Trajectory planner for agile flights in unknown environments

Abstract

Planning high-speed trajectories for UAVs in unknown environments requires extremely fast algorithms able to solve the trajectory generation problem in real-time in order to be able to react quickly to the changing knowledge of the world and that guarantee safety at all times. In this thesis, we first show the computational intractability of solving the planning problem by using the full nonlinear dynamics of the UAV in a complex cluttered known environment. By making use of the differential flatness of the UAV and removing the assumption of a completely known world, we then use a convex decomposition of the space and reformulate the optimization problem of the local planner as a Mixed Integer Quadratic Program (MIQP). The formulation proposed enables the solver to choose the interval allocation (i.e. which interval of the trajectory belongs to which polytope), and the time allocation is computed efficiently using the results of the previous replanning iteration.

We also address the erratic or unstable behavior that usually appears when a hierarchical planning architecture (a slow, low-fidelity global planner guiding a fast, high-fidelity local planner) is adopted. This is a consequence of not capturing higher-order dynamics in the global planner, whose solution is changing constantly. We therefore propose a way to address this interaction, taking into account the dynamics of the UAV to reduce the discrepancy between the local and global planner. Moreover, safety guarantees are usually obtained by having a local planner that plans a trajectory with a final "stop" condition in the free-known space. However, this decision typically leads to slow and conservative trajectories. We propose a way to obtain faster trajectories by enabling the local planner to optimize in both free-known and unknown spaces. Safety guarantees are ensured by always having a feasible, safe back-up trajectory in the free-known space at the start of each replanning step.

The planning framework proposed (called FASTER - FAst and Safe Trajectory PlannER) is validated extensively in simulation and hardware experiments, showing replanning times of 20-65 ms in cluttered environments, with vehicle's speeds up to 7.8 m/s.