Random Finite Set Theory and Optimal Control of Large Collaborative Swarms

Controlling large swarms of robotic agents has many challenges including, but not limited to, computational complexity due to the number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. This work generalizes the swarm state using Random Finite Set (RFS) theory and solves the control problem using Model Predictive Control (MPC) to overcome the aforementioned challenges. Computationally efficient solutions are obtained via the Iterative Linear Quadratic Regulator (ILQR). Information divergence is used to define the distance between the swarm RFS and the desired swarm configuration. Then, a stochastic optimal control problem is formulated using a modified L2^2 distance. Simulation results using MPC and ILQR show that swarm intensities converge to a target destination, and the RFS control formulation can vary in the number of target destinations. ILQR also provides a more computationally efficient solution to the RFS swarm problem when compared to the MPC solution. Lastly, the RFS control solution is applied to a spacecraft relative motion problem showing the viability for this real-world scenario.Comment: arXiv admin note: text overlap with arXiv:1801.0731

Optimal Planning and Guidance Strategies in Coplanar Circular Interplanetary Missions using Electric Solar Wind Sails

Las Velas Solares Eléctricas son un nuevo tipo de propulsión espacial que no requiere de combustible ya que obtiene la energía de los protones del viento solar, y que es potencialmente útil para misiones interplanetarias. Con un modelo propulsivo apropiado, que puede ser obtenido de la literatura, es posible estudiar órbitas óptimas para vuelos interplanetarios. El primer objetivo de este proyecto es estudiar las propiedades de las órbitas de tiempo mínimo en misiones hacia Marte y Júpiter utilizando un método indirecto aplicando las ecuaciones de Euler-Lagrange y el Principio del Mínimo de Pontryagin, y luego hallar dichas órbitas usando métodos de transcripción directa para convertir el problema en un problema de Programación No Lineal. Tras esto, se añaden las perturbaciones del viento solar, y múltiples estrategias de guiado basadas en el Regulador Cuadrático Lineal y el Control Predictivo por Modelo se desarrollan, simulan y comparan, obteniendo resultados satisfactorios.Electric Solar Wind Sails are a new type of spacecraft propellantless propulsion system that gathers its energy from solar wind protons and is potentially useful for interplanetary missions. With an appropriate thrust model, which can be obtained from the literature, one can study optimal orbits for interplanetary flights. The first goal of this project is to study the properties of time-optimal orbits for missions to Mars and Jupiter using an indirect approach by applying Euler-Lagrange equations and Pontryagin’s Minimum Principle, and then compute them with direct transcription methods, converting the problem into Non Linear Programming form. Then, solar wind perturbations are added, and several guidance strategies based on Linear Quadratic Regulator Control and Model Predictive Control are developed, simulated and compared, yielding satisfactory results.Universidad de Sevilla. Grado en Ingeniería Aeroespacial

Piecewise constant model predictive control for autonomous helicopters

This paper introduces an optimisation based control framework for autonomous helicopters. The framework contains a high-level model predictive control (MPC) and a low-level linear controller. The proposed MPC works in a piecewise constant fashion to reduce the computation burden and to increase the time available for performing online optimisation. The linear feedback controller responds to fast dynamics of the helicopter and compensates the low bandwidth of the high-level controller. This configuration allows the computationally intensive algorithm applied on systems with fast dynamics. The stability issues of the high-level MPC and the overall control scheme are discussed. Simulations and flight tests on a small-scale helicopter are carried out to verify the proposed control scheme

Graceful Navigation for Mobile Robots in Dynamic and Uncertain Environments.

