# Path Planning for Highly Automated Driving on Embedded GPUs

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## Abstract

**:**

## 1. Introduction and Related Work

#### 1.1. Motivation

#### 1.2. Related Work

## 2. Methods

#### 2.1. Programming an Embedded GPU

#### 2.2. Overview

- Calculate start values in Frenet coordinates for the path planning algorithm in relation to the current vehicle position.
- Plan different paths with different lengthwise and crosswise variations with respect to the reference path.
- Transform from Frenet coordinates to Cartesian coordinates.
- Calculate the costs for each path and select the best path.

#### 2.3. Frenet Coordinates

- $\mathbf{s}$ is the tangent unit vector, $\mathbf{s}=\frac{\frac{d\overrightarrow{r}}{dl}}{\parallel \frac{d\overrightarrow{r}}{dl}\parallel}$
- $\mathbf{d}$ is the normal unit vector, $\mathbf{d}=\frac{\frac{d\mathbf{s}}{dl}}{\parallel \frac{d\mathbf{s}}{dl}\parallel}$
- $\mathbf{b}$ is the binormal unit vector, $\mathbf{b}=\mathbf{s}\times \mathbf{d}$

- The change of the angle between two polygon courses can only be moderate. Otherwise, there will be jump discontinuity in the polygon course. Since our approach is proposed for highway scenarios, that is not a limitation.
- The polygon course has to be monotonically increasing along the x-axis.
- The path P is an open polygon course and is defined as $P=\{{P}_{1}\to {P}_{2}\to ,\dots ,\to {P}_{n}\}\phantom{\rule{0.277778em}{0ex}}\mathrm{with}\phantom{\rule{0.277778em}{0ex}}{S}_{1}=[{P}_{1},{P}_{2}],{S}_{2}=[{P}_{2},{P}_{3}],\dots ,{S}_{n-1}=[{P}_{n-1},{P}_{n}]$.

#### 2.4. Path Generation

#### 2.5. Rating of Paths

- Distance to the left corridor boundary (${d}_{cl}$) and to the right corridor boundary (${d}_{cr}$).
- A crosswise deviation related to the reference path in the endpoint of the path (${d}_{REF}$).
- Maximum lateral acceleration (${d}_{acclY}$) of the vehicle along the planned path.

## 3. Experiments

#### 3.1. Evaluation Environment

#### 3.2. Evaluation of the Coordinate Transformation from Frenet Coordinates to Cartesian Coordinates

#### 3.3. Evaluation of Lengthwise and Crosswise Path Planning

#### 3.4. Evaluation of the Path Rating

## 4. Conclusion and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

ADAS | Advanced Driver Assistance System |

GPU | Graphics Processing Unit |

CPU | Central Processing Unit |

ECU | Electronic Control Unit |

SIMT | Single Instruction Multiple Thread |

SLAM | Simultaneous Localization and Mapping |

FMA | Fused Multiply Add |

ROI | Region of Interest |

OVM | Own Vehicle Motion |

ESCS | Environment Sensor Coordinate System |

SoC | System-on-Chip |

GPGPU | General Purpose Computation on Graphics Processing Unit |

MIMD | Multiple Instruction, Multiple Data |

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**Figure 1.**Illustration of the: (

**a**) architecture of a desktop GPU; and (

**b**) architecture of an embedded GPU.

**Figure 2.**The planning of one path (red arrow) is illustrated. The road consists of two lanes. The red points are the rating points of this path. These points will later be used to evaluate the course. The green dashed line is the reference path. The orange dashed lines are possibilities for endpoints of paths. The blue points are calculated endpoints of paths. The corridor boundaries are the upper lane marking and the center lane marking. For improved clarity, no paths (red arrows) are drawn to these calculated endpoints.

**Figure 4.**Evaluation of the cost of one path, with two rating points (red points). The road consists of only one lane. The vehicle is too far on the left part of the lane and should be guided back towards the reference path.

**Figure 5.**Evaluation of the coordinate transformation. The number of paths was varied. The number of rating points per path was always 20.

**Figure 6.**Evaluation of the coordinate transformation. The number of rating points for each path was varied. The number of paths was always nine.

**Figure 7.**In this experiment, lengthwise and crosswise path planning was evaluated. The number of rating points per path was set to 20. The number of paths was varied.

**Figure 8.**In this experiment, lengthwise and crosswise path planning was evaluated. The number of rating points per path was varied. The number of paths was set to nine.

**Figure 9.**Evaluation of the cost function. The number of paths was varied. The number of rating points per path was always 20.

**Figure 10.**Evaluation of the cost function. The number of paths was set to nine and the number of rating points for each path was varied.

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**MDPI and ACS Style**

Fickenscher, J.; Schmidt, S.; Hannig, F.; Bouzouraa, M.E.; Teich, J.
Path Planning for Highly Automated Driving on Embedded GPUs. *J. Low Power Electron. Appl.* **2018**, *8*, 35.
https://doi.org/10.3390/jlpea8040035

**AMA Style**

Fickenscher J, Schmidt S, Hannig F, Bouzouraa ME, Teich J.
Path Planning for Highly Automated Driving on Embedded GPUs. *Journal of Low Power Electronics and Applications*. 2018; 8(4):35.
https://doi.org/10.3390/jlpea8040035

**Chicago/Turabian Style**

Fickenscher, Jörg, Sandra Schmidt, Frank Hannig, Mohamed Essayed Bouzouraa, and Jürgen Teich.
2018. "Path Planning for Highly Automated Driving on Embedded GPUs" *Journal of Low Power Electronics and Applications* 8, no. 4: 35.
https://doi.org/10.3390/jlpea8040035