Trajectory Planning for Flights in Multiagent and Dynamic Environments

Abstract

While efficient and fast trajectory planners in static worlds have been extensively proposed for UAVs (Unmanned Aerial Vehicles), a 3D real-time planner for environments with static obstacles, dynamic obstacles, and other planning agents still remains an open problem. The dynamic nature of these environments demands high replanning rates, making this problem especially hard on computationally limited platforms. Existing state-of-the-art planners reduce the computational complexity at the expense of more conservative results by relying on three main simplifications or assumptions: First, the collision avoidance constraints are imposed using the Bernstein and B-Spline polynomial bases, which do not tightly enclose a given interval of a polynomial trajectory. Second, multiagent planners usually make centralized and/or synchronized computation assumptions, which lead to poor scalability with the number of agents or can degrade the overall performance. Finally, position and yaw are decoupled when optimizing perception-aware trajectories, which produces highly conservative results.

This thesis addresses the aforementioned limitations with the following contributions: First, it presents the MINVO basis, a polynomial basis that generates the simplex with minimum volume enclosing a polynomial curve, therefore reducing the conservativeness in the obstacle avoidance constraints. Leveraging the MINVO basis, this thesis then proposes a tractable way to avoid dynamic obstacles by imposing linear separability constraints between the polyhedral enclosures of the intervals of the trajectories. This is then extended to multiagent scenarios, and a decentralized and asynchronous obstacle avoidance algorithm among many replanning agents is presented. Real-time perception-aware planning is achieved by implicitly imposing the underactuated dynamics of the UAV through the Hopf fibration while jointly optimizing the full pose. Finally, a reduction of two orders of magnitude in the computation time is obtained by learning a policy that imitates the optimization-based planner. These proposed contributions are extensively evaluated in simulation, showing up to 32 agents planning in real time, and in real-world experiments, showcasing flights up to 5.8 m/s in unknown dynamic environments with only onboard computation.