task, n ≥ 1 , allows n + 2 distinct input values, and each execution produces at most n + 2 distinct output values. A rendezvous task is said to implement another if an instance of its solution, followed by a protocol based on shared read/write registers, solves the other. The notion of implementation induces a classification of rendezvous tasks of every dimension: two tasks belong to the same class if they implement each other. Previous work on classifying rendezvous tasks only focused on 1-dimensional ones. This paper solves an open problem by presenting the classification of nice rendezvous of arbitrary dimension. An n -dimensional rendezvous task is said to be nice if the q th reduced homology group of its decision space is trivial for q ≠ n , and free for q = n . Well-known examples are set agreement, simplex agreement, and approximation agreement. Each n -dimensional rendezvous task is assigned an algebraic signature, which consists of the n th homology group of the decision space, as well as a distinguished element in the group. It is shown that an n -dimensional nice rendezvous task implements another if and only if there is a homomorphism from its signature to that of the other. Hence the computational power of a nice rendezvous task is completely characterized by its signature. In each dimension, there are infinitely many classes of rendezvous tasks, and exactly countable classes of nice ones. A representative is explicitly constructed for each class of nice rendezvous tasks.