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See detailDistributed high-gain attitude synchronization using rotation vectors
Song, W.; Thunberg, Johan UL; Hu, X. et al

in Journal of Systems Science and Complexity (2015), 28(2), 289-304

This paper addresses attitude synchronization problems for systems of multiple rigid-body agents with directed interconnection topologies. Two scenarios which differ in available information are ... [more ▼]

This paper addresses attitude synchronization problems for systems of multiple rigid-body agents with directed interconnection topologies. Two scenarios which differ in available information are considered. In the first scenario the agents can obtain their rotations and angular velocities relative to an inertial reference frame and transmit these information to their neighbors, while in the second scenario the agents can only obtain their own angular velocities and measure the relative rotations and relative angular velocities of their neighbors. By using rotation vectors and the high gain control, the authors provide torque control laws asymptotically synchronizing the rotations of the system almost globally for the first scenario and with initial rotations of the agents contained in a convex ball of SO(3) for the second scenario. An illustrative example is provided to show the synchronization results for both scenarios. [less ▲]

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See detailDistributed attitude synchronization using backstepping and sliding mode control
Thunberg, Johan UL; Song, W.; Hong, Y. et al

in Control Theory and Technology (2014), 12(1), 48-55

We consider the problem of attitude synchronization for systems of rigid body agents with directed topologies. Two different scenarios for the rotation matrices of the agents are considered. In the first ... [more ▼]

We consider the problem of attitude synchronization for systems of rigid body agents with directed topologies. Two different scenarios for the rotation matrices of the agents are considered. In the first scenario, the rotations are contained in a convex subset of SO(3), which is a ball of radius less than π/2, whereas in the second scenario the agents are contained in a subset of SO(3), which is a ball of radius less than π. Using a control law based on backstepping and sliding mode control, we provide distributed, semi-global, torque control laws for the agents so that the rotations asymptotically synchronize. The control laws for the agents in the first scenario only depend on the relative rotations between neighboring agents, whereas the control laws in the second scenario depend on rotations defined in a global coordinate frame. Illustrative examples are provided where the synchronization is shown for both scenarios. [less ▲]

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See detailAttitude consensus using networks of uncalibrated cameras
Thunberg, Johan UL; Hu, X.

in The proceedings of the 33rd Chinese Control Conference (2014)

This paper addresses the problem of consensus on SO(3) for networks of uncalibrated cameras. Under the assumption of a pinhole camera model, we prove convergence to the consensus manifold for two types of ... [more ▼]

This paper addresses the problem of consensus on SO(3) for networks of uncalibrated cameras. Under the assumption of a pinhole camera model, we prove convergence to the consensus manifold for two types of kinematic control laws, when only conjugate rotation matrices KRK-1 are available among the agents. In these conjugate rotations, the rotation matrices are distorted by the (unknown) intrinsic parameters of the cameras. For the conjugate rotations, we introduce distorted versions of well known local parameterizations of SO(3) and show consensus by using three types of control laws. The control laws are similar to the standard consensus protocol used for systems of agents with single integrator dynamics, where pairwise differences between the states of neighboring agents are used. By considering the restriction to the planar case (when all the rotations have the same rotational axes), we weaken the assumptions on the cameras in the system and consider networks where the camera matrices differ between agents. [less ▲]

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See detailDistributed attitude synchronization control of multi-agent systems with switching topologies
Thunberg, Johan UL; Song, W.; Montijano, E. et al

in Automatica (2014), 50(3), 832-840

This paper addresses the attitude synchronization problem in multi-agent systems with directed and switching interconnection topologies. Two cases for the synchronization problem are discussed under ... [more ▼]

This paper addresses the attitude synchronization problem in multi-agent systems with directed and switching interconnection topologies. Two cases for the synchronization problem are discussed under different assumptions about the measurable information. In the first case the agents can measure their rotations relative to a global reference coordinate frame, whilst in the second case they can only measure the relative rotations between each other. Two intuitive distributed control laws based on the axis–angle representations of the rotations are proposed for the two cases, respectively. The invariance of convex balls in SO(3) is guaranteed. Moreover, attitude synchronization is ensured under the well-known mild switching assumptions, the joint strong connection for the first case and joint quasi-strong connection for the second case. To show the effectiveness of the proposed control schemes, illustrative examples are provided. [less ▲]

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See detailEpipolar visual servoing for multirobot distributed consensus
Montijano, E.; Thunberg, Johan UL; Hu, X. et al

in IEEE Transaction on Robotics (2013), 29(5), 1212-1225

In this paper, we give a distributed solution to the problem of making a team of nonholonomic robots reach consensus about their orientations using monocular cameras. We consider a scheme where the ... [more ▼]

