Метод оптимизации траектории мобильного робота в поле источников-репеллеров

Рассматривается процедура корректировки траектории движения робототехнической платформы (РТП) на плоскости с целью снижения вероятности её поражения/обнаружения в поле конечного числа источников-репеллеров. Каждый из таких источников описан математической моделью некоторого фактора противодействия целостности или скрытности РТП. Указанная процедура основана, с одной стороны, на понятии характерной вероятностной функции системы источников-репеллеров, позволяющем оценивать степень влияния этих источников на движущуюся РТП. Из этого понятия вытекает используемая здесь в качестве показателя оптимизации целевой траектории вероятность её успешного прохождения. С другой стороны, эта процедура базируется на решении локальных оптимизационных задач, позволяющих корректировать отдельные участки исходной траектории с учетом нахождения в их окрестностях конкретных источниковрепеллеров с заданными параметрами. Каждый из таких источников характеризуется потенциалом, частотой воздействия, радиусом действия и параметрами спада поля. Корректировка траектории происходит итерационно и учитывает целевое значение вероятности прохождения. Основным ограничением на вариацию исходной траектории является максимально допустимое отклонение измененной траектории от исходной. Если такого ограничения нет, то задача может потерять смысл, поскольку тогда можно выделить область, охватывающую все препятствия и источники, и обойти её по периметру. Поэтому осуществляется поиск такого локального экстремума, который соответствует допустимой кривой в смысле указанного ограничения. Предлагаемая в настоящей работе итерационная процедура позволяет проводить поиск соответствующих локальных максимумов вероятности прохождения РТП в поле нескольких произвольно расположенных и ориентированных источников в некоторой окрестности исходной траектории. Вначале ставится и решается задача оптимизации траектории при условии движения в поле одного источника с областью действия в виде кругового сектора, затем полученный результат распространяется на случай нескольких аналогичных источников. Основной проблемой исследования является выбор общего вида функционала в каждой точке исходной кривой, а также его коэффициентов настройки. Показано, что выбор этих коэффициентов настройки есть адаптивная процедура, входными переменными которой являются характерные геометрические величины, описывающие текущую траекторию в поле источников. Для устранения осцилляций, возникающих вследствие локальности предлагаемой процедуры, применяются стандартные процедуры медианного сглаживания. Результаты моделирования показывают высокую эффективность предложенной процедуры для корректировки ранее спланированной траектории

Optimization of mobile robot movement on a plane with finite number of repeller sources

The paper considers the problem of planning a mobile robot movement in a conflict environment, which is characterized by the presence of areas that impede the robot to complete the tasks. The main results of path planning in the conflict environment are considered. Special attention is paid to the approaches based on the risk functions and probabilistic methods. The conflict areas, which are formed by point sources that create in the general case asymmetric fields of a continuous type, are observed. A probabilistic description of such fields is proposed, examples of which are the probability of detection or defeat of a mobile robot. As a field description, the concept of characteristic probability function of the source is introduced; which allows us to optimize the movement of the robot in the conflict environment. The connection between the characteristic probability function of the source and the risk function, which can be used to formulate and solve simplified optimization problems, is demonstrated. The algorithm for mobile robot path planning that ensures the given probability of passing the conflict environment is being developed. An upper bound for the probability of the given environment passing under fixed boundary conditions is obtained. A procedure for optimizing the robot path in the conflict environment is proposed, which is characterized by higher computational efficiency achieved by avoiding the search for an exact optimal solution to a suboptimal one. A procedure is proposed for optimizing the robot path in the conflict environment, which is characterized by higher computational efficiency achieved by avoiding the search for an exact optimal solution to a suboptimal one. The proposed algorithms are implemented in the form of a software simulator for a group of ground-based robots and are studied by numerical simulation methods

