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We describe some recent work on randomized motion planning algorithms and consider the problem of motion planning for systems with both kinematic and dynamic constraints. Such a problem is often referred to as kinodynamic motion planning. A rapidly-exploring random tree (RRT) is used for the motion planning of a blimp system, and some techniques for improving the performance of the planner are proposed. Based on a dynamic model of a blimp, dynamic constraints are introduced into the algorithm design and simulations are conducted for trajectory generation.