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This paper presents a kinodynamic motion planner, i.e., Kinodynamic Motion Planning by Interior-Exterior Cell Exploration (KPIECE), which is specifically designed for systems with complex dynamics, where integration backward in time is not possible, and speed of computation is important. A grid-based discretization is used to estimate the coverage of the state space. The coverage estimates help the planner detect the less-explored areas of the state space. An important characteristic of this discretization is that it keeps track of the boundary of the explored region of the state space and focuses exploration on the less covered parts of this boundary. Extensive experiments show that KPIECE provides significant computational gain over existing state-of-the-art methods and allows us to solve some harder, previously unsolvable problems. For some problems, KPIECE is shown to be up to two orders of magnitude faster than existing methods and use up to 40 times less memory. A shared memory parallel implementation is presented as well. This implementation provides better speedup than an embarrassingly parallel implementation by taking advantage of the evolving multicore technology.