# Optimal Object Placement using a Virtual Axis

## TL;DR

This paper introduces a novel method for optimal object placement in robotic workspaces by extending robots with a virtual joint, enabling the use of advanced nonlinear programming for guaranteed reachability and optimization.

## Contribution

The paper proposes a virtual axis extension for robots, allowing reliable and efficient optimization of object placement with guaranteed reachability using nonlinear programming techniques.

## Key findings

- Enables guaranteed reachability of all process positions.
- Facilitates the use of nonlinear programming for placement optimization.
- Improves automation in robotic workspace design.

## Abstract

A basic task in the design of a robotic production cell is the relative placement of robot and workpiece. The fundamental requirement is that the robot can reach all process positions; only then one can think of further optimization. Therefore an algorithm that automatically places an object into the workspace is very desirable. However many iterative optimzation algorithms cannot guarantee that all intermediate steps are reachable, resulting in complicated procedures. We present a novel approach which extends a robot by a virtual prismatic joint - which measures the distance to the workspace - such that any TCP frames are reachable. This allows higher order nonlinear programming algorithms to be used for placement of an object alone as well as the optimal placement under some differentiable criterion.