# Using Pose-Dependent Model Predictive Control for Path Tracking with Bounded Tensions in a 3-DOF Spatial Cable Suspended Parallel Robot

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Dynamic Model of the Suspended Load

## 3. Control Design

#### 3.1. Control Architecture

#### 3.2. Model Formulation for Control Design

#### 3.3. Calculation of the Optimal Tensions

#### 3.4. Calculation of Motor Torques

## 4. Numerical Results

#### 4.1. Description of the Test Case

#### 4.2. Test Cases

#### 4.2.1. Test 1: Point-to-Point Motion through a Position Step Reference

#### 4.2.2. Test 2: Circular Path

#### 4.2.3. Test 3: Gerono’s Lemniscate Path

#### 4.2.4. Test 4: Straight Line

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Path tracking response of the circular path: spatial representation (

**a**) and its contour error (

**b**).

**Figure 8.**Path tracking response of the Gerono’s lemniscate: spatial representation (

**a**) and its contour error (

**b**).

**Figure 10.**Path tracking response of the straight line: spatial representation (

**a**) and its contour error (

**b**).

Parameter | Value |
---|---|

${J}_{m,1},{J}_{m,2},{J}_{m,3}$ | $2.6\times {10}^{-5}{\mathrm{kgm}}^{2}$ |

${f}_{v,1},{f}_{v,2},{f}_{v,3}$ | $3\times {10}^{-5}\mathrm{Nms}/\mathrm{rad}$ |

${r}_{1},{r}_{2},{r}_{3}$ | $0.036\mathrm{m}$ |

$m$ | $2.94\mathrm{kg}$ |

${T}_{\mathrm{min}};{T}_{\mathrm{max}}$ | $5;200\mathrm{N}$ |

${T}_{s}$ | $2\times {10}^{-3}\mathrm{s}$ |

${N}_{c};{N}_{p}$ | $1;90$ |

${R}_{Y};{R}_{\Delta T}$ | ${I}_{240};1\times {10}^{-3}{I}_{3}$ |

${A}_{1}$ | ${\left[\begin{array}{ccc}-0.89& 0.85& 0\end{array}\right]}^{T}$ |

${A}_{2}$ | ${\left[\begin{array}{ccc}0.89& 0.85& 0\end{array}\right]}^{T}$ |

${A}_{3}$ | ${\left[\begin{array}{ccc}0& -0.85& 0\end{array}\right]}^{T}$ |

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**MDPI and ACS Style**

Bettega, J.; Richiedei, D.; Trevisani, A.
Using Pose-Dependent Model Predictive Control for Path Tracking with Bounded Tensions in a 3-DOF Spatial Cable Suspended Parallel Robot. *Machines* **2022**, *10*, 453.
https://doi.org/10.3390/machines10060453

**AMA Style**

Bettega J, Richiedei D, Trevisani A.
Using Pose-Dependent Model Predictive Control for Path Tracking with Bounded Tensions in a 3-DOF Spatial Cable Suspended Parallel Robot. *Machines*. 2022; 10(6):453.
https://doi.org/10.3390/machines10060453

**Chicago/Turabian Style**

Bettega, Jason, Dario Richiedei, and Alberto Trevisani.
2022. "Using Pose-Dependent Model Predictive Control for Path Tracking with Bounded Tensions in a 3-DOF Spatial Cable Suspended Parallel Robot" *Machines* 10, no. 6: 453.
https://doi.org/10.3390/machines10060453