SUMMARY

Kinodynamic motion planning addresses the problem of finding the control inputs to a dynamical system such that that system's trajectory satisfies constraints such as obstacle avoidance or entering a goal set. Motion primitives are a popular tool for kinodynamic motion planning as they allow constructing trajectories that are guaranteed to satisfy the system dynamics without requiring on-demand simulation. This work provides a generalization of motion primitives to systems subject to parametric uncertainty. Quantities of interest in optimal motion planning, including integrated cost terms and constraint indicator functions, are cast as expectations of functions of the terminal state of a motion primitive. Explicit uncertainty quantification via the Koopman operator is used to obtain sample-efficient schemes for evaluating these expectations. The sampling scheme permits casting the planning problem as a Chance-Constrained Markov Decision Process with a finite set of actions, for which a policy can be obtained by forward search on an And/Or graph. Techniques for efficient solution of this search problem are presented. Future work is focused on improvements to the And/Or graph search and on further generalization of the uncertain motion primitive framework.