# Improved Kalman-Filter-Based Model-Predictive Control Method for Trajectory Tracking of Automatic Straddle Carriers

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- Considering the structural characteristics of the ASC, the steering and dynamics of the ASC are analyzed and the mathematical model is established according to Newton’s second law of motion and D’Alembert’s principle.
- (2)
- An improved dynamic Kalman filter algorithm is proposed to compensate for the process and measurement noise and to provide the system state estimation for the considered ASC.
- (3)
- Considering the anti-overturning constraint, the objective function is optimized and the iKFMPC algorithm is designed to ensure smooth operation of the ASC and accurate trajectory tracking.

## 2. Problem Formulation

## 3. Design of the Improved Kalman Filter

## 4. Design of iKFMPC

- (1)
- Considering the system’s ability to follow the desired path of the ASC, the cost function ${J}_{1}$ is set, where $R(k)$ is the desired path;
- (2)
- Considering the constraints on the control increment of the system, the cost function ${J}_{2}$ is set;
- (3)
- Considering the optimal travel distance of the automatic straddle carrier, the cost function ${J}_{3}$ is set;
- (4)
- Considering the constraints on the sideslip angle of the automatic straddle carrier, the cost function ${J}_{4}$ is set;
- (5)
- Considering the tilt angle constraint, the cost function ${J}_{5}$ is set.

**Algorithm 1:**

## 5. Simulation Experiments

#### 5.1. Linear Motion

#### 5.2. Curvilinear Motion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**(

**A**) is the straight-line trajectory tracking diagram of the ASC, (

**B**) is the change of control inputs, and (

**C**,

**D**) are the change of states.

**Figure 4.**(

**A**) is the curve tracking diagram of considered ASC, (

**B**) is the change of control inputs, and (

**C**,

**D**) are the change of states.

Parameters | Numerical Values | Unit | Parameters | Numerical Values | Unit |
---|---|---|---|---|---|

${N}_{p}$ | 50 | _ | ${N}_{c}$ | 50 | _ |

$m$ | 89,000 | $kg$ | ${I}_{z}$ | 1,052,500 | $kg\cdot {m}^{2}$ |

${C}_{f}$ | 560,000 | $N/rad$ | ${C}_{r}$ | 460,000 | $N/rad$ |

${l}_{1}$ | 3.85 | $m$ | ${l}_{2}$ | 1.95 | $m$ |

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**MDPI and ACS Style**

Ding, Z.; Lin, S.; Gu, W.; Zhang, Y.
Improved Kalman-Filter-Based Model-Predictive Control Method for Trajectory Tracking of Automatic Straddle Carriers. *World Electr. Veh. J.* **2023**, *14*, 118.
https://doi.org/10.3390/wevj14050118

**AMA Style**

Ding Z, Lin S, Gu W, Zhang Y.
Improved Kalman-Filter-Based Model-Predictive Control Method for Trajectory Tracking of Automatic Straddle Carriers. *World Electric Vehicle Journal*. 2023; 14(5):118.
https://doi.org/10.3390/wevj14050118

**Chicago/Turabian Style**

Ding, Zonghe, Shuang Lin, Wei Gu, and Yilian Zhang.
2023. "Improved Kalman-Filter-Based Model-Predictive Control Method for Trajectory Tracking of Automatic Straddle Carriers" *World Electric Vehicle Journal* 14, no. 5: 118.
https://doi.org/10.3390/wevj14050118