Naslov
Inverse Kinematics for Serial Kinematic Chains via Sum of Squares Optimization

Autori
Maric, Filip ; Giamou, Matthew ; Khoubyarian, Soroush ; Petrovic, Ivan ; Kelly, Jonathan

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Skup
International Conference on Robotics and Automation (ICRA 2017)

Mjesto i datum
Pariz, Francuska, 31.05.2020. - 31.08.2020

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Kinematics, Manipulation, Robotics

Sažetak
Inverse kinematics is a fundamental challenge for articulated robots: fast and accurate algorithms are needed for translating task-related workspace constraints and goals into feasible joint configurations. In general, inverse kinematics for serial kinematic chains is a difficult nonlinear problem, for which closed form solutions cannot easily be obtained. Therefore, computationally efficient numerical methods that can be adapted to a general class of manipulators are of great importance. In this paper, we use convex optimization techniques to solve the inverse kinematics problem with joint limit constraints for highly redundant serial kinematic chains with spherical joints in two and three dimensions. This is accomplished through a novel formulation of inverse kinematics as a nearest point problem, and with a fast sum of squares solver that exploits the sparsity of kinematic constraints for serial manipulators. Our method has the advantages of post-hoc certification of global optimality and a runtime that scales polynomially with the number of degrees of freedom. Additionally, we prove that our convex relaxation leads to a globally optimal solution when certain conditions are met, and demonstrate empirically that these conditions are common and represent many practical instances. Finally, we provide an open source implementation of our algorithm.

Izvorni jezik
Engleski

Znanstvena područja
Elektrotehnika, Računarstvo, Temeljne tehničke znanosti

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