Nonlinear Model Predictive Horizon for Optimal Trajectory Generation

This paper presents a trajectory generation method for a nonlinear system under closed-loop control (here a quadrotor drone) motivated by the Nonlinear Model Predictive Control (NMPC) method. Unlike NMPC, the proposed method employs a closed-loop system dynamics model within the optimization problem to efficiently generate reference trajectories in real time. We call this approach the Nonlinear Model Predictive Horizon (NMPH). The closed-loop model used within NMPH employs a feedback linearization control law design to decrease the nonconvexity of the optimization problem and thus achieve faster convergence. For robust trajectory planning in a dynamically changing environment, static and dynamic obstacle constraints are supported within the NMPH algorithm. Our algorithm is applied to a quadrotor system to generate optimal reference trajectories in 3D, and several simulation scenarios are provided to validate the features and evaluate the performance of the proposed methodology.