The ability to navigate in everyday environments is a fundamental and necessary skill for any autonomous mobile agent that is intended to work with human users. The presence of pedestrians and other dynamic objects, however, makes the environment inherently dynamic and uncertain. To navigate in such environments, an agent must reason about the near future and make an optimal decision at each time step so that it can move safely toward the goal. Furthermore, for any application intended to carry passengers, it also must be able to move smoothly and comfortably, and the robot behavior needs to be customizable to match the preference of the individual users. Despite decades of progress in the field of motion planning and control, this remains a difficult challenge with existing methods. In this dissertation, we show that safe, comfortable, and customizable mobile robot navigation in dynamic and uncertain environments can be achieved via stochastic model predictive control. We view the problem of navigation in dynamic and uncertain environments as a continuous decision making process, where an agent with short-term predictive capability reasons about its situation and makes an informed decision at each time step. The problem of robot navigation in dynamic and uncertain environments is formulated as an on-line, finite-horizon policy and trajectory optimization problem under uncertainty. With our formulation, planning and control becomes fully integrated, which allows direct optimization of the performance measure. Furthermore, with our approach the problem becomes easy to solve, which allows our algorithm to run in real time on a single core of a typical laptop with off-the-shelf optimization packages. The work presented in this thesis extends the state-of-the-art in analytic control of mobile robots, sampling-based optimal path planning, and stochastic model predictive control. We believe that our work is a significant step toward safe and reliable autonomous navigation that is acceptable to human users.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120760/1/jongjinp_1.pd

Optimal Control Methods for Missile Evasion

Optimal control theory is applied to the study of missile evasion, particularly in the case of a single pursuing missile versus a single evading aircraft. It is proposed to divide the evasion problem into two phases, where the primary considerations are energy and maneuverability, respectively. Traditional evasion tactics are well documented for use in the maneuverability phase. To represent the first phase dominated by energy management, the optimal control problem may be posed in two ways, as a fixed final time problem with the objective of maximizing the final distance between the evader and pursuer, and as a free final time problem with the objective of maximizing the final time when the missile reaches some capture distance away from the evader.These two optimal control problems are studied under several different scenarios regarding assumptions about the pursuer. First, a suboptimal control strategy, proportional navigation, is used for the pursuer. Second, it is assumed that the pursuer acts optimally, requiring the solution of a two-sided optimal control problem, otherwise known as a differential game. The resulting trajectory is known as a minimax, and it can be shown that it accounts for uncertainty in the pursuer\u27s control strategy. Finally, a pursuer whose motion and state are uncertain is studied in the context of Receding Horizon Control and Real Time Optimal Control. The results highlight how updating the optimal control trajectory reduces the uncertainty in the resulting miss distance

DECENTRALIZED ROBUST NONLINEAR MODEL PREDICTIVE CONTROLLER FOR UNMANNED AERIAL SYSTEMS

The nonlinear and unsteady nature of aircraft aerodynamics together with limited practical range of controls and state variables make the use of the linear control theory inadequate especially in the presence of external disturbances, such as wind. In the classical approach, aircraft are controlled by multiple inner and outer loops, designed separately and sequentially. For unmanned aerial systems in particular, control technology must evolve to a point where autonomy is extended to the entire mission flight envelope. This requires advanced controllers that have sufficient robustness, track complex trajectories, and use all the vehicles control capabilities at higher levels of accuracy. In this work, a robust nonlinear model predictive controller is designed to command and control an unmanned aerial system to track complex tight trajectories in the presence of internal and external perturbance. The Flight System developed in this work achieves the above performance by using: 1 A nonlinear guidance algorithm that enables the vehicle to follow an arbitrary trajectory shaped by moving points; 2 A formulation that embeds the guidance logic and trajectory information in the aircraft model, avoiding cross coupling and control degradation; 3 An artificial neural network, designed to adaptively estimate and provide aerodynamic and propulsive forces in real-time; and 4 A mixed sensitivity approach that enhances the robustness for a nonlinear model predictive controller overcoming the effect of un-modeled dynamics, external disturbances such as wind, and measurement additive perturbations, such as noise and biases. These elements have been integrated and tested in simulation and with previously stored flight test data and shown to be feasible

UAV Optimal Cooperative Obstacle Avoidance and Target Tracking in Dynamic Stochastic Environments

