#include <cartpole_dynamics_solver.h>

Inheritance diagram for exotica::CartpoleDynamicsSolver:

Collaboration diagram for exotica::CartpoleDynamicsSolver:

Public Member Functions
	CartpoleDynamicsSolver ()

void	AssignScene (ScenePtr scene_in) override

StateVector	f (const StateVector &x, const ControlVector &u) override
	Computes the forward dynamics of the system. More...

Eigen::MatrixXd	fx (const StateVector &x, const ControlVector &u) override
	Computes the dynamics derivative w.r.t .the state x. More...

Eigen::MatrixXd	fu (const StateVector &x, const ControlVector &u) override
	Computes the dynamics derivative w.r.t .the control input u. More...

Eigen::Tensor< double, 3 >	fxx (const StateVector &x, const ControlVector &u) override

Eigen::Tensor< double, 3 >	fxu (const StateVector &x, const ControlVector &u) override

Public Member Functions inherited from exotica::AbstractDynamicsSolver< T, NX, NU >
	AbstractDynamicsSolver ()

virtual	~AbstractDynamicsSolver ()

virtual void	InstantiateBase (const Initializer &init)
	Instantiates the base properties of the DynamicsSolver. More...

virtual void	AssignScene (std::shared_ptr< Scene > scene_in)
	Passes the Scene of the PlanningProblem to the DynamicsSolver. More...

virtual void	SetDt (double dt_in)
	Sets the timestep dt to be used for integration. More...

virtual StateVector	F (const StateVector &x, const ControlVector &u)
	State transition function. This internally computes the differential dynamics and applies the chosen integration scheme. More...

virtual void	ComputeDerivatives (const StateVector &x, const ControlVector &u)
	Computes derivatives fx, fu, Fx, Fu [single call for efficiency, derivatives can be retrieved with get_fx, get_fu, get_Fx, get_Fu]. More...

const StateDerivative &	get_Fx () const
	Returns derivative Fx computed by ComputeDerivatives. More...

const ControlDerivative &	get_Fu () const
	Returns derivative Fu computed by ComputeDerivatives. More...

const StateDerivative &	get_fx () const
	Returns derivative fx computed by ComputeDerivatives. More...

const ControlDerivative &	get_fu () const
	Returns derivative fu computed by ComputeDerivatives. More...

StateDerivative	fx_fd (const StateVector &x, const ControlVector &u)
	Derivative of the forward dynamics w.r.t. the state [finite differencing]. More...

ControlDerivative	fu_fd (const StateVector &x, const ControlVector &u)
	Derivative of the forward dynamics w.r.t. the control [finite differencing]. More...

const bool &	get_has_second_order_derivatives () const
	Returns whether second-order derivatives are available. More...

virtual Eigen::Tensor< T, 3 >	fuu (const StateVector &x, const ControlVector &u)

StateVector	Simulate (const StateVector &x, const ControlVector &u, T t)
	Simulates the dynamic system from starting state x using control u for t seconds. More...

virtual StateVector	StateDelta (const StateVector &x_1, const StateVector &x_2)
	Return the difference of two state vectors. Used when e.g. angle differences need to be wrapped from [-pi; pi] Returns x_1-x_2. More...

void	StateDelta (const StateVector &x_1, const StateVector &x_2, Eigen::VectorXdRef xout)

virtual Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	dStateDelta (const StateVector &x_1, const StateVector &x_2, const ArgumentPosition first_or_second)
	Return the difference of the StateDelta operation between two state vectors. The ArgumentPosition argument can be used to select whether to take derivative w.r.t. x_1 or x_2. More...

virtual Hessian	ddStateDelta (const StateVector &x_1, const StateVector &x_2, const ArgumentPosition first_or_second)

virtual Eigen::Matrix< T, Eigen::Dynamic, 1 >	GetPosition (Eigen::VectorXdRefConst x_in)
	Returns the position-part of the state vector to update the scene. For types including SE(3) and rotation, convert to the appropriate representation here by overriding this method. More...

int	get_num_controls () const
	Returns number of controls. More...

int	get_num_positions () const
	Returns number of positions. More...

int	get_num_velocities () const
	Returns number of velocities. More...

int	get_num_state () const
	Returns size of state space (nx) More...

int	get_num_state_derivative () const
	Returns size of derivative vector of state space (ndx) More...

T	get_dt () const
	Returns integration timestep dt. More...

