PathSection

An abstract class that is used as a template for Path Sections. More...

#include <PathSection.h>

Inherited by Arc2D, Bernoulli, Circle2D, Line, Polinomial5, Polynomial5, Sinusoid2D

Public Functions

	Name
virtual Eigen::Vector3d	eq_pd(double t) =0 The Path section equation.
virtual Eigen::Vector3d	eq_d_pd(double t) =0 First derivative of the path section equation with respect to path parameter t.
virtual Eigen::Vector3d	eq_dd_pd(double t) =0 Second derivative of the path section equation with respect to the path parameter t.
virtual double	tangent(double t) Default method for computing the tangent to the path section.
virtual double	curvature(double t) Default method for computing the curvature. The default implementation implements the general formula to compute the curvature based on the derivative equations of the path.
virtual double	derivative_norm(double t) Default method for computing the norm of the derivative.
virtual double	getClosestPointGamma(Eigen::Vector3d & coordinate) Default method for getting the gamma of the closed point to the path. By default this method uses gradient Descent algorithm to compute the closest point in the path with the initial guess of gamma=0.0.
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

	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 PathSection;

An abstract class that is used as a template for Path Sections.

Author:

Marcelo Jacinto
Joao Quintas
Joao Cruz
Hung Tuan

Version: 1.0a

Date: 2021

Copyright: MIT

For path sections that can_be_composed the minimum value of gamma will be defaulted to 0 (and cannot be changed) in order not to mess with the Path section switching algorithm. The maximum value can be any greater than 0.

For path sections where can_be_composed = false, the minimum value for gamma if -inf an the maximum value if +inf (but these can be changed)

Public Functions Documentation

function eq_pd

virtual Eigen::Vector3d eq_pd(
    double t
) =0

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

Reimplemented by: Polinomial5::eq_pd, Polynomial5::eq_pd, Line::eq_pd, Sinusoid2D::eq_pd, Circle2D::eq_pd, Bernoulli::eq_pd, Arc2D::eq_pd

function eq_d_pd

virtual Eigen::Vector3d eq_d_pd(
    double t
) =0

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

Parameters:

t The path parameter

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

Reimplemented by: Polinomial5::eq_d_pd, Polynomial5::eq_d_pd, Line::eq_d_pd, Sinusoid2D::eq_d_pd, Circle2D::eq_d_pd, Bernoulli::eq_d_pd, Arc2D::eq_d_pd

function eq_dd_pd

virtual Eigen::Vector3d eq_dd_pd(
    double t
) =0

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

Parameters:

t The path parameter

Return: An Eigen::Vector3d with the second derivative of the path equation with respect to the path paramter

Reimplemented by: Polinomial5::eq_dd_pd, Polynomial5::eq_dd_pd, Line::eq_dd_pd, Circle2D::eq_dd_pd, Bernoulli::eq_dd_pd, Sinusoid2D::eq_dd_pd, Arc2D::eq_dd_pd

function tangent

virtual double tangent(
    double t
)

Default method for computing the tangent to the path section.

Parameters:

t The path parameter

Return: A double with the angle of the tangent to the path

function curvature

virtual double curvature(
    double t
)

Default method for computing the curvature. The default implementation implements the general formula to compute the curvature based on the derivative equations of the path.

Parameters:

t The path parameter

Return: A double with the path curvature

Reimplemented by: Line::curvature, Circle2D::curvature, Bernoulli::curvature, Arc2D::curvature

function derivative_norm

virtual double derivative_norm(
    double t
)

Default method for computing the norm of the derivative.

Parameters:

t The path parameter

Return: A double with the norm of the derivative of the path position pd

function getClosestPointGamma

virtual double getClosestPointGamma(
    Eigen::Vector3d & coordinate
)

Default method for getting the gamma of the closed point to the path. By default this method uses gradient Descent algorithm to compute the closest point in the path with the initial guess of gamma=0.0.

Parameters:

coordinate A Eigen::Vector3d with the coordinates of the vehicle

Return: A double with the closest point in the path

Reimplemented by: Polinomial5::getClosestPointGamma, Polynomial5::getClosestPointGamma, Sinusoid2D::getClosestPointGamma, Line::getClosestPointGamma, Circle2D::getClosestPointGamma, Bernoulli::getClosestPointGamma, Arc2D::getClosestPointGamma

This is not the most efficient way to compute the closest point for several kinds of paths, but it is the most general, hence used as the default one

Method to return the closest point to the path By default just calls the Gradient Descent algorithm

function can_be_composed

bool can_be_composed()

Method to return whether a pathSection can be composed with other path sections or not.

Return: A boolean indicating wether the pathsection can be composed with other sections or not

function limitGamma

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.

Parameters:

t The path parameter also known as gamma

Return: A double with the path parameter limited between the valid bounds

function getMaxGammaValue

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++.

Return: A double with the maximum value that can be achieved with gamma

function getMinGammaValue

double getMinGammaValue()

Method used to get the minimum gamma allowed by the path section By default is the minimum valid number possible in c++.

Return: A double with the minimum value the can be achieved with gamma

function ~PathSection

virtual ~PathSection()

Virtual destructor for the abstract class.

Protected Functions Documentation

function PathSection

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.

Parameters:

can_be_composed A boolean that indicated that if this kind of path can be composed with other path sections or not

function setMaxGammaValue

bool setMaxGammaValue(
    double gamma_max
)

Method to update the max of the gamma parameter Validates if the value received is greater than gamma_min.

Parameters:

gamma_max The desired max value for gamma

Return: True if new value was accepted

function setMinGammaValue

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.

Parameters:

gamma_min The desired min value for gamma

Return: True if the new value was accepted

NOTE: for paths where can_be_composed == true, this function always returns false as it is required for those kinds of segments to start with 0 (but no limit is put on gamma max)

function GradientDescent

double GradientDescent(
    double gamma_o,
    Eigen::Vector3d & x_pos,
    double tolerance
)

Method that implements the gradient descent to minimize the error of ||pd(gamma) - p_vehicle||.

Parameters:

gamma_o The initial guess for the path paramter
x_pos The position of the vehicle
tolerance A constant tweaking parameter

Return: the estimated gamma value that minimizes the error

function getInitialGammaEstimate

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.

Parameters:

x_pos The position of the vehicle
num_partitions The number of divisions to make on the path
min_val The minimum boundary to search in gamma
max_val The maximum boundary to search in gamma

Return: A double with a good gamma to use as an initialization for the estimation

Then grabs the gamma that minimizes the most from all sections

function bisection

double bisection(
    Eigen::Vector3d & x_pos,
    double a,
    double b
)

Method to implement bisection method

Parameters:

x_pos The position of the vehicle
a The left bound for the gamma value
b The right bound for the gamma value

Return: The most likely value of gamma

Updated on 2024-03-07 at 10:30:47 +0000

Last update: March 7, 2024