Fast UAV Trajectory Planning for Time-Optimal and Jerk-Minimal Paths: A Quadratic Programming Approach

A widely adopted approach for trajectory planning in robotics is the decoupled method, in which a geometric path is formulated first for which a kino-dynamically feasible time parameterization is subsequently computed. This paper introduces a novel quadratic programming (QP)-based approach for generating time-optimal and jerk-minimal trajectories for planning in robotics. Our approach maintains the decoupled structure of path planning and time parameterization, ensuring flexibility and computational efficiency. By exploiting the unique structure of the QP formulation, we reduce the dimensionality of the optimization problem and eliminate equality constraints, making it computationally efficient and suitable for online replanning applications. Our algorithm offers comparable performance to traditional Time-Optimal Path Parameterization (TOPP)-based methods and other state-of-the-art techniques, while providing additional benefits such as improved jerk minimization, which is crucial for smoothness in motion and energy optimization. While preserving the robustness of Convex Optimization (CO)-based methods, experiments on dense real-world maps demonstrate that the proposed algorithm performs on par with TOPP-RA in terms of computation time and trajectory duration, and significantly out performs TOPP-RA in terms of path jerk. Furthermore, real-world experiments on a multirotor UAV validate our approach and demonstrate the algorithm’s versatility and applicability to a wide-range of motion planning problems in robotics and engineering.