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Experimental design trade-offs for gene regulatory network inference: an in silico study of the yeast Saccharomyces cerevisiae cell cycle Markdahl, Johan ; Colombo, Nicolo ; Thunberg, Johan et al in Proceedings of the 56th IEEE Conference on Decision and Control (2017, December) Time-series of high throughput gene sequencing data intended for gene regulatory network (GRN) inference are often short due to the high costs of sampling cell systems. Moreover, experimentalists lack a ... [more ▼] Time-series of high throughput gene sequencing data intended for gene regulatory network (GRN) inference are often short due to the high costs of sampling cell systems. Moreover, experimentalists lack a set of quantitative guidelines that prescribe the minimal number of samples required to infer a reliable GRN model. We study the temporal resolution of data vs.quality of GRN inference in order to ultimately overcome this deficit. The evolution of a Markovian jump process model for the Ras/cAMP/PKA pathway of proteins and metabolites in the G1 phase of the Saccharomyces cerevisiae cell cycle is sampled at a number of different rates. For each time-series we infer a linear regression model of the GRN using the LASSO method. The inferred network topology is evaluated in terms of the area under the precision-recall curve (AUPR). By plotting the AUPR against the number of samples, we show that the trade-off has a, roughly speaking, sigmoid shape. An optimal number of samples corresponds to values on the ridge of the sigmoid. [less ▲] Detailed reference viewed: 146 (10 UL)Distributed high-gain attitude synchronization using rotation vectors ; Thunberg, Johan ; 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 ▲] Detailed reference viewed: 107 (4 UL)A solution for Multi-Alignment by Transformation Synchronisation Bernard, Florian ; Thunberg, Johan ; et al in The proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2015) The alignment of a set of objects by means of transformations plays an important role in computer vision. Whilst the case for only two objects can be solved globally, when multiple objects are considered ... [more ▼] The alignment of a set of objects by means of transformations plays an important role in computer vision. Whilst the case for only two objects can be solved globally, when multiple objects are considered usually iterative methods are used. In practice the iterative methods perform well if the relative transformations between any pair of objects are free of noise. However, if only noisy relative transformations are available (e.g. due to missing data or wrong correspondences) the iterative methods may fail. Based on the observation that the underlying noise-free transformations lie in the null space of a matrix that can directly be obtained from pairwise alignments, this paper presents a novel method for the synchronisation of pairwise transformations such that they are globally consistent. Simulations demonstrate that for a high amount of noise, a large proportion of missing data and even for wrong correspondence assignments the method delivers encouraging results. [less ▲] Detailed reference viewed: 224 (38 UL)Distributed attitude synchronization using backstepping and sliding mode control Thunberg, Johan ; ; 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 ▲] Detailed reference viewed: 175 (0 UL)Attitude consensus using networks of uncalibrated cameras Thunberg, Johan ; 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 ▲] Detailed reference viewed: 100 (0 UL)Consensus and Pursuit-Evasion in Nonlinear Multi-Agent Systems Thunberg, Johan Doctoral thesis (2014) Within the field of multi-agent systems theory, we study the problems of consensus and pursuit-evasion. In our study of the consensus problem, we first provide some theoretical results and then consider ... [more ▼] Within the field of multi-agent systems theory, we study the problems of consensus and pursuit-evasion. In our study of the consensus problem, we first provide some theoretical results and then consider the problem of consensus on SO(3) or attitude synchronization. In Chapter 2, for agents with states in Rm, we present two theorems along the lines of Lyapunov’s second method that, under different conditions, guarantee asymptotic state consensus in multi-agent systems where the interconnection topologies are switching. The first theorem is formulated by using the states of the agents in the multiagent system, whereas the second theorem is formulated by using the pairwise states for pairs of agents in the multi-agent system. In Chapter 3, the problem of consensus on SO(3) for a multi-agent system with directed and switching interconnection topologies is addressed. We provide two different types of kinematic control laws for a broad class of local representations of SO(3). The first control law consists of a weighted sum of pairwise differences between positions of neighboring agents, expressed as coordinates in a local representation. The structure of the control law is well known in the consensus community for being used