Planning optimal paths for large numbers of robots is computationally expensive. In this thesis, we present a new framework for multirobot path planning called subdimensional expansion, which initially plans for each robot individually, and then coordinates motion among the robots as needed. More specifically subdimensional expansion initially creates a one-dimensional search space embedded in the joint configuration space of the multirobot system. When the search space is found to be blocked during planning by a robot-robot collision, the dimensionality of the search space is locally increased to ensure that an alternative path can be found. As a result, robots are only coordinated when necessary, which reduces the computational cost of finding a path. Subdimensional expansion is a exible framework that can be used with multiple planning algorithms. For discrete planning problems, subdimensional expansion can be combined with A* to produce the M* algorithm, a complete and optimal multirobot path planning problem. When the configuration space of individual robots is too large to be explored effectively with A*, subdimensional expansion can be combined with probabilistic planning algorithms to produce sRRT and sPRM. M* is then extended to solve variants of the multirobot path planning algorithm. We present the Constraint Manifold Subsearch (CMS) algorithm to solve problems where robots must dynamically form and dissolve teams with other robots to perform cooperative tasks. Uncertainty M* (UM*) is a variant of M* that handles systems with probabilistic dynamics. Finally, we apply M* to multirobot sequential composition. Results are validated with extensive simulations and experiments on multiple physical robots.

"A number of outstanding problems in robotic motion and manipulation involve tasks where degrees of freedom (DoF), be they part of the robot, an object being manipulated, or the surrounding environment, cannot be accurately controlled by the actuators of the robot alone. Rather, they are also controlled by physical properties or interactions - contact, robot dynamics, actuator behavior - that are influenced by the actuators of the robot. In particular, we focus on two important areas of poorly controlled robotic manipulation: motion planning for deformable objects and in deformable environments; and manipulation with uncertainty. Many everyday tasks we wish robots to perform, such as cooking and cleaning, require the robot to manipulate deformable objects. The limitations of real robotic actuators and sensors result in uncertainty that we must address to reliably perform fine manipulation. Notably, both areas share a common principle: contact, which is usually prohibited in motion planners, is not only sometimes unavoidable, but often necessary to accurately complete the task at hand. We make four contributions that enable robot manipulation in these poorly controlled tasks: First, an efficient discretized representation of elastic deformable objects and cost function that assess a ``cost of deformation' for a specific configuration of a deformable object that enables deformable object manipulation tasks to be performed without physical simulation. Second, a method using active learning and inverse-optimal control to build these discretized representations from expert demonstrations. Third, a motion planner and policy-based execution approach to manipulation with uncertainty which incorporates contact with the environment and compliance of the robot to generate motion policies which are then adapted during execution to reflect actual robot behavior. Fourth, work towards the development of an efficient path quality metric for paths executed with actuation uncertainty that can be used inside a motion planner or trajectory optimizer."