Cette thèse propose une stratégie de contrôle avancée pour guider une flotte d'aéronefs sans pilote (UAV) dans un environnement à la fois stochastique et dynamique. Pour ce faire, un simulateur de vol 3D a été développé avec MATLAB® pour tester les algorithmes de la stratégie de guidage en fonctions de différents scénarios. L'objectif des missions simulées est de s'assurer que chaque UAV intercepte une cible ellipsoïdale mobile tout en évitant une panoplie d'obstacles ellipsoïdaux mobiles détectés en route. Les UAVs situés à l'intérieur des limites de communication peuvent coopérer afin d'améliorer leurs performances au cours de la mission. Le simulateur a été conçu de façon à ce que les UAV soient dotés de capteurs et d'appareils de communication de portée limitée. De plus, chaque UAV possède un pilote automatique qui stabilise l'aéronef en vol et un planificateur de trajectoires qui génère les commandes à envoyer au pilote automatique. Au coeur du planificateur de trajectoires se trouve un contrôleur prédictif à horizon fuyant qui détermine les commandes à envoyer à l'UAV. Ces commandes optimisent un critère de performance assujetti à des contraintes. Le critère de performance est conçu de sorte que les UAV atteignent les objectifs de la mission, alors que les contraintes assurent que les commandes générées adhèrent aux limites de manoeuvrabilité de l'aéronef. La planification de trajectoires pour UAV opérant dans un environnement dynamique et stochastique dépend fortement des déplacements anticipés des objets (obstacle, cible). Un filtre de Kalman étendu est donc utilisé pour prédire les trajectoires les plus probables des objets à partir de leurs états estimés. Des stratégies de poursuite et d'évitement ont aussi été développées en fonction des trajectoires prédites des objets détectés. Pour des raisons de sécurité, la conception de stratégies d'évitement de collision à la fois efficaces et robustes est primordiale au guidage d'UAV. Une nouvelle stratégie d'évitement d'obstacles par approche probabiliste a donc été développée. La méthode cherche à minimiser la probabilité de collision entre l'UAV et tous ses obstacles détectés sur l'horizon de prédiction, tout en s'assurant que, à chaque pas de prédiction, la probabilité de collision entre l'UAV et chacun de ses obstacles détectés ne surpasse pas un seuil prescrit. Des simulations sont présentées au cours de cette thèse pour démontrer l'efficacité des algorithmes proposés

On-board three-dimensional constrained entry flight trajectory generation

This dissertation presents a method for on-board generation of three-degree-of-freedom (3DOF) constrained entry trajectory. Given any feasible entry conditions and terminal area energy management (TAEM) interface conditions, this method generates rapidly a 3DOF trajectory featuring a single bank-reversal that satisfies all the entry corridor constraints and meets the TAEM requirements with high precision. First, the longitudinal reference profiles for altitude, velocity, flight path angle, and the corresponding controls with respect to range-to-go, are designed using the quasi-equilibrium glide condition (QEGC). Terminal backward trajectory integration and initial descent approaches are used to make the longitudinal references intrinsically flyable. Then the 3DOF entry trajectory is completed by tracking the longitudinal references with the approximate receding-horizon control method, while the bank-reversal point is searched such that the TAEM heading and distance to the Heading Alignment Circle (HAC) requirements are satisfied within specified precision. For extreme entry cases that marginally allow a single bank-reversal or no bank-reversals, a terminal reference ground path tracking method and a terminal open-loop trajectory search method are developed respectively to complement the on-board 3DOF trajectory generation method. The overall computational load needed by this method for any entry trajectory design amounts to less than integrating the 3DOF trajectory five times on average. Simulations with the X-33 and X-38 vehicle models and a broad range of entry conditions and TAEM interface requirements demonstrate the desired performance of this method. The on-board entry guidance scheme is then completed and tested by integrating this trajectory generation method with a state of art reference trajectory regulation algorithm on a high fidelity simulation software developed at NASA Marshall Space Flight Center. Instead of preloading a reference trajectory, this method generates a 3DOF entry trajectory from the current state in 1 to 2 seconds on the simulator. Then this freshly generated trajectory is used as the reference for the guidance system. The results demonstrate the great potential of this innovative entry guidance method