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Arc2D

Class that implements a 2D arc section. More...

#include <Arc2D.h>

Inherits from PathSection

Public Functions

Name
Arc2D(Eigen::Vector2d start_point, Eigen::Vector2d end_point, Eigen::Vector2d center_point, int direction, double z)
Constructor for the Arc2D class, that receives the desired plane for the arc.
Arc2D(Eigen::Vector2d start_point, Eigen::Vector2d end_point, Eigen::Vector2d center_point, int direction)
Constructor for the Arc2D class, that receives the desired plane for the arc. Assumes the plane is placed at z=0.0 m.
virtual Eigen::Vector3d eq_pd(double t) override
The Path section equation.
virtual Eigen::Vector3d eq_d_pd(double t) override
First derivative of the path section equation with respect to the path parameter t.
virtual Eigen::Vector3d eq_dd_pd(double t) override
Second derivative of the path section equation with respect to the path parameter t.
virtual double curvature(double t) override
Compute the curvature in a simple manner. Computed as 1/Radius.
virtual double getClosestPointGamma(Eigen::Vector3d & coordinate) override
Method for getting the gamma of the closes point to the path in a more efficient manner For an arc it uses a closed form equation to solve this problem.

Additional inherited members

Public Functions inherited from PathSection

Name
virtual double tangent(double t)
Default method for computing the tangent to the path section.
virtual double derivative_norm(double t)
Default method for computing the norm of the derivative.
bool can_be_composed()
Method to return whether a pathSection can be composed with other path sections or not.
double limitGamma(double t)
Method to limit the gamma between the minimum and maximum value By default the maximum gamma is a very high number.
double getMaxGammaValue()
Method used to get the maximum gamma allowed by the path section By the default is the maximum valid number possible in c++.
double getMinGammaValue()
Method used to get the minimum gamma allowed by the path section By default is the minimum valid number possible in c++.
virtual ~PathSection()
Virtual destructor for the abstract class.

Protected Functions inherited from PathSection

Name
PathSection(bool can_be_composed)
Constructor for the abstract class i NOTE: this class is virtual, therefore an object of type PathSection cannot be instantiated in memory. Only derivatives of the class PathSection.
bool setMaxGammaValue(double gamma_max)
Method to update the max of the gamma parameter Validates if the value received is greater than gamma_min.
bool setMinGammaValue(double gamma_min)
Method to update the min value of the gamma parameter Validades if the value is received is smaller than gamma_max.
double GradientDescent(double gamma_o, Eigen::Vector3d & x_pos, double tolerance)
Method that implements the gradient descent to minimize the error of
double getInitialGammaEstimate(Eigen::Vector3d & x_pos, int num_partitions, double min_val, double max_val)
Method to get an initial estimate for the gamma. It divides the section into n sections and search for local minimums in the function that computes the distance of the vehicle inside those sections.
double bisection(Eigen::Vector3d & x_pos, double a, double b)
Method to implement bisection method

Detailed Description

class Arc2D;

Class that implements a 2D arc section.

Author:

  • Marcelo Jacinto
  • Joao Quintas
  • Joao Cruz
  • Hung Tuan

Version: 1.0a

Date: 2021

Copyright: MIT

This class is used as a part of the sections library

Public Functions Documentation

function Arc2D

Arc2D(
    Eigen::Vector2d start_point,
    Eigen::Vector2d end_point,
    Eigen::Vector2d center_point,
    int direction,
    double z
)

Constructor for the Arc2D class, that receives the desired plane for the arc.

Parameters:

  • start_point The 2D start point of the arc
  • end_point The 2D end point of the arc
  • center_point The 2D coordinate with the center of the arc
  • direction An int (-1 or 1) that represents the direction of the arc
  • z The altitude at which to place the arc

Constructor for the Arc2D path. Using this constructor we can specify the plane in which to put the arc

function Arc2D

Arc2D(
    Eigen::Vector2d start_point,
    Eigen::Vector2d end_point,
    Eigen::Vector2d center_point,
    int direction
)

Constructor for the Arc2D class, that receives the desired plane for the arc. Assumes the plane is placed at z=0.0 m.

Parameters:

  • start_point The 2D start point of the arc
  • end_point The 2D end point of the arc
  • center_point The 2D coordinate with the center of the arc
  • direction An int (-1 or 1) that represents the direction of the arc

The constructors for the Arc2D paths Using this constructor we assume the path is place in the plane z = 0

function eq_pd

virtual Eigen::Vector3d eq_pd(
    double t
) override

The Path section equation.

Parameters:

  • t The path parameter

Return: An Eigen::Vector3d with the equation of the path with respect to the path parameter

Reimplements: PathSection::eq_pd

function eq_d_pd

virtual Eigen::Vector3d eq_d_pd(
    double t
) override

First derivative of the path section equation with respect to the path parameter t.

Parameters:

  • t The path parameter t

Return: An Eigen::Vector3d with the equation of the partial derivative with respect to the path parameter

Reimplements: PathSection::eq_d_pd

function eq_dd_pd

virtual Eigen::Vector3d eq_dd_pd(
    double t
) override

Second derivative of the path section equation with respect to the path parameter t.

Parameters:

  • t The path parameter t

Return: An Eigen::Vector3d with the equation of the second order partial derivative with respect to the path parameter

Reimplements: PathSection::eq_dd_pd

function curvature

virtual double curvature(
    double t
) override

Compute the curvature in a simple manner. Computed as 1/Radius.

Parameters:

  • t The path parameter t

Return: A double with the curvature in of that section (1/radius)

Reimplements: PathSection::curvature

function getClosestPointGamma

virtual double getClosestPointGamma(
    Eigen::Vector3d & coordinate
) override

Method for getting the gamma of the closes point to the path in a more efficient manner For an arc it uses a closed form equation to solve this problem.

Parameters:

  • coordinate The coordinate of the vehicle in the 3D space

Return: A double with the gamma corresponding to the closest point in the path

Reimplements: PathSection::getClosestPointGamma

Updated on 2022-09-15 at 17:51:30 +0000

Last update: September 15, 2022
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