Autonomous Path-Following by Approximate Inverse Dynamics and Vector Field Prediction

In this dissertation, we develop two general frameworks for the navigation and control of autonomous vehicles that must follow predefined paths. These frameworks are designed such that they inherently provide accurate navigation and control of a wide class of systems directly from a model of the vehicle's dynamics.;The first framework introduced is the inverse dynamics by radial basis function (IDRBF) algorithm, which exploits the best approximation property of radial basis functions to accurately approximate the inverse dynamics of non-linear systems. This approximation is then used with the known, desired state of the system at a future time point to generate the system input that must be applied to reach the desired state in the specified time interval. The IDRBF algorithm is then tested on two non-linear dynamic systems, and accurate path-following is demonstrated.;The second framework introduced is the predictive vector field (PVF) algorithm. The PVF algorithm uses the equations of motion and constraints of the system to predict a set of reachable states by sampling the system's configuration space. By finding and minimizing a continuous mapping between the system's configuration space and a cost space relating the reachable states of the system with a vector field (VF), one can determine the system inputs required to follow the VF. The PVF algorithm is then tested on the Dubin's vehicle and aircraft models, and accurate path-following is demonstrated.;As the PVF algorithm's performance is dependent on the quality of the underlying system model and VF, algorithms are introduced for automatically generating VFs for constant altitude paths defined by a series of waypoints and for handling modeling uncertainties. Additionally, we provide a mathematical proof showing that this method can automatically produce VFs of the desired form. To handle modeling uncertainties, we enhance the PVF algorithm with the Gaussian process machine learning framework, enabling the algorithm to learn the true system model, online, in the presence of measurement noise. We call this algorithm the PVF-GP algorithm. To demonstrate the PVF-GP algorithm, we compare its performance to the PVF algorithm after introducing modeling uncertainties to the underlying system model and introducing an external wind disturbance. Test results show the PVF-GP algorithm offers dramatically improved path-following performance over the non-learning PVF algorithm.