The robotic platform presented in this thesis is underdamped with high inertia and can store potential energy in its compliant joints, making it ideal for many different types of real-world tasks for which traditional rigid-robots are ill-suited. Some real-world tasks suited to soft robots include high impact tasks like hammering a nail into a wall or moving heavy objects with other robot or human teammates while using relatively little power. Some of the same characteristics which make soft robots useful, such as their underdamped, highly compliant joints, also make motion planning and control for soft robots difficult. In this thesis, a novel method is introduced to take high-level, real world tasks and generate trajectories for soft robots to complete those real world tasks. The generated trajectories are designed to be dynamically and kinematically feasible for a soft robot. An optimization is introduced that uses a cost function to move the tip of a robot from point A to point B in task space. Experiments conducted in simulation and on hardware show that a soft robot with a length of 1.19 meters is able to track a high-speed and dynamic trajectory generated with this optimization with a reported median magnitude of error of 0.032 meters between the planned and actual end effector trajectories. This thesis also introduces an adaptation of a Model Reference Adaptive Controller (MRAC) that causes a high degree of freedom and nonlinear soft robot to behave like a 2nd-order, critically damped system. This allows us to approximate the dynamics of the robot as 2nd-order to more easily generate trajectories for highly dynamic tasks like throwing a ball. An optimization is developed to generate ball-throwing trajectories. Experiments conducted in simulation and on hardware show that a soft robot can throw a ball within 0.13 meters of a goal point in simulation (where the goal point is 2.85 meters from the robot) and 0.5 meters of a goal point on hardware (where the goal point is 2 meters from the robot). The methods developed in this thesis enable soft robots to more easily complete high-level tasks through dynamically and kinematically feasible task and joint space trajectory generation.

The method of singular-perturbation analysis is applied to the determination of range-fuel-time optimal aircraft trajectories. The problem is shown to break down into three sub-problems which are studied separately. In particular, the inner layer containing the altitude path-angle dynamics is analyzed in detail. The outer solutions are discussed in an earlier work. As a step forward in solving the ensuing nonlinear two-point boundary-value problem, linearization of the equations is suggested. Conditions for the stability of the linearized boundary-layer equations are discussed. Also, the question of parameter selection to fit the solution to the split boundary conditions is resolved. Generation of feedback laws for the angle-of-attack from the linear analysis is discussed. Finally, the techniques discussed are applied to a numerical example of a missile. The linearized feedback solution is compared to the exact solution obtained using a multiple shooting method. / Master of Science

Singular subarcs arise in quite a few problems of flight dynamics. The present study is devoted to the specific problem of ascent and acceleration of a vehicle in atmospheric flight in which a variable-thrust arc forms a part of the optimal trajectory. A two-parameter family of singular arcs was generated for time-range-fuel problems of an ascending rocket, using the modelling of Zlatskiy and Kiforenko. The short-term optimality of the singular subarcs has been checked in terms of certain necessary conditions: the classical Clebsch condition, the Kelley condition or the Generalized Legendre-Clebsch condition and the Goh condition. All these are found to be satisfied computationally for all the candidates. The calculations were repeated for simplified thrust-along-the-path modelling and similar results on optimality obtained. / Master of Science

In aircraft research, there is keen interest in the procedure of determining the set of controls required to perform a maneuver from a definition of the trajectory. This is called the inverse problem. It has been proposed that if a complete set of states and state time derivatives can be derived from a trajectory then a model-following solution can allocate the controls necessary for the maneuver. This paper explores the problem of finding the complete state definition and provides a solution that requires numerical differentiation, fixed point iteration and a Newton's method solution to nonlinear equations. It considers trajectories that are smooth, piecewise smooth, and noise ridden. The resulting formulation was coded into a FORTRAN program. When tested against simple smooth maneuvers, the program output was very successful but demonstrated the limitations imposed by the assumptions and approximations in the development. / Master of Science

