Missile trajectory shaping using sampling-based path planning

International audienceThis paper presents missile guidance as a complex robotic problem: a hybrid non-linear system moving in a heterogeneous environment. The proposed solution to this problem combines a sampling-based path planner, Dubins' curves and a locally-optimal guidance law. This algorithm aims to find feasible trajectories that anticipate future flight conditions, especially the loss of manoeuverability at high altitude. Simulated results demonstrate the substantial performance improvements over classical midcourse guidance laws and the benefits of using such methods, well-known in robotics, in the missile guidance field of research

Fast Decision-making under Time and Resource Constraints

Practical decision makers are inherently limited by computational and memory resources as well as the time available in which to make decisions. To cope with these limitations, humans actively seek methods which limit their resource demands by exploiting structure within the environment and exploiting a coupling between their sensing and actuation to form heuristics for fast decision-making. To date, such behavior has not been replicated in artificial agents. This research explores how heuristics may be incorporated into the decision-making process to quickly make high-quality decisions through the analysis of a prominent case study: the outfielder problem. In the outfielder problem, a fielder is required to intercept balls traveling in ballistic trajectories, while the motion of the fielder is constrained to the ground plane. In order to maximize the probability of interception, the agent must make good, yet timely, decisions. Researchers have put forth several heuristic approaches to describe how a fielder may decide how to run based only on immediately available information under different control paradigms. This research statistically quantifies upper bounds on the expected catch rate of a couple notable approaches, given that interception of the ball is theoretically possible if the fielder ran directly towards the landing spot with maximal effort throughout the entire duration of the ball’s flight. Additionally, novel modifications are made to a belief-space variant of iterative Linear Quadratic Gaussian (iLQG), which is an online method that may be used to find locally-optimal policies to continuous Partially Observable Markov Decision Processes (POMDPs) in which Bayesian estimation may reasonably be approximated by an Extended Kalman Filter (EKF). Directional derivatives are used to reduce the computation time of certain matrix derivatives with respect to the variance of the belief state from to , where is the dimension of the belief space. However, the improved algorithm still may not be capable of real-time decision-making by the standards of modern-day computing on mobile platforms, especially in systems with long planning horizons and sparse rewards. The belief-space variant of iLQG is applied to the outfielder problem, which may also indicate its applicability to similar target interception problems with input constraints, such as missile defense

Planification de trajectoire sous contraintes d'aéronef

The focus of this PhD thesis is on the trajectory planning module as a part of autonomous aircraft system. Feasible trajectories for aircraft flying in environment cluttered by obstacles are studied. Since aircraft dynamics are complex, nonlinear and nonholonomic; trajectory planning for such systems is very difficult and challenging.Rapidly-exploring Random Tree or RRT path planner is used as a basis to find a feasible trajectory. The advantage of this algorithm is that it does not consider only the complete vehicle model but also the environment. Two algorithms are developed to find a feasible and optimal solution. The RRT algorithm, combined with a preprocessing of the exploration space, is used for a complete realistic model of the system. However, this approach does not consider any optimal criteria. In order to consider performance criteria, the RRT* algorithm is used based on a simplified model with the help of the artificial potential field as a heuristic to improve the convergence rate to the solution.The algorithms are simulated in an application of hypersonic aerial vehicles, for example, interceptor missiles flying in high altitude. This makes the aerodynamically controlled aircraft have less maneuverability since the air density decreases exponentially with altitude. 3D shortest paths are developed and used as a metric. Therefore, a feasible and optimal trajectory is obtained efficiently. With these results, real-time constraints will be easier to verify if the algorithm is implemented on board the vehicle. In future work, replanning will be considered to improve the performance of the algorithm in case of dynamic environment or changes in the mission.Le sujet de cette thèse porte sur la planification de trajectoire pour un aéronef autonome. Les trajectoires d'aéronefs se déplaçant dans un environnement encombré par des obstacles sont étudiées. La dynamique des aéronefs étant complexe, non linéaire, et non holonome, la planification de trajectoire de ce type de systèmes est un problème très difficile.L'algorithme Rapidly-exploring Random Tree, ou RRT, est utilisé comme planificateur de base. L'avantage de cet algorithme est qu'il permet de considérer des modèles d'aéronefs complets dans un environnement complexe. Deux algorithmes sont développés pour trouver une solution faisable et optimale. Pour un modèle complet, L'algorithme RRT avec un prétraitement de l'espace d'état est utilisé dans le cas d'une prise en compte du modèle complet du système. Cependant, cette méthode ne considère pas de critères optimaux. Pour y remédier, l'algorithme RRT* est utilisé pour un modèle simplifié du système avec l'aide de champs de potentiels artificiels comme heuristique pour améliorer le taux de convergence vers la solution.Les algorithmes sont simulés pour une application d'aéronefs hypersoniques, comme par exemple des missiles intercepteurs volants à haute altitude. Les aéronefs ont donc moins de manœuvrabilité parce que la densité de l'air diminue exponentiellement avec l'altitude. Les chemins les plus courts en 3D sont développés et utilisés comme une métrique. Des trajectoires réalisables et optimales sont obtenues efficacement. A partir de ces résultats, les contraintes de temps réel à bord du véhicule seront plus faciles à vérifier. Dans les travaux futurs, la replanification sera considérée pour améliorer la performance de l'algorithme en cas d'environnement dynamique ou de changements dans la mission

