Riiklik vaktsiinikindlustussüsteem: kuidas hakkab toimima?

Eesti Arst 2022; 101(3):190–19

Planar Cooperative Extremum Seeking with Guaranteed Convergence Using A Three-Robot Formation

In this paper, a combined formation acquisition and cooperative extremum seeking control scheme is proposed for a team of three robots moving on a plane. The extremum seeking task is to find the maximizer of an unknown two-dimensional function on the plane. The function represents the signal strength field due to a source located at maximizer, and is assumed to be locally concave around maximizer and monotonically decreasing in distance to the source location. Taylor expansions of the field function at the location of a particular lead robot and the maximizer are used together with a gradient estimator based on signal strength measurements of the robots to design and analyze the proposed control scheme. The proposed scheme is proven to exponentially and simultaneously (i) acquire the specified geometric formation and (ii) drive the lead robot to a specified neighborhood disk around maximizer, whose radius depends on the specified desired formation size as well as the norm bounds of the Hessian of the field function. The performance of the proposed control scheme is evaluated using a set of simulation experiments.Comment: Presented at the 2018 IEEE Conference on Decision and Control (CDC), Miami Beach, FL, US

Cooperative extremum seeking for a one-dimensional non-linear map using a two-robot formation

This paper presents a cooperative extremum seeking control scheme that uses a linear formation of two robots to find a maximum of an unknown one-dimensional non-linear map. A consensus control algorithm is used to drive the centre of the formation and an integral feedback control loop is proposed to drive the gradient of an unknown field function to zero. Simulation results are provided to evaluate the performance of the proposed method.This research was supported by the Australian Research Council under grant DP16010112

Cooperative source-seeking by means of autonomous mobile robots

This thesis addresses a problem of the source localisation of an unknown non-linear field by means of mobile robots. The source localization problem has been a topic of growing interest and intensive research over the last two decades due to multiple potential applications. These include localisation of illicit substances, environmental pollution monitoring and detection of outflows in the area surrounding a toxic waste storage, surveillance and rescue operations. In our work we consider the minimal number of mobile robots needed to perform gradient estimation at each time instance using only measurements of the field value at mobile robots' current location. We consider the case when no record of the previous measurements is kept in robots' memory and no additional explorations manoeuvres are done by the robots' to collect measurements at several spatially distinct points. For this case the minimal number of mobile robots needed are: two mobile robots for extremum seeking on a line and three mobile robots for a planar source localisation. We present a control that uses the difference of the field measurements to obtain an estimate of the gradient value, and a consensus algorithm for formation acquisition.We use Taylor expansions of the field function and its gradient to carry out the analysis of the error associated with the chosen gradient estimation technique. We show that for a field with bounded second derivative the proposed control scheme is guaranteed to exponentially and simultaneously acquire the specified geometric formation, and drive the lead mobile robot to a neighborhood of the maximizer of the field. We formally establish guaranteed convergence results using Lyapunov's direct method. The size of this neighborhood depends on the specified desired formation size as well as on the norm bound on the second derivative of the field function. Additionally, we propose a modification of the convergence analysis that uses Popov absolute stability criterion to better capture the properties of the non-linear error inputs associated with the system. Further, motivated by realities of the practical implementation, we consider a problem of accurate position estimation for a mobile robot. We design a switching Extended Kalman Filter scheme for mobile robot's position and orientation using the minimal sensor set up, consisting of wheel encoders, IMU and GPS unit. The proposed scheme is able to switch between two measurement models, depending on the available sensor data. We evaluate the proposed algorithm using computer simulations and field experiments. Additionally, we design a Kalman Filter to estimate and compensate the systematic odometry and gyroscope errors