Integrator	get_integrator () const
	Returns used integration scheme. More...

void	set_integrator (Integrator integrator_in)
	Sets integrator type. More...

void	SetIntegrator (const std::string &integrator_in)
	Sets integrator type based on request string. More...

const Eigen::MatrixXd &	get_control_limits ()
	Returns the control limits vector. More...

void	set_control_limits (Eigen::VectorXdRefConst control_limits_low, Eigen::VectorXdRefConst control_limits_high)
	Sets the control limits. More...

const bool &	get_has_state_limits () const
	Returns whether state limits are available. More...

void	ClampToStateLimits (Eigen::Ref< Eigen::VectorXd > state_in)
	Clamps the passed in state to the state limits. More...

virtual ControlVector	InverseDynamics (const StateVector &state)
	Returns a control vector corresponding to the state vector assuming zero acceleration. More...

virtual void	Integrate (const StateVector &x, const StateVector &dx, const double dt, StateVector &xout)
	Integrates without performing dynamics. More...

Public Member Functions inherited from exotica::Object
	Object ()

virtual	~Object ()

virtual std::string	type () const
	Type Information wrapper: must be virtual so that it is polymorphic... More...

std::string	GetObjectName ()

void	InstantiateObject (const Initializer &init)

virtual std::string	Print (const std::string &prepend) const

Public Member Functions inherited from exotica::InstantiableBase
	InstantiableBase ()=default

virtual	~InstantiableBase ()=default

virtual std::vector< Initializer >	GetAllTemplates () const =0

Public Member Functions inherited from exotica::Instantiable< CartpoleDynamicsSolverInitializer >
void	InstantiateInternal (const Initializer &init) override

Initializer	GetInitializerTemplate () override

std::vector< Initializer >	GetAllTemplates () const override

virtual void	Instantiate (const CartpoleDynamicsSolverInitializer &init)

const CartpoleDynamicsSolverInitializer &	GetParameters () const

Private Attributes
double	g_ = 9.81

double	m_c_ = 1
	!< Gravity (m/s^2) More...

double	m_p_ = 1
	!< Cart mass (kg) More...

double	l_ = 1
	!< Pole mass (kg) More...

Additional Inherited Members
Public Types inherited from exotica::AbstractDynamicsSolver< T, NX, NU >
typedef Eigen::Matrix< T, NX, 1 >	StateVector
	Convenience definition for a StateVector containing both position and velocity (dimension NX x 1) More...

typedef Eigen::Matrix< T, NU, 1 >	ControlVector
	Convenience definition for a ControlVector (dimension NU x 1) More...

typedef Eigen::Matrix< T, NX, NX >	StateDerivative
	Convenience definition for a StateDerivative. More...

typedef Eigen::Matrix< T, NX, NU >	ControlDerivative
	Convenience definition for a ControlDerivative. More...

Public Attributes inherited from exotica::Object
std::string	ns_

std::string	object_name_

bool	debug_

Protected Member Functions inherited from exotica::AbstractDynamicsSolver< T, NX, NU >
virtual StateVector	SimulateOneStep (const StateVector &x, const ControlVector &u)
	Integrates the dynamic system from state x with controls u applied for one timestep dt using the selected integrator. More...

void	InitializeSecondOrderDerivatives ()

Protected Attributes inherited from exotica::AbstractDynamicsSolver< T, NX, NU >
int	num_controls_ = -1
	Number of controls in the dynamic system. More...

int	num_positions_ = -1
	Number of positions in the dynamic system. More...

int	num_velocities_ = -1
	Number of velocities in the dynamic system. More...

int	num_state_ = -1
	Size of state space (num_positions + num_velocities) More...

int	num_state_derivative_ = -1
	Size of the tangent vector to the state space (2 * num_velocities) More...

bool	has_second_order_derivatives_ = false
	Whether this solver provides second order derivatives. If false (default), assumed to be all zeros. More...

bool	second_order_derivatives_initialized_ = false
	Whether fxx, fxu and fuu have been initialized to 0. More...

bool	has_state_limits_ = false
	Whether the solver specifies state limits. More...

Eigen::VectorXd	state_limits_lower_
	Lower state limits (configuration and velocity) More...

Eigen::VectorXd	state_limits_upper_
	Upper state limits (configuration and velocity) More...

T	dt_ = 0.01
	Internal timestep used for integration. Defaults to 10ms. More...