In this paper, we give a distributed solution to the problem of making a team of nonholonomic robots reach consensus about their orientations using monocular cameras. We consider a scheme where the motions of the robots are decided using nearest-neighbor rules. Each robot is equipped with a camera and can only exchange visual information with a subset of the other robots. The main contribution of this paper is a new controller that uses the epipoles that are computed from the images provided by neighboring robots, eventually reaching consensus in their orientations without the necessity of directly observing each other. In addition, the controller only requires a partial knowledge of the calibration of the cameras in order to achieve the desired configuration. We also demonstrate that the controller is robust to changes in the topology of the network and we use this robustness to propose strategies to reduce the computational load of the robots. Finally, we test our controller in simulations using a virtual environment and with real robots moving in indoor and outdoor scenarios. [less ▲]

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See detailAnalytical solutions to feedback systems on the special orthogonal group SO(n)
Markdahl, J.; Thunberg, Johan UL; Hoppe, J. et al

in the proceeding of the 52nd Annual Conference on Decision and Control (2013)

This paper provides analytical solutions to the closed-loop kinematics of two almost globally exponentially stabilizing attitude control laws on the special orthogonal group SO(n). By studying the general ... [more ▼]

This paper provides analytical solutions to the closed-loop kinematics of two almost globally exponentially stabilizing attitude control laws on the special orthogonal group SO(n). By studying the general case we give a uniform treatment to the cases of SO(2) and SO(3), which are the most interesting dimensions for application purposes. Working directly with rotation matrices in the case of SO(3) allows us to avoid certain complications which may arise when using local and global many-to-one parameterizations. The analytical solutions provide insight into the transient behaviour of the system and are of theoretical value since they can be used to prove almost global attractiveness of the identity matrix. The practical usefulness of analytical solutions in problems of continuous time actuation subject to piece-wise unavailable or discrete time sensing are illustrated by numerical examples. [less ▲]

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See detailDistributed attitude synchronization control of multi-agent systems with directed topologies
Thunberg, Johan UL; Song, W.; Hong, Y. et al

in the proceedings of the 10th World Congress on Intelligent Control and Automation (2012)

In the present paper we consider the problem of attitude synchronization for a system of rigid body agents. We provide distributed kinematic control laws for two different synchronization problems. In the ... [more ▼]

In the present paper we consider the problem of attitude synchronization for a system of rigid body agents. We provide distributed kinematic control laws for two different synchronization problems. In the two problems the objective is the same, i.e., to synchronize the orientations of the agents, but what is assumed to be measurable by the agents differs. In problem 1 the agents measure their own orientations in a global reference frame, and obtain the orientations of their neighbors by means of communication. In problem 2 the agents only measure the relative orientations to their neighbors. By using the axis-angle representation of the orientation, we show that simple linear control laws solve both synchronization problems. Moreover we show that our proposed control laws work for directed and connected topologies on almost all SO(3) for problem 1 and on convex balls in SO(3) for problem 2. [less ▲]

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See detailDistributed attitude synchronization control of multi-agent systems with time-varying topologies
Song, W.; Thunberg, Johan UL; Hong, Y. et al

in Proceedings of the 10th World Congress on Intelligent Control and Automation (2012)

This paper addresses the attitude synchronization problem of multiple rigid body agents in SO(3) with directed and switching interconnection topologies. Using the axis-angle representation of the ... [more ▼]

This paper addresses the attitude synchronization problem of multiple rigid body agents in SO(3) with directed and switching interconnection topologies. Using the axis-angle representation of the orientation, a distributed controller based on differences between the orientations of agents in a global frame is proposed. In the case of the balanced interconnection graph, the attitude synchronization is achieved with the well-known mild assumption (that is, uniform joint strong connection). To demonstrate the effectiveness of the proposed control scheme, an illustrative example is provided. [less ▲]

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See detailA boolean control network approach to pursuit evasion problems in polygonal environments
Thunberg, Johan UL; Ogren, P.; Hu, X.

in Proceedings of the 2011 IEEE International Conference on Robotics and Automation (ICRA) (2011)

In this paper, the multi pursuer version of the pursuit evasion problem in polygonal environments is addressed. This problem is NP-hard, and therefore we seek good enough, but not optimal solutions. By ... [more ▼]

