Neural Network Algorithm for Intercepting Targets Moving Along Known Trajectories by a Dubins' Car

The task of intercepting a target moving along a rectilinear or circular trajectory by a Dubins' car is formulated as a time-optimal control problem with an arbitrary direction of the car's velocity at the interception moment. To solve this problem and to synthesize interception trajectories, neural network methods of unsupervised learning based on the Deep Deterministic Policy Gradient algorithm are used. The analysis of the obtained control laws and interception trajectories in comparison with the analytical solutions of the interception problem is performed. The mathematical modeling for the parameters of the target movement that the neural network had not seen before during training is carried out. Model experiments are conducted to test the stability of the neural solution. The effectiveness of using neural network methods for the synthesis of interception trajectories for given classes of target movements is shown

Minimum-time lateral interception of a moving target by a Dubins car

This paper presents the problem of lateral interception by a Dubins car of a target that moves along an a priori known trajectory. This trajectory is given by two coordinates of a planar location and one angle of a heading orientation, every one of them is a continuous function of time. The optimal trajectory planning problem of constructing minimum-time trajectories for a Dubins car in the presence of a priory known time-dependent wind vector field is a special case of the presented problem. Using the properties of the three-dimensional reachable set of a Dubins car, it is proved that the optimal interception point belongs to a part of an analytically described surface in the three-dimensional space. The analytical description of the surface makes it possible to obtain 10 algebraic equations for calculating parameters of the optimal control that implements the minimum-time lateral interception. These equations are generally transcendental and can be simplified for particular cases of target motion (e.g. resting target, straight-line uniform target motion). Finally, some particular cases of the optimal lateral interception validate developments of the paper and highlight the necessity to consider each of 10 algebraic equations in general case.Comment: 16 pages, 19 figure

Time-Optimal Control Problem of Two Non-Synchronous Oscillators

The time-optimal control problem for a system consisting of two non-synchronous oscillators is considered. Each oscillator is controlled with a shared limited scalar control. The objective of the control is to accelerate the oscillatory system to a given specific position, where the first oscillator must have non-zero phase coordinates, but the second one must remain motionless at the terminal moment. For an arbitrary number of unknown switching moments that determine the optimal relay control, the necessary extremum conditions in the form of nonlinear matrix equalities are proposed. The study of the necessary/sufficient conditions of the extremum made it possible to describe the reachability set in the phase space of the first oscillator, to find an analytical form of the curve corresponding to the two-switching control class, which also separates the reachability set of the three switching-control class. The corresponding theorems are proved and the dependence of the criteria on control constraints is shown. Matrix conditions for different classes of control switchings are found. All of the obtained analytical results are numerically validated and illustrated with mathematical modeling

Time-Optimal Control Problem of Two Non-Synchronous Oscillators

The time-optimal control problem for a system consisting of two non-synchronous oscillators is considered. Each oscillator is controlled with a shared limited scalar control. The objective of the control is to accelerate the oscillatory system to a given specific position, where the first oscillator must have non-zero phase coordinates, but the second one must remain motionless at the terminal moment. For an arbitrary number of unknown switching moments that determine the optimal relay control, the necessary extremum conditions in the form of nonlinear matrix equalities are proposed. The study of the necessary/sufficient conditions of the extremum made it possible to describe the reachability set in the phase space of the first oscillator, to find an analytical form of the curve corresponding to the two-switching control class, which also separates the reachability set of the three switching-control class. The corresponding theorems are proved and the dependence of the criteria on control constraints is shown. Matrix conditions for different classes of control switchings are found. All of the obtained analytical results are numerically validated and illustrated with mathematical modeling

2D Optimal Trajectory Planning Problem in Threat Environment for UUV with Non-Uniform Radiation Pattern

Path planning is necessary in many applications using unmanned underwater vehicles (UUVs). The main class of tasks is the planning of safe routes with minimal energy costs and/or minimal levels of emitted physical and information signals. Since the action planner is on board the UUV, the main focus is on methods and algorithms that allow it to build reference trajectories while minimizing the number of calculations. The study is devoted to the problem of the optimal route planning for a UUV with a non-uniform radiation pattern. The problem is stated in the form of two point variational problem for which necessary and sufficient optimality conditions are proved. Particular attention is paid to cases where optimality conditions are not met. These cases are directly related to found specific forms of a radiation pattern. Sufficient optimality conditions are extended on the class of two-link and multi-link motion paths. Software tools have been developed and computer simulations have been performed for various types of radiation patterns

Path Planning in Threat Environment for UUV with Non-Uniform Radiation Pattern

The problem of optimal trajectory planning of the unmanned underwater vehicle (UUV) is considered and analytically solved. The task is to minimize the risk of detection of the moving object by a static sonar while moving between two given points on a plane. The detection is based on the primary acoustic field radiated by the object with a non-uniform radiation pattern. In the first part of the article, the probability of non-detection is derived. Further, it is used as an optimization criterion. The non-uniform radiation pattern of the object differentiates this work from previous research in the area. The optimal trajectory and velocity law of the moving object are found, as well as the criterion value on it