Real-time Planning of Minimum-time Trajectories for Agile UAV Flight

We address the challenge of real-time planning of minimum-time trajectories over multiple waypoints, onboard multirotor UAVs. Previous works demonstrated that achieving a truly time-optimal trajectory is computationally too demanding to enable frequent replanning during agile flight, especially on less powerful flight computers. Our approach overcomes this stumbling block by utilizing a point-mass model with a novel iterative thrust decomposition algorithm, enabling the UAV to use all of its collective thrust, something previous point-mass approaches could not achieve. The approach enables gravity and drag modeling integration, significantly reducing tracking errors in high-speed trajectories, which is proven through an ablation study. When combined with a new multi-waypoint optimization algorithm, which uses a gradient-based method to converge to optimal velocities in waypoints, the proposed method generates minimum-time multi-waypoint trajectories within milliseconds. The proposed approach, which we provide as open-source package, is validated both in simulation and in real-world, using Nonlinear Model Predictive Control. With accelerations of up to 3.5g and speeds over 100 km/h, trajectories generated by the proposed method yield similar or even smaller tracking errors than the trajectories generated for a full multirotor model.

CTopPRM: Clustering Topological PRM for Planning Multiple Distinct Paths in 3D Environments

In this paper, we propose a new method called Clustering Topological PRM (CTopPRM) for finding multiple homotopically distinct paths in 3D cluttered environments. Finding such distinct paths, e.g., going around an obstacle from a different side, is useful in many applications. Among others, using multiple distinct paths is necessary for optimization-based trajectory planners where found trajectories are restricted to only a single homotopy class of a given path. Distinct paths can also be used to guide sampling-based motion planning and thus increase the effectiveness of planning in environments with narrow passages. Graph-based representation called roadmap is a common representation for path planning and also for finding multiple distinct paths. However, challenging environments with multiple narrow passages require a densely sampled roadmap to capture the connectivity of the environment. Searching such a dense roadmap for multiple paths is computationally too expensive. Therefore, the majority of existing methods construct only a sparse roadmap which, however, struggles to find all distinct paths in challenging environments. To this end, we propose the CTopPRM which creates a sparse graph by clustering an initially sampled dense roadmap. Such a reduced roadmap allows fast identification of homotopically distinct paths captured in the dense roadmap. We show, that compared to the existing methods the CTopPRM improves the probability of finding all distinct paths by almost 20% in tested environments, during same run-time. The source code of our method is released as an open-source package.