In open-chain robots, the forward and inverse kinematics problems are foundational for manipulating the robot. The forward kinematics takes as input the position of each joint of the robot and computes the position and orientation of the robot’s end-effector. Commonly used methods for solving the forward kinematics problem include the product of exponentials formula and the Denavit-Hartenberg (D-H) representation. In this paper, we focus on a specific Python implementation of the product of exponentials (POE) formula (modern_robotics package), which is one of the most popular implementations used in production, with nearly 1000 stars on Github, and has been downloaded over 5000 times in the last year. This POE implementation does not natively support computation in parallel for multiple inputs. Also, the product of exponentials implementation cannot be used in machine learning models that use automatic differentiation, such as neural networks. This paper contributes a parallelized, automatically differentiable implementation of the modern_robotics Python implementation using PyTorch, one of the most popular deep learning frameworks. We achieve this by introducing a natural extension using PyTorch tensors to the special orthogonal group so(3) and the special euclidean group se(3). The newly introduced extensions form a group themselves, and all operations needed for the POE formula can be implemented in them in parallel, leading to significant speedup on our hardware - both on CPU (over 200 times) and especially on GPU (over 1600 times), compared to a naive sequential implementation in Python.
Parallelized Forward Kinematics Using Product of Exponentials in PyTorch
Mechan. Machine Science
International Conference on Robotics in Alpe-Adria Danube Region ; 2022 ; Klagenfurt, Austria June 08, 2022 - June 10, 2022
2022-04-23
8 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
PyTorch and automatic differentiation
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