This thesis tackles the Integrated Task and Motion Planning (ITMP) Problem. The ITMP problem extends classical task planning with actions that require a motion plan. The agent seeks a sequence of actions and the necessary motions to achieve the goal.

The user partially specifies the task plan by providing the actions' known parameters. An SMT solver, then, discovers values for the unkown parameters that satisfies constraints requiring the task plan to achieve the goal. The SMT solver utilizes an annotated Probabilistic Roadmap (PRM) to query for motion planning information.

A sampling algorithm generates the PRM's vertices to permit a mobile manipulator to grasp numerous object configurations. Each iteration samples several base configurations and adds a base configuration to the PRM that increases the object configurations grasped from its vertices.

Our results indicate that increasing the samples per iteration improves the probability the SMT solver discovers a satisfying assignment without adversely affecting the resulting task plan.