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A major goal in robot motion planning and control is to be able to specify a task in a high-level, expressive language and have the robot(s) to automatically convert the specification into a set of low-level primitives, such as feedback controllers and communication protocols, to accomplish the task. The robots can vary from manipulator arms used in manufacturing or surgery, to autonomous vehicles used in search and rescue or in planetary exploration, and to smart wheel chairs for disabled people. They are subject to mechanical constraints (e.g., a carlike robot cannot move sideways,an airplane cannot stop in place) and have limited computation, sensing, and communication capabilities. The environments can be cluttered with possibly moving and shape-changing obstacles and can con tain dynamic (moving, appearing, or disappearing) targets. One of the major challenges in this area is the development of a computationally efficient frame work accommodating both the robot constraints and the complexity of the environment, while, at the same time, allowing for a large spectrum of task specifications.