Solving the analytical inverse kinematics (IK) of redundant manipulators in
real time is a difficult problem in robotics since its solution for a given
target pose is not unique. Moreover, choosing the optimal IK solution with
respect to application-specific demands helps to improve the robustness and to
increase the success rate when driving the manipulator from its current
configuration towards a desired pose. This is necessary, especially in
high-dynamic tasks like catching objects in mid-flights. To compute a suitable
target configuration in the joint space for a given target pose in the
trajectory planning context, various factors such as travel time or
manipulability must be considered. However, these factors increase the
complexity of the overall problem which impedes real-time implementation. In
this paper, a real-time framework to compute the analytical inverse kinematics
of a redundant robot is presented. To this end, the analytical IK of the
redundant manipulator is parameterized by so-called redundancy parameters,
which are combined with a target pose to yield a unique IK solution. Most
existing works in the literature either try to approximate the direct mapping
from the desired pose of the manipulator to the solution of the IK or cluster
the entire workspace to find IK solutions. In contrast, the proposed framework
directly learns these redundancy parameters by using a neural network (NN) that
provides the optimal IK solution with respect to the manipulability and the
closeness to the current robot configuration. Monte Carlo simulations show the
effectiveness of the proposed approach which is accurate and real-time capable
($\approx $ \SI{32}{\micro\second}) on the KUKA LBR iiwa 14 R820.

PREPRINT

# Machine Learning-based Framework for Optimally Solving the Analytical Inverse Kinematics for Redundant Manipulators

Minh Nhat Vu, Florian Beck, Christian Hartl-Nesic, Anh Nguyen, Andreas Kugi

Submitted on 8 November 2022

## Abstract

## Preprint

Subject: Computer Science - Robotics