The capability to perform rendezvous and proximity operations about space objects is central to the next generation of space situational awareness. The ability to diagnose and respond to spacecraft anomalies is often hampered by the lack of capability to perform inspection or testing on the target vehicle in flight. While some limited ability to perform inspection can be provided by an extensible boom, such as the robotic arms deployed on the space shuttle and space station, a free-flying companion vehicle provides maximum flexibility of movement about the target. Safe and efficient utilization of a companion vehicle requires trajectories capable of minimizing spacecraft resources, e.g., time or fuel, while adhering to complex path and state constraints. This paper develops an efficient solution method capable of handling complex constraints based on a grid search A* algorithm and compares solution results against a state-of-the-art nonlinear optimization method. Trajectories are investigated that include nonlinear constraints, such as complex keep-out-regions and thruster plume impingement, that may be required for inspection of a specific target area in a complex environment. This work is widely applicable and can be expanded to apply to a variety of satellite relative motion trajectory planning problems. / The capability to perform rendezvous and proximity operations about space objects is central to the next generation of space situational awareness. The ability to diagnose and respond to spacecraft anomalies is often hampered by the lack of capability to perform inspection or testing on the target vehicle in flight. While some limited ability to perform inspection can be provided by an extensible boom, such as the robotic arms deployed on the space shuttle and space station, a free-flying companion vehicle provides maximum flexibility of movement about the target. Safe and efficient utilization of a companion vehicle requires trajectories capable of minimizing spacecraft resources, e.g., time or fuel, while adhering to complex path and state constraints. This paper develops an efficient solution method capable of handling complex constraints based on a grid search A* algorithm and compares solution results against a state-of-the-art nonlinear optimization method. Trajectories are investigated that include complex nonlinear constraints, such as complex keep-out-regions and thruster plume impingement, that may be required for inspection of a specific target area in a complex environment. This work is widely applicable and can be expanded to apply to a variety of satellite relative motion trajectory planning problems. / Master of Science / The ability of one satellite to perform actions near a second space satellite or other space object is important for understanding the space environment and accomplishing space mission goals. The development of a method to plan the path that one satellite takes near a second satellite such that fuel usage is minimized and other constraints satisfied is important for accomplishing mission goals. This thesis focuses on developing a fast solution method capable of handling complex constraints that can be applied to plan paths satellite relative motion operations. The solution method developed in this thesis is then compared to an existing solution method to determine the efficiency and accuracy of the method.

Consider the problem of developing an algorithm that computes optimal preprogrammed evasive maneuvers for a Maneuvering Reentry Vehicle (MaRV) attacking a target defended with Anti-Ballistic Missiles (ABMs). The problem is large in terms of the number of optimization parameters, and perhaps in terms of the number of nonlinear constraints. Since both MaRV and ABM trajectories are expensive to compute, rapid convergence of the optimization algorithm is of prime concern. This paper examines a discontinuity in the cost function that degrades both the speed and the reliability of optimizer convergence. A solution is offered, proposing that the optimization algorithm be operated in a new parameter space, in which the discontinuity occurs at infinity. Effectively, the mapping prevents the optimization algorithm from crossing the discontinuity thereby improving optimizer convergence. Results comparing convergence with and without the parameter mapping demonstrate the effectiveness of the procedure. / Master of Science

A spacecraft tour trajectory is a trajectory in which a spacecraft visits a number of objects in sequence. The target objects may consist of satellites, moons, planets or any other body in orbit, and the spacecraft may visit these in a variety of ways, for example flying by or rendezvousing with them. The key characteristic is the target object sequence which can be represented as a discrete set of decisions that must be made along the trajectory. When this sequence is free to be chosen, the result is a hybrid discrete-continuous optimization problem that combines the challenges of discrete and combinatorial optimization with continuous optimization. The problem can be viewed as a generalization of the traveling salesman problem; such problems are NP-hard and their computational complexity grows exponentially with the problem size. The focus of this dissertation is the development of a novel methodology for the solution of spacecraft tour trajectory optimization problems. A general model for spacecraft tour trajectories is first developed which defines the parameterization and decision variables for use in the rest of the work. A global search methodology based on the tabu search metaheuristic is then developed. The tabu search approach is extended to operate on a tree-based solution representation and neighborhood structure, which is shown to be especially efficient for problems with expensive solution evaluations. Concepts of tabu search including recency-based tabu memory and strategic intensification and diversification are then applied to ensure a diverse exploration of the search space. The result is an automated, adaptive and efficient search algorithm for spacecraft tour trajectory optimization problems. The algorithm is deterministic, and results in a diverse population of feasible solutions upon termination. A novel numerical search space pruning approach is then developed, based on computing upper bounds to the reachable domain of the spacecraft, to accelerate the search. Finally, the overall methodology is applied to the fourth annual Global Trajectory Optimization Competition (GTOC4), resulting in previously unknown solutions to the problem, including one exceeding the best known in the literature. / text

