A significant challenge of autonomous robotics in transportation, exploration, and search-and-rescue missions lies in the area of motion planning. The overall objective is to enable robots to automatically plan the low-level motions needed to accomplish assigned high-level tasks. Toward this goal, this thesis proposes a novel multi-layered approach, termed Synergic Combination of Layers of Planning ( SyCLoP ), that synergically combines high-level discrete planning and low-level motion planning. High-level discrete planning, which draws from research in AI and logic, guides low-level motion planning during the search for a solution. Information gathered during the search is in turn fed back from the low-level to the high-level layer in order to improve the high-level plan in the next iteration. In this way, high-level plans become increasingly useful in guiding the low-level motion planner toward a solution. This synergic combination of high-level discrete planning and low-level motion planning allows SyCLoP to solve motion-planning problems with respect to rich models of the robot and the physical world. This facilitates the design of feedback controllers that enable the robot to execute in the physical world solutions obtained in simulation. In particular, SyCLoP effectively solves challenging motion-planning problems that incorporate robot dynamics, physics-based simulations, and hybrid systems. Hybrid systems move beyond continuous models by employing discrete logic to instantaneously modify the underlying robot dynamics to respond to mishaps or unanticipated changes in the environment. Experiments in this thesis show that SyCLoP obtains significant computational speedup of one to two orders of magnitude when compared to state-of-the-art motion planners. In addition to planning motions that allow the robot to reach a desired destination while avoiding collisions, SyCLoP can take into account high-level tasks specified using the expressiveness of linear temporal logic (LTL). LTL allows for complex specifications, such as sequencing, coverage, and other combinations of temporal objectives. Going beyond motion planning, SyCLoP also provides a useful framework for discovering violations of safety properties in hybrid systems.