A new algorithm for real-time motion planning of agile autonomous vehicles is presented, based on a probabilistic roadmap approach. The algorithm uses Lyapunov functions to construct a roadmap that effectively handles system dynamics and moving obstacles. It is applicable to a wide range of dynamical systems, including traditional state-space systems and hybrid systems. The algorithm is designed for real-time motion planning in dynamic environments with moving obstacles, and is particularly well-suited for integrated guidance and control architectures. The algorithm is tested on a small autonomous helicopter, demonstrating its effectiveness in navigating through obstacles and achieving mission goals. The algorithm is shown to be probabilistically complete and computationally efficient, with performance bounds derived based on the environment's expansiveness. The algorithm is able to handle complex, high-dimensional dynamics and is applicable to a variety of autonomous systems, including those with attitude motion planning requirements. The paper concludes that the algorithm provides a robust and efficient solution for real-time motion planning in dynamic environments.A new algorithm for real-time motion planning of agile autonomous vehicles is presented, based on a probabilistic roadmap approach. The algorithm uses Lyapunov functions to construct a roadmap that effectively handles system dynamics and moving obstacles. It is applicable to a wide range of dynamical systems, including traditional state-space systems and hybrid systems. The algorithm is designed for real-time motion planning in dynamic environments with moving obstacles, and is particularly well-suited for integrated guidance and control architectures. The algorithm is tested on a small autonomous helicopter, demonstrating its effectiveness in navigating through obstacles and achieving mission goals. The algorithm is shown to be probabilistically complete and computationally efficient, with performance bounds derived based on the environment's expansiveness. The algorithm is able to handle complex, high-dimensional dynamics and is applicable to a variety of autonomous systems, including those with attitude motion planning requirements. The paper concludes that the algorithm provides a robust and efficient solution for real-time motion planning in dynamic environments.