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For quadrotor trajectory planning, describing a polynomial trajectory through coefficients and end-derivatives both enjoy their own convenience in energy minimization. We name them double descriptions of polynomial trajectories. The transformation between them, causing most of the inefficiency and instability, is formally analyzed in this paper. Leveraging its analytic structure, we design a linear-complexity scheme for both jerk/snap minimization and parameter gradient evaluation, which possesses efficiency, stability, flexibility, and scalability. With the help of our scheme, generating an energy optimal (minimum snap) trajectory only costs 1 $mu s$ per piece at the scale up to 1,000,000 pieces. Moreover, generating large-scale energy-time optimal trajectories is also accelerated by an order of magnitude against conventional methods.
We study the problem of training sequential generative models for capturing coordinated multi-agent trajectory behavior, such as offensive basketball gameplay. When modeling such settings, it is often beneficial to design hierarchical models that can
This paper discusses a large-scale and long-term mapping and localization scenario using the maplab open-source framework. We present a brief overview of the specific algorithms in the system that enable building a consistent map from multiple sessio
Multi-vehicle interaction behavior classification and analysis offer in-depth knowledge to make an efficient decision for autonomous vehicles. This paper aims to cluster a wide range of driving encounter scenarios based only on multi-vehicle GPS traj
In this paper, we present a method to efficiently generate large, free, and guaranteed convex space among arbitrarily cluttered obstacles. Our method operates directly on point clouds, avoids expensive calculations, and processes thousands of points
Recently, an abundant amount of urban vehicle trajectory data has been collected in road networks. Many studies have used machine learning algorithms to analyze patterns in vehicle trajectories to predict location sequences of individual travelers. U