The Design and Implementation of Motion Planning Problems Given Parameter Uncertainty

This thesis explores the potential for utilizing direct methods in optimal control to solve trajectory optimization problems with uncertain parameters. Parameter uncertainty extends traditional optimal control problems by inserting constant but unknown uncertainty into problem components such as the cost function or the state dynamics. The objective in these problems becomes to minimize the cost function, subject to all available information, such as a range of values or prior distribution for the uncertain parameter. Research into this topic has historically been motivated by applications in optimal search theory. However, the development of more general numerical methods and optimality conditions creates the potential to address a greater variety of problems. The goal of this thesis is to facilitate the maturation of optimal control problems with parameter uncertainty into a tool of wider applicability. This is approached by addressing three aspects of progressing prior research: the development of more realistic and interactive kinematic and performance models for application in problems with parameter uncertainty, the development of a general mathematical framework for parameter uncertainty problems, and a numerical algorithm for generating solutions.