# Temporally Coupled Dynamical Movement Primitives in Cartesian Space

## TL;DR

This paper introduces a control system for robot orientation in Cartesian space using temporally coupled dynamical movement primitives and unit quaternions, addressing topological challenges for stable feedback control.

## Contribution

It presents a novel control approach leveraging the contractibility of unit quaternions to enable stable orientation control in Cartesian space.

## Key findings

- Control system verified experimentally on an industrial robot.
- Addresses topological issues in orientation control using quaternion representation.
- Demonstrates stable, continuous control of robot orientation.

## Abstract

Control of robot orientation in Cartesian space implicates some difficulties, because the rotation group SO(3) is not contractible, and only globally contractible state spaces support continuous and globally asymptotically stable feedback control systems. In this paper, unit quaternions are used to represent orientations, and it is first shown that the unit quaternion set minus one single point is contractible. This is used to design a control system for temporally coupled dynamical movement primitives (DMPs) in Cartesian space. The functionality of the control system is verified experimentally on an industrial robot.

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Source: https://tomesphere.com/paper/1905.11176