TOP-UAV: Open-Source Time-Optimal Trajectory Planner for Point-Masses Under Acceleration and Velocity Constraints

Abstract

In the latest research for unmanned aerial vehicles (UAVs), time-optimal trajectory planning of a point-mass with acceleration as control input and constrained maximum velocity (TOT-PMAV) has proved to be very promising for UAV behavior planning. They can be calculated within microseconds and tracked with high precision by modern trajectory tracking controllers like model predictive control (MPC). However, recent research shows that the state-of-the-art (SOTA) approach to generate these time-optimal trajectories is based on an invalid method to synchronize the coordinate axes which sometimes yields trajectories that miss the desired final state by far. Hence, an alternative approach was proposed that claims to resolve this issue. However, it still needs mathematical proof of its correctness. In this work, we provide the missing proof and mathematically demonstrate the problems arising from the SOTA approach. Further, since neither the SOTA nor the alternative solution approach utilizes the full kinematic capacity of a UAV, we propose an improved solution approach to the TOT-PMAV that better exploits kinematic properties and yields, on average, up to 14% faster trajectories. We substantiate our findings with an extensive computational study, show in which situations the SOTA is likely to fail and provide metrics to measure the consequence during failure. To enable reproducibility, our code is open-source.