Air-Combat Strategy Using Approximate Dynamic Programming

Unmanned Aircraft Systems (UAS) have the potential to perform many of the dangerous missions currently own by manned aircraft. Yet, the complexity of some tasks, such as air combat, have precluded UAS from successfully carrying out these missions autonomously. This paper presents a formulation of a level flight, fixed velocity, one-on-one air combat maneuvering problem and an approximate dynamic programming (ADP) approach for computing an efficient approximation of the optimal policy. In the version of the problem formulation considered, the aircraft learning the optimal policy is given a slight performance advantage. This ADP approach provides a fast response to a rapidly changing tactical situation, long planning horizons, and good performance without explicit coding of air combat tactics. The method's success is due to extensive feature development, reward shaping and trajectory sampling. An accompanying fast and e ffective rollout-based policy extraction method is used to accomplish on-line implementation. Simulation results are provided that demonstrate the robustness of the method against an opponent beginning from both off ensive and defensive situations. Flight results are also presented using micro-UAS own at MIT's Real-time indoor Autonomous Vehicle test ENvironment (RAVEN).Defense University Research Instrumentation Program (U.S.) (grant number FA9550-07-1-0321)United States. Air Force Office of Scientific Research (AFOSR # FA9550-08-1-0086)American Society for Engineering Education (National Defense Science and Engineering Graduate Fellowship

Path Following by a Quadrotor Using Virtual Target Pursuit Guidance

Quadrotors, being more agile than fixed-wing vehicles, are the ideal candidates for autonomous missions in small, compact spaces. The immense challenge to navigate such environments is fulfilled by the concept of path following. Path following is the method of tracking/tracing a fixed, pre-defined path with minimum position error while exerting the lowest possible control effort. In this work, the missile guidance technique of pure pursuit is adopted and modified for a 3D quadrotor model to follow fixed, compact trajectories. A specialized hardware testing platform is developed to test this algorithm. The results obtained from simulation and flight tests are compared to results from another technique called differential flatness. A small part of this thesis also deals with the stability analysis of the modified 3D pure pursuit algorithm to track trajectories expending lower control effort

A Survey of path following control strategies for UAVs focused on quadrotors

The trajectory control problem, defined as making a vehicle follow a pre-established path in space, can be solved by means of trajectory tracking or path following. In the trajectory tracking problem a timed reference position is tracked. The path following approach removes any time dependence of the problem, resulting in many advantages on the control performance and design. An exhaustive review of path following algorithms applied to quadrotor vehicles has been carried out, the most relevant are studied in this paper. Then, four of these algorithms have been implemented and compared in a quadrotor simulation platform: Backstepping and Feedback Linearisation control-oriented algorithms and NLGL and Carrot-Chasing geometric algorithms.Peer ReviewedPostprint (author's final draft

Astrodynamics-optimization theory and guidance theory Research achievements review series no. 15-16

Review of research achievements in astrodynamics, optimization theory, and guidance theor

Three-dimensional biased proportional navigation guidance based on spatial rotation of predicted final velocity

This study presents the design of three-dimensional biased proportional navigation guidance laws for arrival at a stationary target along a desired direction based on spatial rotation of predicted final velocity vector. The focus is on full constructive derivation using vector-form expressions without introducing local representation of rotation such as Euler angles or quaternions. The proposed approach synthesises the bias command in the form of an angular velocity vector through realisation of the predictive control design philosophy, the direction which has been unexplored in a three-dimensional setting. The proposed approach avoids heuristic choices and approximations in the design process and hence overcomes the limitation of earlier studies. The vector-form design approach provides theoretical and practical advantages including rigour in derivation, clear geometric understandings about the problem provided by identification of the most effective direction for rotation of final velocity, independence from selection of a fixed coordinate system, avoidance of singularities in local representations, more direct trajectory shaping, and simple implementation

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics