Linear-time Differential Inverse Kinematics: an Augmented Lagrangian Perspective

Bruce Wingo1, 2, Ajay Suresha Sathya1, Stephane Caron1, Seth Hutchinson2, Justin Carpentier1,
1Authors are with INRIA Willow.
2Authors are with Georgia Tech IRIM.
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Abstract

Differential inverse kinematics is a core robotics problem whose state-of-the-art solutions are currently based on quadratic programming. we revisit it from the perspective of augmented Lagrangian methods (AL) and the related alternating direction method of multipliers (ADMM).

By embracing AL techniques in the spirit of the rigid-body dynamics algorithms proposed by Featherstone, we introduce a method that solves equality-constrained differential IK problems with linear-time complexity. Combined with the ADMM strategy popularized by OSQP, we handle the same class of problems as QP-based differential IK, but scaling linearly with problem dimensions rather than cubically.

We implement our approach as C++ open-source software and evaluate it on a benchmark of robotic-arm and humanoid-locomotion tasks. We measure computation times 2--3$\times$ shorter than the QP-based state of the art.

Our code is made open-source at https://github.com/Simple-Robotics/Loik.

Performance benchmarks

The performance of LOIK, is evaluated against existing differential IK formulations with state-of-the-art QP solver backends, such as OSQP and ProxQP.

A benchmark is designed for trajectory tracking tasks, collected over a variety of robots, ranging from fixed-base robotic arms to high-degrees-of-freedom humanoids. On average, LoIK is 2 to 3 times faster at solving differential IK problems than state-of-the-art QP solvers.

benchmark timings

Detailed analysis

solution details

Related Links

This work heavily relies on the Pinocchio library.

BibTeX

@article{loik2024,
  author    = {Wingo, Bruce and Sathya, Ajay Suresha and Caron, Stephane and Hutchinson, Seth and Carpentier, Justin},
  title     = {Linear-time Differential Inverse Kinematics: an Augmented Lagrangian Perspective.},
  journal   = {Robotics: Science and Systems},
  year      = {2024},
}