Kaveh Fathian

Globally asymptotically stable distributed control for distance and bearing based multi-agent formations

We present a continuous, distributed control scheme for formation control of multi-agent systems based on local position measurements. The desired formation is defined in terms of both inter-agent distances and bearing angles. If the sensing topology among agents satisfy certain sufficient conditions, it is shown that the control globally stabilizes the agents to any feasible desired formation. Simulations for up to 32 agents starting from random positions on the plane verifies that agents can successfully converge to the desired formation with no knowledge of the global coordinate frame.

Distributed control of cyclic formations with local relative position measurements

We propose a distributed control scheme for cyclic formations of multi-agent systems using relative position measurements in local coordinate frames. It is assumed that agents cannot communicate with each other and do not have access to global position information. For the case of three and four agents with desired formation defined as a regular polygon, we prove that under the proposed control, starting from almost any initial condition, agents converge to the desired configuration. Moreover, it is shown that the control is robust to the failure of any single agent. From Monte Carlo analysis, a conjecture is proposed to extend the results to any number of agents.

Virtual Thermal Sensing and Control of Heat Distribution Using State Estimation

Many industrial applications require or can be improved by strict control of the temperature distribution on a surface. This initial investigation presents modeling and control of heat flow on an aluminum plate. Temperature distribution is modeled using a dense equivalent electrical circuit. An observer is designed based on the model to estimate the temperature distribution on the plate. The estimation is used in a controller to regulate the temperature of a desired point on the plate, given discrete heat input elements but no cooling elements. Experiments are conducted to compare the realism of the heat flow model and efficacy of the control method with experimental data. Results show that the steady state error between the actual and estimated temperatures at different points on the surface is always less than 0.5°C, which indicates accurate estimation of the temperature. The RMS error between desired and actual temperatures through all experiments is less than 2°C which indicates fast regulation and low steady state error.Copyright

A new approach for solving the Five-Point Relative Pose Problem for vision-based estimation and control

The problem of finding the relative camera pose between two calibrated camera views given five matched feature points is called the Five Point Relative Pose Problem. There exists a variety of solutions in the literature. However, existing methods rely on solving an optimization problem that is based on the Essential matrix. The Essential matrix has fundamental weaknesses, and introduces these weaknesses into algorithms that employ it. In this paper, we propose a new and practical method eschews the essential matrix by representing the pose estimation problem in the quaternion space. The new method has numerous advantages. Unlike the Essential Matrix, it is not prone to problems when faced with coplanar points or zero translation between two camera views. Rotation, scaled translation, and scaled depth of the points with respect to both camera frames are simultaneously recovered. Furthermore, the algorithm is robust to noise and can be easily extended to more than five points. Investigations using simulated images under noise have validated the new method and verify that the algorithm can be used in practical context such as Position Based Visual Servoing.

Camera relative pose estimation for visual servoing using quaternions

Abstract We present a novel approach to estimate the rotation and translation between two camera views from a minimum of five matched points in the images. Our approach simultaneously recovers the 3D structure of the points up to a common scale factor, and is immune to a variety of problems that plague existing methods that are based on the Euclidean homography or Essential matrix. Methods based on homography only function when feature points are coplanar in 3D space. Methods based on the Essential matrix often lose accuracy as the translation between two camera views goes to zero or when points are coplanar. By recovering the rotation and translation independently using quaternions, our algorithm eschews the shortcomings of these methods. Moreover, we do not impose any constraints on the 3D configuration of the points (such as coplanar or non-coplanar constraints). Our method is particularly well-suited for Position-Based Visual Servoing (PBVS) applications. Investigations using both simulations and experiments validate the new method. Comparisons between the proposed algorithm and the existing algorithms establish that our algorithm is robust to noise. A Matlab implementation of our algorithm is available online and free.

Distributed formation control under arbitrarily changing topology

The problem of controlling a group of agents to achieve a desired geometric formation is considered. We provide sufficient conditions under which agents autonomously achieve any feasible desired formation, while the sensing topology among them can change arbitrarily. The desired formation is defined in terms of inter-agent distances and angles. Agents do not need to have a common or global coordinate frame, and local relative position measurements of their neighbors suffices to achieve the desired formation. Stability analysis, illustrative examples, and simulation results are provided.