Quadrotor dynamics with quaternion representation Based on D. Mellinger, N. Michael, and V. Kumar, "Trajectory generation and control for precise aggressive maneuvers with quadrotors", Proceedings of the 12th International Symposium on Experimental Robotics (ISER 2010), 2010. Cf. https://journals.sagepub.com/doi/abs/10.1177/0278364911434236. More...

#include <quadrotor_dynamics_solver.h>

Inheritance diagram for exotica::QuadrotorDynamicsSolver:

Collaboration diagram for exotica::QuadrotorDynamicsSolver:

Public Member Functions
	QuadrotorDynamicsSolver ()

void	AssignScene (ScenePtr scene_in) override

StateVector	f (const StateVector &x, const ControlVector &u) override
	Forward dynamics. This computes the differential dynamics. More...

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

Eigen::MatrixXd	fu (const StateVector &x, const ControlVector &u) override
	Derivative of the forward dynamics w.r.t. the control. More...

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 >	fxx (const StateVector &x, const ControlVector &u)

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

virtual Eigen::Tensor< T, 3 >	fxu (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< QuadrotorDynamicsSolverInitializer >
void	InstantiateInternal (const Initializer &init) override

Initializer	GetInitializerTemplate () override

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

virtual void	Instantiate (const QuadrotorDynamicsSolverInitializer &init)

const QuadrotorDynamicsSolverInitializer &	GetParameters () const

Private Attributes
Eigen::Matrix3d	J_
	Inertia matrix. More...

Eigen::Matrix3d	J_inv_
	Inverted inertia matrix. More...

double	mass_ = .5
	Mass. More...

double	g_ = 9.81
	Gravity (m/s^2) More...

double	L_ = 0.1750
	Distance between motors. More...

double	k_f_ = 1
	Thrust coefficient, 6.11*10^-8;. More...

double	k_m_ = 0.0245
	Moment coefficient. 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< QuadrotorDynamicsSolverInitializer >
QuadrotorDynamicsSolverInitializer	parameters_

Detailed Description

Quadrotor dynamics with quaternion representation Based on D. Mellinger, N. Michael, and V. Kumar, "Trajectory generation and control for precise aggressive maneuvers with quadrotors", Proceedings of the 12th International Symposium on Experimental Robotics (ISER 2010), 2010. Cf. https://journals.sagepub.com/doi/abs/10.1177/0278364911434236.

StateVector X ∈ R^12 = [x, y, z, r, p, y, xdot, ydot, zdot, omega1, omega2, omega3]

Constructor & Destructor Documentation

◆ QuadrotorDynamicsSolver()

exotica::QuadrotorDynamicsSolver::QuadrotorDynamicsSolver ( )

Member Function Documentation

◆ AssignScene()

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

override

◆ f()

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

overridevirtual

Forward dynamics. This computes the differential dynamics.

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

◆ fu()

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

overridevirtual

Derivative of the forward dynamics w.r.t. the control.

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

◆ fx()

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

overridevirtual

Derivative of the forward dynamics w.r.t. the state.

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

Member Data Documentation

◆ g_

double exotica::QuadrotorDynamicsSolver::g_ = 9.81

private

Gravity (m/s^2)

◆ J_

Eigen::Matrix3d exotica::QuadrotorDynamicsSolver::J_

private

Inertia matrix.

◆ J_inv_

Eigen::Matrix3d exotica::QuadrotorDynamicsSolver::J_inv_

private

Inverted inertia matrix.

◆ k_f_

double exotica::QuadrotorDynamicsSolver::k_f_ = 1

private

Thrust coefficient, 6.11*10^-8;.

◆ k_m_

double exotica::QuadrotorDynamicsSolver::k_m_ = 0.0245

private

Moment coefficient.

◆ L_

double exotica::QuadrotorDynamicsSolver::L_ = 0.1750

private

Distance between motors.

◆ mass_

double exotica::QuadrotorDynamicsSolver::mass_ = .5

private

Mass.

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

/tmp/exotica/exotations/dynamics_solvers/exotica_quadrotor_dynamics_solver/include/exotica_quadrotor_dynamics_solver/quadrotor_dynamics_solver.h

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ QuadrotorDynamicsSolver()

Member Function Documentation

◆ AssignScene()

◆ f()

◆ fu()

◆ fx()

Member Data Documentation

◆ g_

◆ J_

◆ J_inv_

◆ k_f_

◆ k_m_

◆ L_

◆ mass_