Alternating Minimization Based Trajectory Generation for Quadrotor Aggressive Flight

TL;DR

This paper introduces a fast, efficient framework for generating large-scale, spatial-temporal optimal trajectories for aggressive quadrotor flight, leveraging alternating minimization and polynomial theory.

Contribution

It presents a novel alternating minimization approach that improves computational efficiency and scalability for real-time trajectory planning in aggressive quadrotor flights.

Findings

Outperforms state-of-the-art methods in efficiency and optimality

Demonstrates successful aggressive flight in obstacle-dense environments

Provides theoretical analysis of convergence rates

Abstract

With much research has been conducted into trajectory planning for quadrotors, planning with spatial and temporal optimal trajectories in real-time is still challenging. In this paper, we propose a framework for generating large-scale piecewise polynomial trajectories for aggressive autonomous flights, with highlights on its superior computational efficiency and simultaneous spatial-temporal optimality. Exploiting the implicitly decoupled structure of the planning problem, we conduct alternating minimization between boundary conditions and time durations of trajectory pieces. In each minimization phase, we leverage the algebraic convenience of the sub-problem to escape poor local minima and achieve the lowest time consumption. Theoretical analysis for the global/local convergence rate of our proposed method is provided. Moreover, based on polynomial theory, an extremely fast feasibility check method is designed for various kinds of constraints. By incorporating the method into our alternating structure, a constrained minimization algorithm is constructed to optimize trajectories on the premise of feasibility. Benchmark evaluation shows that our algorithm outperforms state-of-the-art methods regarding efficiency, optimality, and scalability. Aggressive flight experiments in a limited space with dense obstacles are presented to demonstrate the performance of the proposed algorithm. We release our implementation as an open-source ros-package.