This article illustrates the use of unsupervised probabilistic learning techniques for the analysis of planetary reentry trajectories. A three-degree-of-freedom model was employed to generate optimal trajectories that comprise the training datasets. The algorithm first extracts the intrinsic structure in the data via a diffusion map approach. We find that data resides on manifolds of much lower dimensionality compared to the high-dimensional state space that describes each trajectory. Using the diffusion coordinates on the graph of training samples, the probabilistic framework subsequently augments the original data with samples that are statistically consistent with the original set. The augmented samples are then used to construct conditional statistics that are ultimately assembled in a path planning algorithm. In this framework, the controls are determined stage by stage during the flight to adapt to changing mission objectives in real-time.
There are many scenarios in which a mobile agent may not want its path to be predictable. Examples include preserving privacy or confusing an adversary. However, this desire for deception can conflict with the need for a low path cost. Optimal plans such as those produced by RRT∗ may have low path cost, but their optimality makes them predictable. Similarly, a deceptive path that features numerous zig-zags may take too long to reach the goal. We address this trade-off by drawing inspiration from adversarial machine learning. We propose a new planning algorithm, which we title Adversarial RRT*. Adversarial RRT∗ attempts to deceive machine learning classifiers by incorporating a predicted measure of deception into the planner cost function. Adversarial RRT∗ considers both path cost and a measure of predicted deceptiveness in order to produce a trajectory with low path cost that still has deceptive properties. We demonstrate the performance of Adversarial RRT*, with two measures of deception, using a simulated Dubins vehicle. We show how Adversarial RRT∗ can decrease cumulative RNN accuracy across paths to 10%, compared to 46% cumulative accuracy on near-optimal RRT∗ paths, while keeping path length within 16% of optimal. We also present an example demonstration where the Adversarial RRT∗ planner attempts to safely deliver a high value package while an adversary observes the path and tries to intercept the package.
This report investigates the use of unsupervised probabilistic learning techniques for the analysis of hypersonic trajectories. The algorithm first extracts the intrinsic structure in the data via a diffusion map approach. Using the diffusion coordinates on the graph of training samples, the probabilistic framework augments the original data with samples that are statistically consistent with the original set. The augmented samples are then used to construct conditional statistics that are ultimately assembled in a path-planing algorithm. In this framework the controls are determined stage by stage during the flight to adapt to changing mission objectives in real-time. A 3DOF model was employed to generate optimal hypersonic trajectories that comprise the training datasets. The diffusion map algorithm identfied that data resides on manifolds of much lower dimensionality compared to the high-dimensional state space that describes each trajectory. In addition to the path-planing worflow we also propose an algorithm that utilizes the diffusion map coordinates along the manifold to label and possibly remove outlier samples from the training data. This algorithm can be used to both identify edge cases for further analysis as well as to remove them from the training set to create a more robust set of samples to be used for the path-planing process.
Problems in optimal control may exhibit a bang-bang or singular control structure. These qualities pose challenges with indirect solution methods when the control law is discontinuous or indefinite. Recent efforts in control regularization strategies have sought to overcome these difficulties. These methods approximate a smoothed mapping of the constrained multi-stage Hamiltonian boundary value problem, resolving the singular/bang arcs into a single-stage problem. This work investigates the use of control saturation functions for error-control regularization. A key feature of the new approach is to eliminate ambiguity of the control law derived from the necessary conditions for optimality. The method is shown to have improved stability in numerical continuation due to the removal of small error terms from the control law. A well-known classical problem with analytical solutions is studied, as well as a more applied problem involving atmospheric flight of a maneuvering reentry vehicle.