Robotics: Science and Systems XVIII

SymForce: Symbolic Computation and Code Generation for Robotics

Hayk Martiros, Aaron Miller, Nathan Bucki, Bradley Solliday, Ryan Kennedy, Jack Zhu, Tung Dang, Dominic Pattison, Harrison Zheng, Teo Tomic, Peter Henry, Gareth Cross, Josiah VanderMey, Alvin Sun, Samuel Wang, Kristen Holtz


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. Code is available at



    AUTHOR    = {Hayk Martiros AND Aaron Miller AND Nathan Bucki AND Bradley Solliday AND Ryan Kennedy AND Jack Zhu AND Tung Dang AND Dominic Pattison AND Harrison Zheng AND Teo Tomic AND Peter Henry AND Gareth Cross AND Josiah VanderMey AND Alvin Sun AND Samuel Wang AND Kristen Holtz}, 
    TITLE     = {{SymForce: Symbolic Computation and Code Generation for Robotics}}, 
    BOOKTITLE = {Proceedings of Robotics: Science and Systems}, 
    YEAR      = {2022}, 
    ADDRESS   = {New York City, NY, USA}, 
    MONTH     = {June}, 
    DOI       = {10.15607/RSS.2022.XVIII.041}