This paper is concerned with a Minimum-Time Intercept Problem (MTIP), for which a Dubins vehicle is guided from a position with a prescribed initial orientation angle to intercept a moving target in minimum time. Some geometric properties for the solution of the MTIP are presented, showing that the solution path must lie in a sufficient family of 4 candidates. In addition, necessary and sufficient conditions for optimality of each candidate are established. When the target's velocity is constant, by employing the geometric properties, those 4 candidates are transformed to a class of sufficiently smooth real-valued functions. In order to compute all the 4 candidates, an efficient and robust algorithm to find all the zeros of sufficiently smooth real-valued functions is developed. Since the MTIP with a constant target's velocity is equivalent to the path planning problem of Dubins vehicle in a constant drift field, developing such an algorithm also enables efficiently finding the shortest Dubins path in a constant drift field. Finally, some numerical examples are presented, demonstrating and verifying the developments of the paper.
We present a path planning problem for a pursuer to intercept a target traveling on a circle. The pursuer considered here has limited yaw rate, and therefore its path should satisfy the kinematic constraints. We assume that the distance between initial position of the pursuer and any point on the target circle is greater than four times the minimum turn radius of the pursuer. We prove the continuity of the Dubins paths of type Circle-Straight line-Circle with respect to the position on the target circle. This is used to prove that the optimal interception path is a Dubins path, and we present …
The minimum-time path for intercepting a moving target with a prescribed impact angle is studied in the paper. The candidate paths from Pontryagin's maximum principle are analyzed, so that each candidate is related to a zero of a real-valued function. It is found that the real-valued functions or their first-order derivatives can be converted to polynomials of at most fourth degree. As a result, each canidate path can be computed within a constant time by embedding a standard polynomial solver into the typical bisection method. The control strategy along the shortest candidate eventually gives…
We propose predefined-time consensus-based cooperative guidance laws for a swarm of interceptors to simultaneously capture a target capable of executing various kinds of motions. Unlike leader-follower cooperative guidance techniques, the swarm of interceptors has no leader and each interceptor executes its own guidance command in a distributive fashion, thus obviating the residency of the mission over a single interceptor. We first design cooperative guidance commands subject to target's mobility, followed by the same when the target is stationary, and also account for interceptors' changing …
Cooperative Integrated Estimation-Guidance for Simultaneous Interception of Moving Targets
Intelligent Systems & Control (ISaC) Lab, Department of Aerospace Engineering, Indian Institute of Technology Bombay（智能系统与控制实验室，航空航天工程系，印度理工学院班加罗尔）；Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati（智能系统引导、自主、学习与控制实验室，航空航天工程与工程力学系，辛辛那提大学）
Intelligent Systems & Control (ISaC) Lab, Department of Aerospace Engineering, Indian Institute of Technology Bombay（智能系统与控制实验室，航空航天工程系，印度理工学院孟买分校）；Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati（智能系统引导、自主性、学习与控制（GALACxIS）实验室，航空航天工程与工程力学系，辛辛那提大学）
This paper presents an optimal guidance approach for a UAV navigation between two given points in 3D considering the wind influence. The proposed cost function to be minimized involves the weighting of the travel time and the control energy. An analytical expression is derived for the optimal cost yielding a fourth-order polynomial whose positive real roots correspond to the optimal travel times. The optimization problem is shown to be equivalent to the Zero-Effort-Miss/Zero-Effort-Velocity (ZEM/ZEV) optimal guidance approach for the case of a constant wind acceleration. Case studies for the r…
In this paper we develop a geometric analysis and a numerical algorithm, based on indirect methods, to solve optimal guidance of endo-atmospheric launch vehicle systems under mixed control-state constraints. Two main difficulties are addressed. First, we tackle the presence of Euler singularities by introducing a representation of the configuration manifold in appropriate local charts. In these local coordinates, not only the problem is free from Euler singularities but also it can be recast as an optimal control problem with only pure control constraints. The second issue concerns the initial…
In this work, we propose a novel missile guidance algorithm that combines deep learning based trajectory prediction with nonlinear model predictive control. Although missile guidance and threat interception is a well-studied problem, existing algorithms' performance degrades significantly when the target is pulling high acceleration attack maneuvers while rapidly changing its direction. We argue that since most threats execute similar attack maneuvers, these nonlinear trajectory patterns can be processed with modern machine learning methods to build high accuracy trajectory prediction algorith…