In this paper, the multi pursuer version of the pursuit evasion problem in polygonal environments is addressed. This problem is NP-hard, and therefore we seek good enough, but not optimal solutions. By modeling the problem as a Boolean Control Network, we can efficiently keep track of which regions are cleared, and which are not, while the input nodes of the network are used to represent the motion of the pursuers. The environment is partitioned into a set of convex regions, where each region correspond to a set of nodes in the network. The method is implemented in ANSI C, and efficiently solves complex environments containing multiple loops and requiring so-called recontamination. The provided examples demonstrate the effectiveness of the method in terms of computational time. [less ▲]

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See detailOptimal output consensus control for systems of agents with continuous linear dynamics
Thunberg, Johan UL; Hu, X.

in Proceedings of 18th IFAC World Congress (2011)

In this paper we study the output consensus problem for systems of agents with linear continuous, time invariant dynamics. We derive control laws with minimal energy that solves the problem, while using ... [more ▼]

In this paper we study the output consensus problem for systems of agents with linear continuous, time invariant dynamics. We derive control laws with minimal energy that solves the problem, while using only relative information. Instead of considering a fixed communication topology for the agents, and derive the optimal control for that topology, we derive the optimal control law for any communication topology between the agents. We show that the optimal control uses only relative information but requires the connectivity graph to be complete and in general requires measurements of the state errors. We identify the cases where the optimal control is only based on output errors, and show that in the infinite time horizon case, the optimal controller can always be expressed as a dynamic controller that is only based on the output errors. Regarding the theoretic contributions of this paper, the control laws are derived using methods from linear vector space optimization and are given in closed form. To the authors knowledge these methods have not been used within this context before. [less ▲]

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See detailDistributed attitude synchronization control
Thunberg, Johan UL; Montijano, E.; Hu, X.

in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) (2011)

In this paper we consider the problem of constructing feedback control laws for a system of n agents that shall synchronize their attitudes in SO(3). We propose distributed controllers for two ... [more ▼]

In this paper we consider the problem of constructing feedback control laws for a system of n agents that shall synchronize their attitudes in SO(3). We propose distributed controllers for two synchronization problems, in which the objective is the same, to synchronize the orientations, but what the agents can perceive or communicate differs. In the first problem the agents can measure their orientation to a common reference object, and either communicate with the neighbors or estimate the relative orientation to their neighbors. In the second problem the agents can, without communication, only measure the relative orientation to the neighbors. For the first problem we present a controller which will lead to synchronization, provided the neighborhood graph is connected. For the second problem we present a controller that will lead to synchronization provided the neighborhood graph is connected and the agents initially are contained within a geodesic ball of radius π/2, which is the maximal convex set in SO(3). [less ▲]

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See detailMulti-robot distributed visual consensus using epipoles
Montijano, E.; Thunberg, Johan UL; Hu, X. et al

in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) (2011)

In this paper we give a distributed solution to the problem of making a team of non-holonomic robots achieve the same heading (attitude consensus problem) using vision sensors with limited field of view ... [more ▼]

In this paper we give a distributed solution to the problem of making a team of non-holonomic robots achieve the same heading (attitude consensus problem) using vision sensors with limited field of view. The use of cameras with constrained field of view limits the information the robots perceive compared to other omnidirectional sensors. This makes the consensus problem more complicated, because the robots will not always be able to observe other robots. By using structure from motion computed from images, the robots can estimate the difference in their headings from common observations of the environment without the necessity of directly observe each other. In this way, the robots achieve the consensus in their headings while observing the environment instead of each other. The contribution of the paper is a new controller that uses the epipoles computed from pairs of images to estimate the misalignment between neighbor robots. In addition, the control is robust to changes in the topology of the network and does not require to know the calibration of the cameras in order to achieve the desired configuration. To the best of our knowledge, this is the first time that the epipoles are used in multi-robot consensus, putting their properties in value. [less ▲]

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See detailOptimal output consensus control and outlier detection
Thunberg, Johan UL; Hu, X.

in Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (2010)

In this paper we study the output consensus problem for systems of agents with linear continuous time invariant dynamics, and derive control laws that minimize a conical combination of the energies of the ... [more ▼]

In this paper we study the output consensus problem for systems of agents with linear continuous time invariant dynamics, and derive control laws that minimize a conical combination of the energies of the agents control signals, while only using local information. We show that the optimal control requires the connectivity graph to be complete and in general requires measurements of the state errors. We identify the cases where the optimal control is only based on output errors, and show that in the infinite time horizon case, the optimal control can always be expressed as a dynamic control that is only based on the output errors. We also give a Lemma for the position of the equilibrium point for a large class of agent dynamics. As a second part of this paper we consider the problem of outlier detection, in which an agent wants to deduce if an other agent is using the consensus controller, or if it is an outlier that uses a different controller. We introduce the outlier detection equation. [less ▲]

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