Convex optimization of launch vehicle ascent trajectories

This thesis investigates the use of convex optimization techniques for the ascent trajectory design and guidance of a launch vehicle. An optimized mission design and the implementation of a minimum-propellant guidance scheme are key to increasing the rocket carrying capacity and cutting the costs of access to space. However, the complexity of the launch vehicle optimal control problem (OCP), due to the high sensitivity to the optimization parameters and the numerous nonlinear constraints, make the application of traditional optimization methods somewhat unappealing, as either significant computational costs or accurate initialization points are required. Instead, recent convex optimization algorithms theoretically guarantee convergence in polynomial time regardless of the initial point. The main challenge consists in converting the nonconvex ascent problem into an equivalent convex OCP. To this end, lossless and successive convexification methods are employed on the launch vehicle problem to set up a sequential convex optimization algorithm that converges to the solution of the original problem in a short time. Motivated by the computational efficiency and reliability of the devised optimization strategy, the thesis also investigates the suitability of the convex optimization approach for the computational guidance of a launch vehicle upper stage in a model predictive control (MPC) framework. Being MPC based on recursively solving onboard an OCP to determine the optimal control actions, the resulting guidance scheme is not only performance-oriented but intrinsically robust to model uncertainties and random disturbances thanks to the closed-loop architecture. The characteristics of real-world launch vehicles are taken into account by considering rocket configurations inspired to SpaceX's Falcon 9 and ESA's VEGA as case studies. Extensive numerical results prove the convergence properties and the efficiency of the approach, posing convex optimization as a promising tool for launch vehicle ascent trajectory design and guidance algorithms

Dual-Quaternion-Based Fault-Tolerant Control for Spacecraft Tracking With Finite-Time Convergence

Results are presented for a study of dual-quaternion-based fault-tolerant control for spacecraft tracking. First, a six-degrees-of-freedom dynamic model under a dual-quaternion-based description is employed to describe the relative coupled motion of a target-pursuer spacecraft tracking system. Then, a novel fault-tolerant control method is proposed to enable the pursuer to track the attitude and the position of the target even though its actuators have multiple faults. Furthermore, based on a novel time-varying sliding manifold, finite-time stability of the closed-loop system is theoretically guaranteed, and the convergence time of the system can be given explicitly. Multiple-task capability of the proposed control law is further demonstrated in the presence of disturbances and parametric uncertainties. Finally, numerical simulations are presented to demonstrate the effectiveness and advantages of the proposed control method

Swarm assignment and trajectory optimization using variable-swarm, distributed auction assignment and sequential convex programming

This paper presents a distributed, guidance and control algorithm for reconfiguring swarms composed of hundreds to thousands of agents with limited communication and computation capabilities. This algorithm solves both the optimal assignment and collision-free trajectory generation for robotic swarms, in an integrated manner, when given the desired shape of the swarm (without pre-assigned terminal positions). The optimal assignment problem is solved using a distributed auction assignment that can vary the number of target positions in the assignment, and the collision-free trajectories are generated using sequential convex programming. Finally, model predictive control is used to solve the assignment and trajectory generation in real time using a receding horizon. The model predictive control formulation uses current state measurements to resolve for the optimal assignment and trajectory. The implementation of the distributed auction algorithm and sequential convex programming using model predictive control produces the swarm assignment and trajectory optimization (SATO) algorithm that transfers a swarm of robots or vehicles to a desired shape in a distributed fashion. Once the desired shape is uploaded to the swarm, the algorithm determines where each robot goes and how it should get there in a fuel-efficient, collision-free manner. Results of flight experiments using multiple quadcopters show the effectiveness of the proposed SATO algorithm

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

Robust H8 Control for Rendezvous in Near-Circular Orbit

Rendezvous entails a pre-arranged meeting between two spacecraft orbiting around a celestial body. A technology that enables its application in assembly, maintenance and crew exchange serve as example of the importance of orbital rendezvous towards maintaining a stronghold and sustained presence in space exploration. The main focus of this dissertation leans towards the development of a robust controller for optimal rendezvous between an active spacecraft, designated as the chaser, capable of performing any necessary manoeuvres to reach a passive spacecraft, known as the target, that is assumed to thrust-free. [...]Rendezvous em órbita representa um encontro previamente meditado entre dois veiculos espaciais que se encontra a orbitrar um corpo celestial. A tecnologia que permita a aplicação de rendezvous em órbitra para realizar montagens, manutenção ou troca de tripulação serve de exemplo para demonstrar a importância de rendezvous em orbita para continuar com uma presença forte na exploração espacial. [...

RBF-based supervisor path following control for ASV with time-varying ocean disturbance

1028-1036A robust model-free path following controller is developed for autonomous surface vehicle (ASV) with time-varying ocean disturbance. First, the geometrical relationship between ASV and virtual tracking point on the reference path is investigated. The differentiations of tracking errors are described with the relative motion method, which greatly simplified the direct differential of tracking errors. Furthermore, the control law for the desired angular velocity of the vehicle and virtual tracking point are built based on the Lyapunov theory. Second, the traditional proportional-integral-derivative (PID) controller is developed based on the desired velocities and state feedback. The radial basic function (RBF) neural network taking as inputs the desired surge velocity and yaw angular velocity is developed as the supervisor to PID controller. Besides, RBF controller tunes weights according to the output errors between the PID controller and supervisor controller, based on the gradient descent method. Hence, PID controller and RBF supervisor controller act as feedback and feed forward control of the system, respectively. Finally, comparative path following simulation for straight path and sine path illustrate the performance of the proposed supervisor control system. The PID controller term reports loss of control even in the unknown disturbance

A Survey on Aerial Swarm Robotics

The use of aerial swarms to solve real-world problems has been increasing steadily, accompanied by falling prices and improving performance of communication, sensing, and processing hardware. The commoditization of hardware has reduced unit costs, thereby lowering the barriers to entry to the field of aerial swarm robotics. A key enabling technology for swarms is the family of algorithms that allow the individual members of the swarm to communicate and allocate tasks amongst themselves, plan their trajectories, and coordinate their flight in such a way that the overall objectives of the swarm are achieved efficiently. These algorithms, often organized in a hierarchical fashion, endow the swarm with autonomy at every level, and the role of a human operator can be reduced, in principle, to interactions at a higher level without direct intervention. This technology depends on the clever and innovative application of theoretical tools from control and estimation. This paper reviews the state of the art of these theoretical tools, specifically focusing on how they have been developed for, and applied to, aerial swarms. Aerial swarms differ from swarms of ground-based vehicles in two respects: they operate in a three-dimensional space and the dynamics of individual vehicles adds an extra layer of complexity. We review dynamic modeling and conditions for stability and controllability that are essential in order to achieve cooperative flight and distributed sensing. The main sections of this paper focus on major results covering trajectory generation, task allocation, adversarial control, distributed sensing, monitoring, and mapping. Wherever possible, we indicate how the physics and subsystem technologies of aerial robots are brought to bear on these individual areas