Uncertainty-Anticipating Stochastic Optimal Feedback Control of Autonomous Vehicle Models
Control of autonomous vehicle teams has emerged as a key topic in the control and robotics communities, owing to a growing range of applications that can benefit from the increased functionality provided by multiple vehicles. However, the mathematical analysis of the vehicle control problems is complicated by their nonholonomic and kinodynamic constraints, and, due to environmental uncertainties and information flow constraints, the vehicles operate with heightened uncertainty about the team's future motion. In this dissertation, we are motivated by autonomous vehicle control problems that highlight these uncertainties, with in particular attention paid to the uncertainty in the future motion of a secondary agent. Focusing on the Dubins vehicle and unicycle model, we propose a stochastic modeling and optimal feedback control approach that anticipates the uncertainty inherent to the systems. We first consider the application of a Dubins vehicle that should maintain a nominal distance from a target with an unknown future trajectory, such as a tagged animal or vehicle. Stochasticity is introduced in the problem by assuming that the target's motion can be modeled as a Wiener process, and the possibility for the loss of target observations is modeled using stochastic transitions between discrete states. An optimal control policy that is consistent with the stochastic kinematics is computed and is shown to perform well both in the case of a Brownian target and for natural, smooth target motion. We also characterize the resulting optimal feedback control laws in comparison to their deterministic counterparts for the case of a Dubins vehicle in a stochastically varying wind. Turning to the case of multiple vehicles, we develop a method using a Kalman smoothing algorithm for multiple vehicles to enhance an underlying analytic feedback control. The vehicles achieve a formation optimally and in a manner that is robust to uncertainty. To deal with a key implementation issue of these controllers on autonomous vehicle systems, we propose a self-triggering scheme for stochastic control systems, whereby the time points at which the control loop should be closed are computed from predictions of the process in a way that ensures stability.