Sree-Pavan-Coast / hybrid_a_star_g2

Hybrid A* Planing with G2 Continuity

Introduction

This repository is derived from Open Space Planer submodule, Apollo planning module, replacing the original G1 exploring and RS curves with G2.

Prerequisite

Before compiling, we should do some preperation.

• Install dependencies.

  • glog

    cd ~ 
    mkdir Source
    cd Source
    git clone https://github.com/google/glog.git
    sudo apt-get install autoconf automake libtool
    cd glog
    mkdir build
    cmake ..
    make
    sudo make install

  • protobuf

    cd ~/Source
    sudo apt-get install autoconf automake libtool curl make g++ unzip
    wget  https://github.com/protocolbuffers/protobuf/releases/download/v3.7.1/protobuf-cpp-3.7.1.tar.gz
    tar -xzvf protobuf-cpp-3.7.1.tar.gz
    cd protobuf-3.7.1
    ./autogen.sh
    ./configure
    make
    make check
    sudo make install
    sudo ldconfig

  • osqp

    cd Source
    git clone --recursive https://github.com/oxfordcontrol/osqp
    cd osqp
    mkdir build && cd build
    cmake -G "Unix Makefiles" ..
    cmake --build .
    sudo make install

G2 Continuity

Different from the original Apollo with Bicycle Model exploring new nodes and connecting with Reed Shepp curves, we use Clothoid curves for exploration and impove Reed Shepp curves with continuous curvature. More details, please refer here.

To fit the main skeleton of Apollo, we add a new feature, kappa, to Node3d, and change the method Next_node_generator in HybridAStar to Next_node_generator_clothoid.

Denote $\kappa$ as the curvature of a node and $\delta$ as the steer wheel angle. There are three scenarios in total:

• Move towards a straight line;

  $\delta \rightarrow 0$ && $\kappa \rightarrow 0$

• Move towards a circle;

  $\delta \rightarrow \delta_{max}$ && $\kappa \rightarrow \kappa_{max}$

• Move towards a Clothoid curve.

  $0< \delta < \delta_{max}$

We use the following ODEs for Clothoid exploring

$$\begin{cases} d \kappa = A ds \\ d \theta = \kappa (s) ds \\ dx = \cos \left(\theta(s)\right)ds \\ dy = \sin \left(\theta(s)\right)ds \end{cases}$$