# Inverse Kinematics with Forward Dynamics Solvers for Sampled Motion Tracking

## TL;DR

This paper introduces an enhanced inverse kinematics solver that leverages forward dynamics with the mass matrix to improve convergence and smoothness in robot motion tracking, demonstrated on a UR10 robot.

## Contribution

It presents a novel dynamics-based IK solver that extends the Jacobian transpose method using the robot's mass matrix for better performance and smoothness.

## Key findings

- Superior convergence compared to plain Jacobian method
- Improved motion smoothness and quality
- Easy to implement with standard robotics libraries

## Abstract

Tracking Cartesian motion with end~effectors is a fundamental task in robot control. For motion that is not known in advance, the solvers must find fast solutions to the inverse kinematics (IK) problem for discretely sampled target poses. On joint control level, however, the robot's actuators operate in a continuous domain, requiring smooth transitions between individual states. In this work, we present a boost to the well-known Jacobian transpose method to address this goal, using the mass matrix of a virtually conditioned twin of the manipulator. Results on the UR10 show superior convergence and quality of our dynamics-based solver against the plain Jacobian method. Our algorithm is straightforward to implement as a controller, using common robotics libraries.