US 12,282,524 B2
Computer-implemented computation of tangent-space jacobian
Hayk Martirosyan, San Francisco, CA (US); Aaron Christopher Miller, San Francisco, CA (US); Nathan Leo Bucki, San Mateo, CA (US); Bradley Matthew Solliday, San Francisco, CA (US); Ryan David Kennedy, San Francisco, CA (US); Jack Louis Zhu, San Mateo, CA (US); Teodor Tomic, Redwood City, CA (US); Yixiao Sun, Stanford, CA (US); Josiah Timothy VanderMey, Redwood City, CA (US); Gareth Benoit Cross, San Carlos, CA (US); Peter Benjamin Henry, San Francisco, CA (US); Dominic William Pattison, Cupertino, CA (US); Samuel Shenghung Wang, Mountain View, CA (US); Kristen Marie Holtz, Menlo Park, CA (US); and Harrison Zheng, Palo Alto, CA (US)
Assigned to Skydio, Inc., San Mateo, CA (US)
Filed by Skydio, Inc., San Mateo, CA (US)
Filed on Jan. 27, 2023, as Appl. No. 18/161,028.
Claims priority of provisional application 63/344,755, filed on May 23, 2022.
Claims priority of provisional application 63/304,537, filed on Jan. 28, 2022.
Prior Publication US 2023/0244231 A1, Aug. 3, 2023
Int. Cl. G06F 17/16 (2006.01); B64C 39/02 (2023.01); B64U 10/00 (2023.01); G05D 1/00 (2024.01); G06F 9/52 (2006.01); G06F 17/18 (2006.01); G06V 10/75 (2022.01); B64U 101/30 (2023.01)
CPC G06F 17/16 (2013.01) [B64C 39/024 (2013.01); B64U 10/00 (2023.01); G05D 1/0022 (2013.01); G05D 1/0038 (2013.01); G05D 1/0088 (2013.01); G05D 1/0825 (2013.01); G05D 1/101 (2013.01); G06F 9/526 (2013.01); G06F 17/18 (2013.01); G06V 10/751 (2022.01); B64U 2101/30 (2023.01); B64U 2201/00 (2023.01); B64U 2201/10 (2023.01); B64U 2201/20 (2023.01)] 18 Claims
OG exemplary drawing
 
1. A method comprising:
accessing a first symbolic expression for an output matrix as a function of an input matrix at a computing device comprising processing circuitry and memory;
computing, at a first component of the processing circuitry, a first Jacobian of the input matrix with respect to an input tangent space;
computing, at a second component of the processing circuitry, a second Jacobian of the output matrix with respect to the input matrix;
computing, at a third component of the processing circuitry, a third Jacobian of an output tangent space with respect to the input matrix;
applying symbolic matrix multiplication to the first Jacobian, the second Jacobian, and the third Jacobian to obtain a second symbolic expression for the output tangent space with respect to the input tangent space; and
controlling operation of an unmanned aerial vehicle based on the second symbolic expression, wherein the controlling operation controls movement of the unmanned aerial vehicle based on cost functions.