This paper solves the rendezvous problem for a network of underactuated rigid bodies such as quadrotor helicopters. A control strategy is presented that makes the centres of mass of the vehicles converge to an arbitrarily small neighborhood of one another. The convergence is global, and each vehicle can compute its own control input using only an on-board camera and a three-axis rate gyroscope. No global positioning system is required, nor any information about the vehicles' attitudes.
A passivity-based solution of the attitude synchronization problem for kinematic vehicle models is proposed in @cite_0 . @cite_26 @cite_21 @cite_11 , the same problem is investigated for dynamic vehicle models. The proposed controllers do not require measurements of the angular velocity, but they do require absolute attitude measurements. @cite_37 , the authors use the energy shaping approach to design local and distributed controllers for attitude synchronization. The same approach is adopted in @cite_1 to design two attitude synchronization controllers, both local and distributed. The first controller achieves almost-global synchronization for directed connected graphs. However, the controller design is based on distributed observers @cite_9 , and therefore requires auxiliary states to be communicated among neighboring vehicles. It also employs an angular velocity dissipation term that forces all vehicle angular velocities to zero in steady-state. The second controller in @cite_1 does not restrict the final angular velocities, and does not require communication, but it requires an undirected sensing graph, and guarantees only local convergence.
@cite_37 @cite_26 @cite_9 @cite_21 @cite_1 @cite_0 @cite_11
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We address stable synchronization of a network of rotating and translating rigid bodies in three-dimensional space. Motivated by applications that require coordinated spinning spacecraft or diving underwater vehicles, we prove control laws that stably couple and coordinate the dynamics of multiple rigid bodies. We design decentralized, energy shaping control laws for each individual rigid body that depend on the relative orientation and relative position of its neighbors. Energy methods are used to prove stability of the coordinated multi-body dynamical system. To prove exponential stability, we break symmetry and consider a controlled dissipation term that requires each individual to measure its own velocity. The control laws are illustrated in simulation for a network of spinning rigid bodies. In this paper, distributed cooperative attitude synchronization and tracking problems are considered for multiple rigid bodies with attitudes represented by modified rodriguez parameters. Two distributed control laws are proposed and analyzed. The first control law applies a passivity approach for distributed attitude synchronization. The control law guarantees attitude synchronization without the requirement for absolute angular velocity measurements and relative angular velocity measurements between neighboring rigid bodies. The second control law incorporates a time-varying reference attitude, where the reference attitude is allowed to be available to only a subset of the group members under general directed information exchange. The control law guarantees that all rigid bodies track the time-varying reference attitude as long as a virtual leader whose attitude is the time-varying reference attitude has a directed path to all other rigid bodies in the group. Simulation results are presented to demonstrate the effectiveness of the two control laws. In this paper, we study the behavior of a network of N agents, each evolving on the circle. We propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the (possibly time-varying and unidirectional) communication graphs. The global convergence analysis on the N-torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the Euclidean space. We consider the coordinated attitude control problem for a group of spacecraft, without velocity measurements. Our approach is based on the introduction of auxiliary dynamical systems (playing the role of velocity observers in a certain sense) to generate the individual and relative damping terms in the absence of the actual angular velocities and relative angular velocities. Our main focus, in this technical note, is to address the following two problems: 1) Design a velocity-free attitude tracking and synchronization control scheme, that allows the team members to align their attitudes and track a time-varying reference trajectory (simultaneously). 2) Design a velocity-free synchronization control scheme, in the case where no reference attitude is specified, and all spacecraft are required to reach a consensus by aligning their attitudes with the same final time-varying attitude. In this work, one important and novel feature (besides the non-requirement of the angular velocity measurements), consists in the fact that the control torques are naturally bounded and the designer can arbitrarily assign the desired bounds on the control torques, a priori, through the control gains, regardless of the angular velocities. Throughout this technical note, the communication flow between spacecraft is assumed to be undirected. Simulation results of a scenario of four spacecraft are provided to show the effectiveness of the proposed control schemes. Control laws to synchronize attitudes in a swarm of fully actuated rigid bodies, in the absence of a common reference attitude or hierarchy in the swarm, are proposed in [Smith, T. R., Hanssmann, H., & Leonard, N.E. (2001). Orientation control of multiple underwater vehicles with symmetry-breaking potentials. In Proc. 40th IEEE conf. decision and control (pp. 4598-4603); Nair, S., Leonard, N. E. (2007). Stable synchronization of rigid body networks. Networks and Heterogeneous Media, 2(4), 595-624]. The present paper studies two separate extensions with the same energy shaping approach: (i) locally synchronizing the rigid bodies' attitudes, but without restricting their final motion and (ii) relaxing the communication topology from undirected, fixed and connected to directed, varying and uniformly connected. The specific strategies that must be developed for these extensions illustrate the limitations of attitude control with reduced information. Highlighting the control of networked robotic systems, this book synthesizes a unified passivity-based approach to an emerging cross-disciplinary subject. Thanks to this unified approach, readers can access various state-of-the-art research fields by studying only the background foundations associated with passivity. In addition to the theoretical results and techniques,the authors provide experimental case studies on testbeds of robotic systems including networked haptic devices, visual robotic systems, robotic network systems and visual sensor network systems.The text begins with an introduction to passivity and passivity-based control together with the other foundations needed in this book. The main body of the book consists of three parts. The first examines how passivity can be utilized for bilateral teleoperation and demonstrates the inherent robustness of the passivity-based controller against communication delays. The second part emphasizes passivitys usefulness for visual feedback control and estimation. Convergence is rigorously proved even when other passive components are interconnected. The passivity approach is also differentiated from other methodologies. The third part presents the unified passivity-based control-design methodology for multi-agent systems. This scheme is shown to be either immediately applicable or easily extendable to the solution of various motion coordination problems including 3-D attitude pose synchronization, flocking control and cooperative motion estimation.Academic researchers and practitioners working in systems and control and or robotics will appreciate the potential of the elegant and novel approach to the control of networked robots presented here. The limited background required and the case-study work described also make the text appropriate for and, it is hoped, inspiring to students.