<div>Optimization of atmospheric flight control has long been performed on the ground, prior to mission flight due to large computational requirements used to solve non-linear programming problems. Onboard trajectory optimization enables the creation of new reference trajectories and updates to guidance coefficients in real time. This thesis summarizes the methods involved in solving optimal control problems in real time using convexification and Sequential Convex Programming (SCP). The following investigation provided insight in assessing the use of state of the art SCP optimization architectures and convexification of the hypersonic equations of motion[ 1 ]–[ 3 ] with different control schemes for the purposes of enabling on-board trajectory optimization capabilities.</div><div>An architecture was constructed to solve convexified optimal control problems using direct population of sparse matrices in triplet form and an embedded conic solver to enable rapid turn around of optimized trajectories. The results of this show that convexified optimal control problems can be solved quickly and efficiently which holds promise in autonomous trajectory design to better overcome unexpected environments and mission parameter changes. It was observed that angle of attack control problems can be successfully convexified and solved using SCP methods. However, the use of multiple coupled controls is not guaranteed to be successful with this method when they act in the same plane as one another. The results of this thesis demonstrate that state of the art SCP methods have the capacity to enable onboard trajectory optimization with both angle of attack control and bank angle control schemes.</div><div><br></div>

Simulation of maneuvers with multibody models of rotorcraft vehicles is an important research area due to its complexity. During the maneuvering flight, some important design limitations are encountered such as maximum loads and maximum turning rates near the proximity of the flight envelope. This increases the demand on high fidelity models in order to define appropriate controls to steer the model close to the desired trajectory while staying inside the boundaries. A framework based on the hierarchical decomposition of the problem is used for this study. The system should be capable of generating the track by itself based on the given criteria and also capable of piloting the model of the vehicle along this track. The generated track must be compatible with the dynamic characteristics of the vehicle. Defining the constraints for the maneuver is of crucial importance when the vehicle is operating close to its performance boundaries. In order to make the problem computationally feasible, two models of the same vehicle are used where the reduced model captures the coarse level flight dynamics, while the fine scale comprehensive model represents the plant. The problem is defined by introducing planning layer and control layer strategies. The planning layer stands for solving the optimal control problem for a specific maneuver of a reduced vehicle model. The control layer takes the resulting optimal trajectory as an optimal reference path, then tracks it by using a non-linear model predictive formulation and accordingly steers the multibody model. Reduced models for the planning and tracking layers are adapted by using neural network approach online to optimize the predictive capabilities of planner and tracker. Optimal neural network architecture is obtained to augment the reduced model in the best way. The methodology of adaptive learning rate is experimented with different strategies. Some useful training modes and algorithms are proposed for these type of applications. It is observed that the neural network increased the predictive capabilities of the reduced model in a robust way. The proposed framework is demonstrated on a maneuvering problem by studying an obstacle avoidance example with violent pull-up and pull-down.

A supercavitating vehicle, a next-generation underwater vehicle capable of changing the paradigm of modern marine warfare, exploits supercavitation as a means to reduce drag and achieve extremely high submerged speeds. In supercavitating flows, a low-density gaseous cavity entirely envelops the vehicle and as a result the vehicle is in contact with liquid water only at its nose and partially over the afterbody. Hence, the vehicle experiences a substantially reduced skin drag and can achieve much higher speed than conventional vehicles. The development of a controllable and maneuvering supercavitating vehicle has been confronted with various challenging problems such as the potential instability of the vehicle, the unsteady nature of cavity dynamics, the complex and non-linear nature of the interaction between vehicle and cavity. Furthermore, major questions still need to be resolved regarding the basic configuration of the vehicle itself, including its control surfaces, the control system, and the cavity dynamics. In order to answer these fundamental questions, together with many similar ones, this dissertation develops an integrated simulation-based design tool to optimize the vehicle configuration subjected to operational design requirements, while predicting the complex coupled behavior of the vehicle for each design configuration. Particularly, this research attempts to include maneuvering flight as well as various operating trim conditions directly in the vehicle configurational optimization. This integrated approach provides significant improvement in performance in the preliminary design phase and indicates that trade-offs between various performance indexes are required due to their conflicting requirements. This dissertation also investigates trim conditions and dynamic characteristics of supercavitating vehicles through a full 6 DOF model. The influence of operating conditions, and cavity models and their memory effects on trim is analyzed and discussed. Unique characteristics are identified, e.g. the cavity memory effects introduce a favorable stabilizing effect by providing restoring fins and planing forces. Furthermore, this research investigates the flight envelope of a supercavitating vehicle, which is significantly different from that of a conventional vehicle due to different hydrodynamic coefficients as well as unique operational conditions.