in systems of agents in the Euclidean space, and here we show that the same type of control law can be used in the context of consensus on SO(3). In a later part of this chapter, based on the kinematic control laws, we introduce torque control laws for a system of rigid bodies in space and show that the system reaches consensus when these control laws are used. Chapter 4 addresses the problem of consensus on SO(3) for networks of uncalibrated cameras. Under the assumption that each agent uses a camera in order to measure its rotation, we prove convergence to the consensus set for two types of kinematic control laws, where only conjugate rotation matrices are available for the agents. In these conjugate rotations, the rotation matrix can be seen as distorted by the (unknown) intrinsic parameters of the camera. For the conjugate rotations we introduce distorted versions of well known local parameterizations of SO(3) and show consensus by using control laws that are similar to the ones in Chapter 3, with the difference that the distorted local representations are used instead. In Chapter 5, we study the output consensus problem for homogeneous systems of agents with linear continuous time-invariant dynamics. We derive control laws that solve the problem, while minimizing a cost functional of the control signal. Instead of considering a fixed communication topology for the system, we derive the optimal control law without any restrictions on the topology. We show that for all linear output controllable homogeneous systems, the optimal control law uses only relative information but requires the connectivity graph to be complete and in general requires measurements of the state errors. We identify cases where the optimal control law is only based on output errors. In Chapter 6, we address the multi-pursuer version of the visibility pursuit-evasion problem in polygonal environments. By discretizing the problem and applying a Mixed Integer Linear Programming (MILP) framework, we are able to address problems requiring so-called recontamination and also impose additional constraints, such as connectivity between the pursuers. The proposed MILP formulation is less conservative than solutions based on graph discretizations of the environment, but still somewhat more conservative than the original underlying problem. It is well known that MILPs, as well as multi-pursuer pursuit-evasion problems, are NP-hard. Therefore we apply an iterative Receding Horizon Control (RHC) scheme, where a number of smaller MILPs are solved over shorter planning horizons. The proposed approach is illustrated by a number of solved examples. [less ▲] Detailed reference viewed: 125 (10 UL)Distributed attitude synchronization control of multi-agent systems with switching topologies Thunberg, Johan ; ; 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 ▲] Detailed reference viewed: 118 (2 UL)Epipolar visual servoing for multirobot distributed consensus ; Thunberg, Johan ; 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 ▲] Detailed reference viewed: 86 (1 UL)Analytical solutions to feedback systems on the special orthogonal group SO(n) ; Thunberg, Johan ; 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 ▲] Detailed reference viewed: 105 (3 UL)A transformation of the position based visual servoing problem into a convex optimization problem ; Thunberg, Johan ; in Proceedings of the 51th IEEE Conference on Decision and Control (2012) Here we address the problem of moving a camera from an initial pose to a final pose. The trajectory between the two poses is subject to constraints on the camera motion and the visibility, where we have ... [more ▼] Here we address the problem of moving a camera from an initial pose to a final pose. The trajectory between the two poses is subject to constraints on the camera motion and the visibility, where we have bounds on the allowed velocities and accelerations of the camera and require that a set of point features are visible for the camera. We assume that the pose is possible to retrieve from the observations of the point features, i.e., we have a Position Based Visual Servoing Problem with constraints. We introduce a two step method that transforms the problem into a convex optimization problem with linear constraints. In the first step the rotational motion is restricted to be of a certain type. This restriction allows us to retrieve an explicit solution of the rotational motion that is optimal in terms of minimizing geodesic distance. Furthermore, this restriction guarantees that the rotational motion satisfies the constraints. Using the explicit solution, we can formulate a convex optimization problem for the translational motion, where we include constraints on workspace and visibility. [less ▲] Detailed reference viewed: 98 (0 UL)Distributed attitude synchronization control of multi-agent systems with directed topologies Thunberg, Johan ; ; 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 ▲] Detailed reference viewed: 110 (0 UL)Distributed attitude synchronization control of multi-agent systems with time-varying topologies ; Thunberg, Johan ; 