Inverted Pendulum on a cart. More...

#include <inverted-pendulum.hh>

Inheritance diagram for dynamicgraph::tutorial::InvertedPendulum:

Public Member Functions
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...

	InvertedPendulum (const std::string &inName)
	Constructor by name. More...

	~InvertedPendulum ()

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...

Public Member Functions inherited from dynamicgraph::Entity
virtual void	display (std::ostream &os) const

std::ostream &	displaySignalList (std::ostream &os) const

	Entity (const std::string &name)

const std::string &	getCommandList () const

LoggerVerbosity	getLoggerVerbosityLevel ()

LoggerVerbosity	getLoggerVerbosityLevel ()

const std::string &	getName () const

command::Command *	getNewStyleCommand (const std::string &cmdName)

CommandMap_t	getNewStyleCommandMap ()

SignalBase< int > &	getSignal (const std::string &signalName)

const SignalBase< int > &	getSignal (const std::string &signalName) const

SignalMap	getSignalMap () const

double	getStreamPrintPeriod ()

double	getStreamPrintPeriod ()

double	getTimeSample ()

double	getTimeSample ()

bool	hasSignal (const std::string &signame) const

Logger &	logger ()

Logger const &	logger () const

Logger &	logger ()

Logger const &	logger () const

void	sendMsg (const std::string &msg, MsgType t=MSG_TYPE_INFO, const std::string &lineId="")

void	sendMsg (const std::string &msg, MsgType t=MSG_TYPE_INFO, const std::string &lineId="")

void	setLoggerVerbosityLevel (LoggerVerbosity lv)

void	setLoggerVerbosityLevel (LoggerVerbosity lv)

bool	setStreamPrintPeriod (double t)

bool	setStreamPrintPeriod (double t)

bool	setTimeSample (double t)

bool	setTimeSample (double t)

virtual SignalBase< int > *	test ()

virtual void	test2 (SignalBase< int > *)

virtual std::ostream &	writeCompletionList (std::ostream &os) const

virtual std::ostream &	writeGraph (std::ostream &os) const

virtual	~Entity ()

Static Public Attributes
static const std::string	CLASS_NAME

Private Member Functions
::dynamicgraph::Vector	computeDynamics (const ::dynamicgraph::Vector &inState, const double &inControl, double inTimeStep)
	Compute the evolution of the state of the pendulum. More...

Private Attributes
double	cartMass_
	Mass of the cart. More...

SignalPtr< double, int >	forceSIN
	Input force acting on the inverted pendulum. More...

double	pendulumLength_
	Length of the pendulum. More...

double	pendulumMass_
	Mass of the pendulum. More...

Signal< ::dynamicgraph::Vector, int >	stateSOUT
	State of the inverted pendulum. More...

double	viscosity_
	Viscosity coefficient. More...

Additional Inherited Members
Public Types inherited from dynamicgraph::Entity
typedef std::map< const std::string, command::Command *>	CommandMap_t

typedef std::map< std::string, SignalBase< int > *>	SignalMap

Protected Member Functions inherited from dynamicgraph::Entity
void	addCommand (const std::string &name, command::Command *command)

void	entityDeregistration ()

void	entityRegistration ()

void	signalDeregistration (const std::string &name)

void	signalRegistration (const SignalArray< int > &signals)

Protected Attributes inherited from dynamicgraph::Entity
CommandMap_t	commandMap

Logger	logger_

std::string	name

SignalMap	signalMap

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,
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 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.

Definition at line 72 of file inverted-pendulum.hh.

Constructor & Destructor Documentation

◆ InvertedPendulum()

InvertedPendulum::InvertedPendulum ( const std::string & inName )

Constructor by name.

Definition at line 29 of file inverted-pendulum.cpp.

◆ ~InvertedPendulum()

InvertedPendulum::~InvertedPendulum ( )

Definition at line 115 of file inverted-pendulum.cpp.

Member Function Documentation

◆ computeDynamics()

Vector InvertedPendulum::computeDynamics	(	const ::dynamicgraph::Vector &	inState,
		const double &	inControl,
		double	inTimeStep
	)

private

Compute the evolution of the state of the pendulum.

Definition at line 117 of file inverted-pendulum.cpp.

◆ getCartMass()

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

inline

Get the mass of the cart.

Definition at line 104 of file inverted-pendulum.hh.

◆ getClassName()

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

inlinevirtual

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

Reimplemented from dynamicgraph::Entity.

Definition at line 82 of file inverted-pendulum.hh.

◆ getDocString()

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

inlinevirtual

Header documentation of the python class.

Reimplemented from dynamicgraph::Entity.

Definition at line 85 of file inverted-pendulum.hh.

◆ getPendulumLength()

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

inline

Get the length of the pendulum.

Definition at line 124 of file inverted-pendulum.hh.

◆ getPendulumMass()

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

inline

Get the mass of the pendulum.

Definition at line 114 of file inverted-pendulum.hh.

◆ incr()

void InvertedPendulum::incr ( double inTimeStep )

Integrate equation of motion over time step given as input.

Definition at line 160 of file inverted-pendulum.cpp.

◆ setCartMass()

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

inline

Set the mass of the cart.

Definition at line 99 of file inverted-pendulum.hh.

◆ setPendulumLength()

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

inline

Set the length of the cart.

Definition at line 119 of file inverted-pendulum.hh.

◆ setPendulumMass()

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

inline

Set the mass of the cart.

Definition at line 109 of file inverted-pendulum.hh.

Member Data Documentation

◆ cartMass_

double dynamicgraph::tutorial::InvertedPendulum::cartMass_

private

Mass of the cart.

Definition at line 147 of file inverted-pendulum.hh.

◆ CLASS_NAME

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

static

Definition at line 134 of file inverted-pendulum.hh.

◆ forceSIN

SignalPtr<double, int> dynamicgraph::tutorial::InvertedPendulum::forceSIN

private

Input force acting on the inverted pendulum.

Definition at line 140 of file inverted-pendulum.hh.

◆ pendulumLength_

double dynamicgraph::tutorial::InvertedPendulum::pendulumLength_

private

Length of the pendulum.

Definition at line 151 of file inverted-pendulum.hh.

◆ pendulumMass_

double dynamicgraph::tutorial::InvertedPendulum::pendulumMass_

private

Mass of the pendulum.

Definition at line 149 of file inverted-pendulum.hh.

◆ stateSOUT

Signal< ::dynamicgraph::Vector, int> dynamicgraph::tutorial::InvertedPendulum::stateSOUT

private

State of the inverted pendulum.

Definition at line 144 of file inverted-pendulum.hh.

◆ viscosity_

double dynamicgraph::tutorial::InvertedPendulum::viscosity_

private

Viscosity coefficient.

Definition at line 153 of file inverted-pendulum.hh.

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

Public Member Functions

Static Public Attributes

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ InvertedPendulum()

◆ ~InvertedPendulum()

Member Function Documentation

◆ computeDynamics()

◆ getCartMass()

◆ getClassName()

◆ getDocString()

◆ getPendulumLength()

◆ getPendulumMass()

◆ incr()

◆ setCartMass()

◆ setPendulumLength()

◆ setPendulumMass()

Member Data Documentation

◆ cartMass_

◆ CLASS_NAME

◆ forceSIN

◆ pendulumLength_

◆ pendulumMass_

◆ stateSOUT

◆ viscosity_