In this paper, for any homogeneous system of agents with linear continuous time dynamics, we formulate an optimal control problem. In this problem a convex cost functional of the control signals of the agents shall be minimized, while the outputs of the agents shall coincide at some given finite time. This is an instance of the rendezvous or finite time consensus problem. We solve this problem wit

This paper addresses the consensus problem and the formation problem on SE(3) in multi-agent systems with directed and switching interconnection topologies. Several control laws are introduced for the consensus problem. By a simple transformation, it is shown that the proposed control laws can be used for the formation problem. The design is first conducted on the kinematic level, where the veloci

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 tr

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

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

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

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

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 observ

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

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

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 communic

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 orien

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 conser

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 effici

Many important problems involving a group of unmanned ground vehicles (UGVs) are closely related to the multi traviling salesman problem (m-TSP). This paper comprises a comparative study of a number of algorithms proposed in the litterature to solve m-TSPs occuring in robotics. The investigated algoritms include two mixed integer linear programming (MILP) formulations, a market based approach (MA)

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

Vehicle-to-vehicle (V2V) communication is the key technology enabling platooning. This letter proposes an analytical framework that combines the characteristics of V2V communication (packet loss probabilities and packet transmission delays) with the physical mobility characteristics of vehicles (speed, distance between vehicles and their brake capacities). First, we present the feasible region of

The reconstruction of an object’s shape or surface from a set of 3D points plays an important role in medical image analysis, e.g. in anatomy reconstruction from tomographic measurements or in the process of aligning intra-operative navigation and preoperative planning data. In such scenarios, one usually has to deal with sparse data, which significantly aggravates the problem of reconstruction. H

The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take geometric consistency between points into account. Computationally, the multi-matching problem is difficult. It can be phrased as simultaneously solving multiple (

Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence methods aim to find a solution between pairs of shapes, even if multiple instances of the same class are available. While isometries are often studied in shape