dynamicgraph::tutorial::InvertedPendulum Class Reference

Inverted Pendulum on a cart. More...

#include <dynamic-graph/tutorial/inverted-pendulum.hh>

Inheritance diagram for dynamicgraph::tutorial::InvertedPendulum:

Collaboration diagram for dynamicgraph::tutorial::InvertedPendulum:

Public Member Functions
	InvertedPendulum (const std::string &inName)
	Constructor by name. More...
	~InvertedPendulum ()
virtual const std::string &	getClassName (void) const
	Each entity should provide the name of the class it belongs to. More...
virtual std::string	getDocString () const
	Header documentation of the python class. More...
void	incr (double inTimeStep)
	Integrate equation of motion over time step given as input. More...
Parameters
void	setCartMass (const double &inMass)
	Set the mass of the cart. More...
double	getCartMass () const
	Get the mass of the cart. More...
void	setPendulumMass (const double &inMass)
	Set the mass of the cart. More...
double	getPendulumMass () const
	Get the mass of the pendulum. More...
void	setPendulumLength (const double &inLength)
	Set the length of the cart. More...
double	getPendulumLength () const
	Get the length of the pendulum. More...

Static Public Attributes
static const std::string	CLASS_NAME

Detailed Description

Inverted Pendulum on a cart.

This class represents the classical inverted pendulum on a cart. The equation of motion is:

\begin{eqnarray*} \left ( M + m \right ) \ddot x - m l \ddot \theta \cos \theta + m l \dot \theta^2 \sin \theta &=& F\\ m l (-g \sin \theta - \ddot x \cos \theta + l \ddot \theta) &=& 0 \end{eqnarray*}

where

• the state is a vector of dimension 4 \((x,\theta,\dot{x},\dot{\theta})\) represented by signal stateSOUT,
• \(x\) is the position of the cart on an horizontal axis, \(\theta\) is the angle of the pendulum with respect to the vertical axis,
• the input is a vector of dimension 1 \((F)\) reprensented by signal forceSIN,
• m, M and l are respectively the mass of the pendulum, the mass of the cart and the length of the pendulum.

A more natural form of the above equation for roboticists is

\[ \textbf{M}(\textbf{q})\ddot{\textbf{q}} + \textbf{N}(\textbf{q},\dot{\textbf{q}})\dot{\textbf{q}} + \textbf{G}(\textbf{q}) = \textbf{F} \]

where

\begin{eqnarray*} \textbf{q} &=& (x, \theta) \\ \textbf{M}(\textbf{q}) &=& \left( \begin{array}{cc} M + m & -m\ l\ \cos\theta \\ -m\ l\ \cos\theta & m\ l^2 \end{array}\right) \\ \textbf{N}(\textbf{q},\dot{\textbf{q}}) &=& \left( \begin{array}{cc} 0 & m\ l\ \dot{\theta} \sin\theta \\ 0 & 0 \end{array}\right)\\ \textbf{G}(\textbf{q}) &=& \left( \begin{array}{c} 0 \\ -m\ l\ g\ \sin\theta \end{array}\right)\\ \textbf{F} &=& \left( \begin{array}{c} F \\ 0 \end{array}\right) \end{eqnarray*}

In order to make the system intrinsically stable, we add some viscosity by rewriting:

\begin{eqnarray*} \textbf{N}(\textbf{q},\dot{\textbf{q}}) &=& \left( \begin{array}{cc} \lambda & m\ l\ \dot{\theta} \sin\theta\\ 0 & \lambda \end{array}\right) \end{eqnarray*}

where \(\lambda\) is a positive coefficient.

Constructor & Destructor Documentation

InvertedPendulum()

dynamicgraph::tutorial::InvertedPendulum::InvertedPendulum

(

const std::string &

inName

)

Constructor by name.

~InvertedPendulum()

dynamicgraph::tutorial::InvertedPendulum::~InvertedPendulum

(

)

Member Function Documentation

getCartMass()

double dynamicgraph::tutorial::InvertedPendulum::getCartMass ( ) const

inline

Get the mass of the cart.

getClassName()

virtual const std::string& dynamicgraph::tutorial::InvertedPendulum::getClassName ( void  ) const

inlinevirtual

Each entity should provide the name of the class it belongs to.

getDocString()

virtual std::string dynamicgraph::tutorial::InvertedPendulum::getDocString ( ) const

inlinevirtual

Header documentation of the python class.

getPendulumLength()

double dynamicgraph::tutorial::InvertedPendulum::getPendulumLength ( ) const

inline

Get the length of the pendulum.

getPendulumMass()

double dynamicgraph::tutorial::InvertedPendulum::getPendulumMass ( ) const

inline

Get the mass of the pendulum.

incr()

void dynamicgraph::tutorial::InvertedPendulum::incr

(

double

inTimeStep

)

Integrate equation of motion over time step given as input.

setCartMass()

void dynamicgraph::tutorial::InvertedPendulum::setCartMass ( const double &  inMass )

inline

Set the mass of the cart.

setPendulumLength()

void dynamicgraph::tutorial::InvertedPendulum::setPendulumLength ( const double &  inLength )

inline

Set the length of the cart.

setPendulumMass()

void dynamicgraph::tutorial::InvertedPendulum::setPendulumMass ( const double &  inMass )

inline

Set the mass of the cart.

Member Data Documentation

CLASS_NAME

const std::string dynamicgraph::tutorial::InvertedPendulum::CLASS_NAME

static

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The documentation for this class was generated from the following file:

• include/dynamic-graph/tutorial/inverted-pendulum.hh