This grant will support theoretical research into the geometric and control problems of grasping non-rigid and compliant objects. Related control problems will also be studied, such as task planning, non-holonomic motion planning, representation of compliance uncertainty, and decomposition of tasks into homogeneous subtasks such as grasping, re-grasping, and finger gaiting. The research is likely to integrate combinatorial task-planning algorithms with motion planning based on differentiable manifold theory. Experimental verification of promising algorithms is also planned.