Manifold Geometry with Fast Automatic Derivatives and Coordinate Frame Semantics Checking in C++

Koppel, Leonid; Waslander, Steven L.

doi:10.1109/crv.2018.00027

Cited by 6 publications

(5 citation statements)

References 19 publications

(52 reference statements)

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“…Manif [13] is a C++ library with handwritten Lie group operations. The wave geometry library [14] provides expression template-based automatic differentiation of Lie groups in C++. SymForce is inspired by GTSAM and Sophus.…”

Section: Related Workmentioning

confidence: 99%

SymForce: Symbolic Computation and Code Generation for Robotics

Hayk¹,

Miller²,

Bucki³

et al. 2022

Preprint

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We present SymForce, a fast symbolic computation and code generation library for robotics applications like computer vision, state estimation, motion planning, and controls. SymForce combines the development speed and flexibility of symbolic mathematics with the performance of autogenerated, highly optimized code in C++ or any target runtime language. SymForce provides geometry and camera types, Lie group operations, and branchless singularity handling for creating and analyzing complex symbolic expressions in Python, built on top of SymPy. Generated functions can be integrated as factors into our tangent space nonlinear optimizer, which is highly optimized for real-time production use. We introduce novel methods to automatically compute tangent space Jacobians, eliminating the need for bug-prone handwritten derivatives. This workflow enables faster runtime code, faster development time, and fewer lines of handwritten code versus the state-of-the-art. Our experiments demonstrate that our approach can yield order of magnitude speedups on computational tasks core to robotics.

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Section: Related Workmentioning

confidence: 99%

SymForce: Symbolic Computation and Code Generation for Robotics

Hayk¹,

Miller²,

Bucki³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Manif [16] is a C++ library with handwritten Lie group operations. The wave geometry library [17] provides expression template-based automatic differentiation of Lie groups in C++. LieTorch [18] implements Lie groups in PyTorch.…”

Section: Related Workmentioning

confidence: 99%

SymForce: Symbolic Computation and Code Generation for Robotics

Hayk¹,

Miller²,

Bucki³

et al. 2022

Robotics: Science and Systems XVIII

View full text Add to dashboard Cite

We present SymForce, a library for fast symbolic computation, code generation, and nonlinear optimization for robotics applications like computer vision, motion planning, and controls. SymForce combines the development speed and flexibility of symbolic math with the performance of autogenerated, highly optimized code in C++ or any target runtime language. SymForce provides geometry and camera types, Lie group operations, and branchless singularity handling for creating and analyzing complex symbolic expressions in Python, built on top of SymPy. Generated functions can be integrated as factors into our tangent-space nonlinear optimizer, which is highly optimized for real-time production use. We introduce novel methods to automatically compute tangent-space Jacobians, eliminating the need for bug-prone handwritten derivatives. This workflow enables faster runtime code, faster development time, and fewer lines of handwritten code versus the state-of-the-art. Our experiments demonstrate that our approach can yield order of magnitude speedups on computational tasks core to robotics.

show abstract

“…Libraries such as GTSAM [12] and g2o [14] provide general frameworks for solving nonlinear least-squares and MAP inference problems involving manifold elements such as camera poses. GTSAM and Koppel et al [17] provide frameworks which can perform automatic differentiation over lie groups. However, these frameworks are tailored to the computation of Jacobian matrices and cannot be readily used within the computation graphs for training neural networks.…”

Section: Related Workmentioning

confidence: 99%

Tangent Space Backpropagation for 3D Transformation Groups

Teed

Deng

2021

2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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We address the problem of performing backpropagation for computation graphs involving 3D transformation groups SO(3), SE(3), and Sim(3). 3D transformation groups are widely used in 3D vision and robotics, but they do not form vector spaces and instead lie on smooth manifolds. The standard backpropagation approach, which embeds 3D transformations in Euclidean spaces, suffers from numerical difficulties. We introduce a new library, which exploits the group structure of 3D transformations and performs backpropagation in the tangent spaces of manifolds. We show that our approach is numerically more stable, easier to implement, and beneficial to a diverse set of tasks. Our plug-and-play PyTorch library is available at https: //github.com/princeton-vl/lietorch

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Manifold Geometry with Fast Automatic Derivatives and Coordinate Frame Semantics Checking in C++

Cited by 6 publications

References 19 publications

SymForce: Symbolic Computation and Code Generation for Robotics

SymForce: Symbolic Computation and Code Generation for Robotics

SymForce: Symbolic Computation and Code Generation for Robotics

Tangent Space Backpropagation for 3D Transformation Groups

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