This paper presents a new algorithm for real-time motion planning in agile autonomous vehicles operating in dynamic environments. The algorithm is based on the probabilistic roadmap approach, which has been shown to be efficient and complete for robots with many degrees of freedom. The authors extend this approach to handle system dynamics and moving obstacles using a Lyapunov function-based method. The algorithm can be applied to both continuous state-space and hybrid systems, including traditional state space systems and hybrid systems with discrete and continuous dynamics. The paper includes a detailed planning framework, system dynamics modeling, and an analysis of the algorithm's performance. Simulation results using a small autonomous helicopter demonstrate the algorithm's effectiveness, showing fast and reliable performance even in complex environments with moving obstacles. The algorithm's efficiency and adaptability to different vehicle dynamics make it a promising solution for real-time motion planning in agile autonomous vehicles.This paper presents a new algorithm for real-time motion planning in agile autonomous vehicles operating in dynamic environments. The algorithm is based on the probabilistic roadmap approach, which has been shown to be efficient and complete for robots with many degrees of freedom. The authors extend this approach to handle system dynamics and moving obstacles using a Lyapunov function-based method. The algorithm can be applied to both continuous state-space and hybrid systems, including traditional state space systems and hybrid systems with discrete and continuous dynamics. The paper includes a detailed planning framework, system dynamics modeling, and an analysis of the algorithm's performance. Simulation results using a small autonomous helicopter demonstrate the algorithm's effectiveness, showing fast and reliable performance even in complex environments with moving obstacles. The algorithm's efficiency and adaptability to different vehicle dynamics make it a promising solution for real-time motion planning in agile autonomous vehicles.