Integrator	integrator_ = Integrator::RK1
	Chosen integrator. Defaults to Euler (RK1). More...

Eigen::MatrixXd	control_limits_
	ControlLimits. Default is empty vector. More...

Eigen::Tensor< T, 3 >	fxx_default_

Eigen::Tensor< T, 3 >	fuu_default_

Eigen::Tensor< T, 3 >	fxu_default_

Eigen::MatrixXd	fx_
	Internal storage of differential dynamics partial derivative fx computed by ComputeDerivatives. More...

Eigen::MatrixXd	fu_
	Internal storage of differential dynamics partial derivative fu computed by ComputeDerivatives. More...

Eigen::MatrixXd	Fx_
	Internal storage of state transition partial derivative Fx computed by ComputeDerivatives. More...

Eigen::MatrixXd	Fu_
	Internal storage of state transition partial derivative Fu computed by ComputeDerivatives. More...

Protected Attributes inherited from exotica::Instantiable< CartpoleDynamicsSolverInitializer >
CartpoleDynamicsSolverInitializer	parameters_

Detailed Description

StateVector X ∈ R^4 = [x, theta, x_dot, theta_dot] Refer to http://underactuated.mit.edu/acrobot.html#cart_pole for a derivation of the cartpole dynamics.

Constructor & Destructor Documentation

◆ CartpoleDynamicsSolver()

exotica::CartpoleDynamicsSolver::CartpoleDynamicsSolver ( )

Member Function Documentation

◆ AssignScene()

void exotica::CartpoleDynamicsSolver::AssignScene ( ScenePtr scene_in )

override

◆ f()

StateVector exotica::CartpoleDynamicsSolver::f	(	const StateVector &	x,
		const ControlVector &	u
	)

overridevirtual

Computes the forward dynamics of the system.

Parameters

x	The state vector.
u	The control input.

Returns: The dynamics transition function.

Implements exotica::AbstractDynamicsSolver< T, NX, NU >.

◆ fu()

Eigen::MatrixXd exotica::CartpoleDynamicsSolver::fu	(	const StateVector &	x,
		const ControlVector &	u
	)

overridevirtual

Computes the dynamics derivative w.r.t .the control input u.

Parameters

x	The state vector.
u	The control input

Returns: The derivative of the dynamics function w.r.t. u evaluated at (x, u).

Reimplemented from exotica::AbstractDynamicsSolver< T, NX, NU >.

◆ fx()

Eigen::MatrixXd exotica::CartpoleDynamicsSolver::fx	(	const StateVector &	x,
		const ControlVector &	u
	)

overridevirtual

Computes the dynamics derivative w.r.t .the state x.

Parameters

x	The state vector.
u	The control input.

Returns: The derivative of the dynamics function w.r.t. x evaluated at (x, u).

Reimplemented from exotica::AbstractDynamicsSolver< T, NX, NU >.

◆ fxu()

Eigen::Tensor<double, 3> exotica::CartpoleDynamicsSolver::fxu	(	const StateVector &	x,
		const ControlVector &	u
	)

overridevirtual

Reimplemented from exotica::AbstractDynamicsSolver< T, NX, NU >.

◆ fxx()

Eigen::Tensor<double, 3> exotica::CartpoleDynamicsSolver::fxx	(	const StateVector &	x,
		const ControlVector &	u
	)

overridevirtual

Reimplemented from exotica::AbstractDynamicsSolver< T, NX, NU >.

Member Data Documentation

◆ g_

double exotica::CartpoleDynamicsSolver::g_ = 9.81

private

◆ l_

double exotica::CartpoleDynamicsSolver::l_ = 1

private

!< Pole mass (kg)

◆ m_c_

double exotica::CartpoleDynamicsSolver::m_c_ = 1

private

!< Gravity (m/s^2)

◆ m_p_

double exotica::CartpoleDynamicsSolver::m_p_ = 1

private

!< Cart mass (kg)

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

/tmp/exotica/exotations/dynamics_solvers/exotica_cartpole_dynamics_solver/include/exotica_cartpole_dynamics_solver/cartpole_dynamics_solver.h

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ CartpoleDynamicsSolver()

Member Function Documentation

◆ AssignScene()

◆ f()

◆ fu()

◆ fx()

◆ fxu()

◆ fxx()

Member Data Documentation

◆ g_

◆ l_

◆ m_c_

◆ m_p_