Bubble Planner: Planning High-speed Smooth Quadrotor Trajectories using Receding Corridors

Ren, Yunfan; Zhu, Fangcheng; Liu, Wenyi; Wang, Zhepei; Lin, Yi; Gao, Fei; Zhang, Fu

doi:10.48550/arxiv.2202.12177

Cited by 1 publication

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“…A key result we show now is that this point cluster coordinate C i is completely sufficient to represent the matrix A i required in the BA optimization (9). According to (7), we have…”

Section: Point Clustermentioning

confidence: 94%

“…where l ∈ {2, 3} and we omitted the exact number of eigenvalues in the cost function for brevity. Note that the matrix A i in (9) depends on the lidar pose T since each involved point p ijk depends on the pose (see (7) and ( 2)). Hence the decision variables of the resultant optimization in (9) involve the lidar pose T only, which dramatically reduces the optimization dimension (hence computation time).…”

Section: B Elimination Of Feature Parametersmentioning

confidence: 99%

“…Nij k=1 p ijk = pi as is defined in (7). Now, substituting the optimum solution q ⋆ i = pi into (60) leads to:…”

Section: Mp J=1mentioning

confidence: 99%

“…{u3007335,xliuaa}@connect.hku.hk, fuzhang@hku.hk 2 https://github.com/hku-mars/BALM (DDAA) depth measurements, lidar sensors have the ability to build a dense and accurate 3D map of the environment in realtime and at a relatively low computation cost. These unique advantages have made lidar sensors essential to a variety of applications that require real-time, dense, and accurate 3D mapping of the environment, such as autonomous driving [3,4], unmanned aerial vehicles navigation [5]- [7], and realtime mobile mapping [8]- [10]. This trend becomes even more evident with recent developments in lidar technologies which have enabled the commercialization and mass production of lightweight and high-performance solid-state lidars at a significantly lower cost [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Efficient and Consistent Bundle Adjustment on Lidar Point Clouds

Liu¹,

Liu²,

Zhang³

2022

Preprint

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Bundle Adjustment (BA) refers to the problem of simultaneous determination of sensor poses and scene geometry, which is a fundamental problem in robot vision. This paper presents an efficient and consistent bundle adjustment method for lidar sensors. The method employs edge and plane features to represent the scene geometry, and directly minimizes the natural Euclidean distance from each raw point to the respective geometry feature. A nice property of this formulation is that the geometry features can be analytically solved, drastically reducing the dimension of the numerical optimization. To represent and solve the resultant optimization problem more efficiently, this paper then proposes a novel concept point clusters, which encodes all raw points associated to the same feature by a compact set of parameters, the point cluster coordinates. We derive the closed-form derivatives, up to the second order, of the BA optimization based on the point cluster coordinates and show their theoretical properties such as the null spaces and sparsity. Based on these theoretical results, this paper develops an efficient second-order BA solver. Besides estimating the lidar poses, the solver also exploits the second order information to estimate the pose uncertainty caused by measurement noises, leading to consistent estimates of lidar poses. Moreover, thanks to the use of point cluster, the developed solver fundamentally avoids the enumeration of each raw point (which is very time-consuming due to the large number) in all steps of the optimization: cost evaluation, derivatives evaluation and uncertainty evaluation.The proposed method is extensively evaluated at different levels: consistency, accuracy, and computation efficiency in both simulated and actual environments. Benchmark evaluation on 19 real-world open sequences covering various datasets (Hilti, NTU-VIRAL and UrbanLoco), environments (campus, urban streets, offices, laboratory, and construction sites), lidar types (Ouster OS0-64, Ouster OS1-16, Velodyne HDL 32E), and motion types (handheld, UAV-based, and ground vehicles-based) shows that our method achieves consistently and significantly higher performance than other state-of-the-art counterparts in terms of localization accuracy, mapping quality, and computation efficiency. In particular, our method achieves a mapping accuracy at a level of the lidar measurement noise (i.e., a few centimeters) while processing all sequences in less than half minute on a standard desktop CPU. Finally, we show how our proposed method effectively improves the accuracy and/or computation efficiency of some important robotic techniques, including lidarinertial odometry, multi-lidar extrinsic calibration, and highaccuracy global mapping. The implementation of our method is open sourced to benefit the robotics community and beyond 2 .

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“…A key result we show now is that this point cluster coordinate C i is completely sufficient to represent the matrix A i required in the BA optimization (9). According to (7), we have…”

Section: Point Clustermentioning

confidence: 94%

Section: B Elimination Of Feature Parametersmentioning

confidence: 99%

“…Nij k=1 p ijk = pi as is defined in (7). Now, substituting the optimum solution q ⋆ i = pi into (60) leads to:…”

Section: Mp J=1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient and Consistent Bundle Adjustment on Lidar Point Clouds

Liu¹,

Liu²,

Zhang³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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Bubble Planner: Planning High-speed Smooth Quadrotor Trajectories using Receding Corridors

Cited by 1 publication

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Efficient and Consistent Bundle Adjustment on Lidar Point Clouds

Efficient and Consistent Bundle Adjustment on Lidar Point Clouds

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