Real-Time Reachable Set-Based Model Predictive Control for Safe Trajectory Tracking of Quadrotors

This paper presents a unified framework for autonomous quadrotor navigation that integrates real-time reachable set computations with Model Predictive Control (MPC) to ensure both safety and adaptability in complex environments. The proposed method employs zonotopes to represent the set of possible future UAV states and control deviations robustly. Reachable set tubes are computed online through iterative propagation of these zonotopes using the system dynamics. A collision avoidance mechanism detects intersections between predicted reachable sets and environmental obstacles, followed by a zonotope contraction procedure to define safe, under-approximated flight corridors. These dynamically generated safe regions are incorporated as constraints within the MPC optimization problem. The proposed reachable set-based MPC framework enhances trajectory tracking and obstacle avoidance performance. Its effectiveness is demonstrated through MATLAB and Python simulations involving static obstacles, highlighting its ability to achieve safe and reliable navigation.