Trajectory Planning Algorithms in Two-Dimensional Environment with Obstacles

This article proposes algorithms for planning and controlling the movement of a mobile robot in a two-dimensional stationary environment with obstacles. The task is to reduce the length of the planned path, take into account the dynamic constraints of the robot and obtain a smooth trajectory. To take into account the dynamic constraints of the mobile robot, virtual obstacles are added to the map to cover the unfeasible sectors of the movement. This way of accounting for dynamic constraints allows the use of map-oriented methods without increasing their complexity. An improved version of the rapidly exploring random tree algorithm (multi-parent nodes RRT – MPN-RRT) is proposed as a global planning algorithm. Several parent nodes decrease the length of the planned path in comprise with the original one-node version of RRT. The shortest path on the constructed graph is found using the ant colony optimization algorithm. It is shown that the use of two-parent nodes can reduce the average path length for an urban environment with a low building density. To solve the problem of slow convergence of algorithms based on random search and path smoothing, the RRT algorithm is supplemented with a local optimization algorithm. The RRT algorithm searches for a global path, which is smoothed and optimized by an iterative local algorithm. The lower-level control algorithms developed in this article automatically decrease the robot’s velocity when approaching obstacles or turning. The overall efficiency of the developed algorithms is demonstrated by numerical simulation methods using a large number of experiments

Adaptive Control Algorithm of the Synchronous Generator

The article discusses the the problem of controlling a synchronous generator, namely, maintaining the stability of the control object in the conditions of occurrence of noise and disturbances in the regulatory process. The model of a synchronous generator is represented by a system of differential equations of Park-Gorev, where state variables are computed relative to synchronously rotating d, q-axis. Management of synchronous generator is proposed to organize on the basis of the position-path control using algorithms to adapt with the reference model. Basic control law directed on the stabilizing indicators the frequency generated by the current and the required power level, which is achieved by controlling the mechanical torque on the shaft of the turbine and the value of the excitation voltage of the synchronous generator. Modification of the classic adaptation algorithm using the reference model, allowing to minimize the error of the reference regulation and the model under investigation within the prescribed limits, produced by means of the introduction of additional variables controller adaptation in the model. Сarried out the mathematical modeling of control provided influence on the studied model of continuous nonlinear and unmeasured the disturbance. Simulation results confirm the high level accuracy of tracking and adaptation investigated model with respect to the reference, and the present value of the loop error depends on parameters performance of regulator

Impact of the Feeder Aerodynamics Characteristics on the Power of Control Actions in Steady and Transient Regimes

In this paper we consider one of the problems in the development of control system for the feeder for MAAT transportation system. This problem is connected with estimation of inboard energy requirements. Traditionally such estimation is made on the basis of static relations. They allow assessing the power required to move a solid body with a constant air speed. However a contribution from aerodynamic forces and moments can vary depending on a regime of motion (value of linear and angular accelerations, angle of attack, etc). Because of that fact, this work investigates the estimation of the total required inboard energy and contribution of aerodynamic forces and moments to it in specified feeder motion regimes. The method of assessment is based on the feeder model, which is built on the equations of the rigid body. This paper contains general structure of feeder mathematical model, which includes equations of statics, dynamics and control mechanisms. The example of the exact feeder shape gives the application of this models with the details in terms of aerodynamic characteristics, inertial mass parameters and locations of control mechanisms. Feeder model is complemented by the external environment model, including the wind flow model. Development of the latter models is investigated in the talk “Probabilistic Approaches to Estimation of Flight Environment for Feeder of Multibody Transport Airship System”, presented on this conference. Three main feeder motion regimes were chosen for the estimation of the required power. These three regimes are hovering in one point, motion along a straight line and motion along a specified circle. Steady motion is considered along with transient regimes, when the feeder is moving to the specified trajectories. The results allow assessing the required power for steady and transient regimes for each considered trajectory, different values of air speed, different locations of centre of gravity and different angles of attack. Additionally, study of Kalman controllability and Lyapunov stability was made for the special feeder motion regimes. The conclusions about the optimal feeder shape are given based on this work.Peer reviewe