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With much research has been conducted into trajectory planning forquadrotors, planning with spatial and temporal optimal trajectories inreal-time is still challenging. In this paper, we propose a framework forgenerating large-scale piecewise polynomial trajectories for aggressiveautonomous flights, with highlights on its superior computational efficiencyand simultaneous spatial-temporal optimality. Exploiting the implicitlydecoupled structure of the planning problem, we conduct alternatingminimization between boundary conditions and time durations of trajectorypieces. In each minimization phase, we leverage the algebraic convenience ofthe sub-problem to escape poor local minima and achieve the lowest timeconsumption. Theoretical analysis for the global/local convergence rate of ourproposed method is provided. Moreover, based on polynomial theory, an extremelyfast feasibility check method is designed for various kinds of constraints. Byincorporating the method into our alternating structure, a constrainedminimization algorithm is constructed to optimize trajectories on the premiseof feasibility. Benchmark evaluation shows that our algorithm outperformsstate-of-the-art methods regarding efficiency, optimality, and scalability.Aggressive flight experiments in a limited space with dense obstacles arepresented to demonstrate the performance of the proposed algorithm. We releaseour implementation as an open-source ros-package.

Alternating Minimization Based Trajectory Generation for Quadrotor Aggressive Flight