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 ▲] Detailed reference viewed: 93 (0 UL)A mixed integer linear programming approach to pursuit evasion problems with optional connectivity constraints Thunberg, Johan ; in Autonomous Robots (2011), 31(4), 333-343 In this paper, we address the multi pursuer version of the pursuit evasion problem in polygonal environments. By discretizing the problem, and applying a Mixed Integer Linear Programming (MILP) framework ... [more ▼] In this paper, we address the multi pursuer version of the pursuit evasion problem in polygonal environments. By discretizing the problem, and applying a Mixed Integer Linear Programming (MILP) framework, we are able to address problems requiring so-called recontamination and also impose additional constraints, such as connectivity between the pursuers. The proposed MILP formulation is less conservative than solutions based on graph discretizations of the environment, but still somewhat more conservative than the original underlying problem. It is well known that MILPs, as well as multi pursuer pursuit evasion problems, are NP-hard. Therefore we apply an iterative Receding Horizon Control (RHC) scheme where a number of smaller MILPs are solved over shorter planning horizons. The proposed approach is implemented in Matlab/Cplex and illustrated by a number of solved examples. [less ▲] Detailed reference viewed: 113 (0 UL)Distributed attitude synchronization control Thunberg, Johan ; ; 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 ▲] Detailed reference viewed: 92 (0 UL)A boolean control network approach to pursuit evasion problems in polygonal environments Thunberg, Johan ; ; 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 ▲] Detailed reference viewed: 93 (0 UL)Multi-robot distributed visual consensus using epipoles ; Thunberg, Johan ; 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 ▲] Detailed reference viewed: 81 (0 UL)Optimal output consensus control for systems of agents with continuous linear dynamics Thunberg, Johan ; 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 ▲] Detailed reference viewed: 89 (0 UL)An iterative Mixed Integer Linear Programming Approach to pursuit evasion problems in polygonal environments Thunberg, Johan ; in Proceedings of the 2010 IEEE International Conference on Robotics and Automation (ICRA) (2010) In this paper, we address the multi pursuer version of the pursuit evasion problem in polygonal environments. It is well known that this problem is NP-hard, and therefore we seek efficient, but not ... [more ▼] In this paper, we address the multi pursuer version of the pursuit evasion problem in polygonal environments. It is well known that this problem is NP-hard, and therefore we seek efficient, but not optimal, solutions by relaxing the problem and applying the tools of Mixed Integer Linear Programming (MILP) and Receding Horizon Control (RHC). Approaches using MILP and RHC are known to produce efficient algorithms in other path planning domains, such as obstacle avoidance. Here we show how the MILP formalism can be used in a pursuit evasion setting to capture the motion of the pursuers as well as the partitioning of the pursuit search region into a cleared and a contaminated part. RHC is furthermore a well known way of balancing performance and computation requirements by iteratively solving path planning problems over a receding planning horizon, and adapt the length of that horizon to the computational resources available. The proposed approach is implemented in Matlab/Cplex and illustrated by a number of solved examples. [less ▲] Detailed reference viewed: 124 (0 UL)Optimal output consensus control and outlier detection Thunberg, Johan ; 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 ▲] Detailed reference viewed: 43 (0 UL)Towards optimal positioning of surveillance UGVs ; ; Thunberg, Johan in Optimization and Cooperative Control Strategies (2009) Unmanned Ground Vehicles (UGVs) equipped with surveillance cameras present a flexible complement to the numerous stationary sensors being used in security applications today. However, to take full ... [more ▼] Unmanned Ground Vehicles (UGVs) equipped with surveillance cameras present a flexible complement to the numerous stationary sensors being used in security applications today. However, to take full advantage of the flexibility and speed offered by a group of UGV platforms, a fast way to compute desired camera locations to cover an area or a set of buildings, e.g., in response to an alarm, is needed. Building upon earlier results in terrain guarding and sensor placement we propose a way to find candidate guard positions that satisfy a large set of view angle and range constraints simulataneously. Since the original problem is NP-complete, we do not seek to find the true optimal set of guard positions. Instead, a near optimal subset of the candidate points is chosen using a scheme with a known approximation ratio of O(log(n)). A number of examples are presented to illustrate the approach. [less ▲] Detailed reference viewed: 98 (1 UL) |
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