#include <linear_quadratic_regulator.h>

Description

template<int STATES, int INPUTS>
class LinearQuadraticRegulator< STATES, INPUTS >

Class implements an LQR controller. This finds the optimal gain matrix K where:

u = K(r - x)

K is optimized to minimize a cost function:

∞

J = ∑ xₖᵀQxₖ + uₖᵀRuₖ k=0

Where Q and R are the state and control cost matrices.

Template Parameters

STATES	The number of states in the system.
INPUTS	The number of inputs to the system.

Inheritance diagram for LinearQuadraticRegulator< STATES, INPUTS >:

[legend]

Public Types
using	MatrixA = EMat<STATES, STATES>
using	MatrixB = EMat<STATES, INPUTS>
using	VectorX = EVec<STATES>
using	VectorU = EVec<INPUTS>

Public Member Functions
template<int OUTPUTS>
	LinearQuadraticRegulator (LinearSystem< STATES, INPUTS, OUTPUTS > &plant, const VectorX &Qtolerances, const VectorU &Rtolerances, const units::Time &dt)
	LinearQuadraticRegulator (const MatrixA &A, const MatrixB &B, const VectorX &Qtolerances, const VectorU &Rtolerances, const units::Time &dt)
	LinearQuadraticRegulator (const MatrixA &A, const MatrixB &B, const EMat< STATES, STATES > &Q, const EMat< INPUTS, INPUTS > &R, const units::Time &dt)
void	reset () override
	Resets the internal state of the LQR.
VectorU	update (const VectorX &x, const VectorX &r, const units::Time &dt=10_ms) override
template<int OUTPUTS>
void	latency_compensate (LinearSystem< STATES, INPUTS, OUTPUTS > &plant, const units::Time &dt, const units::Time &input_delay)
Public Member Functions inherited from Feedback< EVec< STATES >, EVec< INPUTS > >
virtual EVec< INPUTS >	update (const EVec< STATES > &state, const EVec< STATES > &reference, const units::Time &dt)=0
	Updates the control loop output.
EVec< INPUTS >	get_output ()
	Gets the last saved output value.
EVec< INPUTS >	get_last_error ()
	Gets the last saved error.
EVec< STATES >	get_reference ()
	Gets the currently stored reference state.
EVec< STATES >	get_state ()
	Gets the currently stored state.

Additional Inherited Members
Public Attributes inherited from Feedback< EVec< STATES >, EVec< INPUTS > >
EVec< INPUTS >	output_min_
EVec< INPUTS >	output_max_
Protected Attributes inherited from Feedback< EVec< STATES >, EVec< INPUTS > >
EVec< STATES >	reference_
EVec< STATES >	state_
EVec< STATES >	last_error_
EVec< INPUTS >	output_

Constructor & Destructor Documentation

◆ LinearQuadraticRegulator() [1/3]

template<int STATES, int INPUTS>

template<int OUTPUTS>

LinearQuadraticRegulator< STATES, INPUTS >::LinearQuadraticRegulator	(	LinearSystem< STATES, INPUTS, OUTPUTS > &	plant,
		const VectorX &	Qtolerances,
		const VectorU &	Rtolerances,
		const units::Time &	dt )

inline

Constructs an LQR given a plant, a vector of tolerances for the states and inputs, and the timestep in seconds.

Template Parameters

OUTPUTS The number of outputs of the plant.

Parameters

plant	The linear system to control.
Qtolerances	A vector of tolerances for each state.
Rtolerances	A vector of tolerances for each input.

◆ LinearQuadraticRegulator() [2/3]

template<int STATES, int INPUTS>

LinearQuadraticRegulator< STATES, INPUTS >::LinearQuadraticRegulator	(	const MatrixA &	A,
		const MatrixB &	B,
		const VectorX &	Qtolerances,
		const VectorU &	Rtolerances,
		const units::Time &	dt )

inline

Constructs an LQR given state and input matrices, a vector of tolerances for the states and inputs, and the timestep in seconds.

Parameters

A	The state matrix of the linear system.
B	The input matrix of the linear system.
Qtolerances	A vector of tolerances for each state.
Rtolerances	A vector of tolerances for each input.

◆ LinearQuadraticRegulator() [3/3]

template<int STATES, int INPUTS>

LinearQuadraticRegulator< STATES, INPUTS >::LinearQuadraticRegulator	(	const MatrixA &	A,
		const MatrixB &	B,
		const EMat< STATES, STATES > &	Q,
		const EMat< INPUTS, INPUTS > &	R,
		const units::Time &	dt )

inline

Constructs an LQR given state and input matrices, the cost matrices of states and inputs, and the timestep in seconds.

Parameters

A	The state matrix of the linear system.
B	The input matrix of the linear system.
Q	The cost matrix of the states.
R	The cost matrix of the inputs.

Member Function Documentation

◆ latency_compensate()

template<int STATES, int INPUTS>

template<int OUTPUTS>

void LinearQuadraticRegulator< STATES, INPUTS >::latency_compensate	(	LinearSystem< STATES, INPUTS, OUTPUTS > &	plant,
		const units::Time &	dt,
		const units::Time &	input_delay )

inline

Recomputes K to work for a time delayed state.

Kdelay = K(A - BK)^(delay / dt)

Template Parameters

OUTPUTS The number of outputs of the plant

Parameters

plant	The linear system.
dt	The timestep in seconds.
input_delay	The time delay of the system.

◆ reset()

template<int STATES, int INPUTS>

void LinearQuadraticRegulator< STATES, INPUTS >::reset ( )

inlineoverridevirtual

Resets the internal state of the LQR.

Implements Feedback< EVec< STATES >, EVec< INPUTS > >.

◆ update()

template<int STATES, int INPUTS>

VectorU LinearQuadraticRegulator< STATES, INPUTS >::update	(	const VectorX &	x,
		const VectorX &	r,
		const units::Time &	dt = 10_ms )

inlineoverride

Computes the control input u as:

u = K(r - x)

Parameters

x	The current state.
r	The reference state.
dt	the timestep since the last time this method was called

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

core/math/controls/linear_quadratic_regulator.h

Description

Public Types

Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ LinearQuadraticRegulator() [1/3]

◆ LinearQuadraticRegulator() [2/3]

◆ LinearQuadraticRegulator() [3/3]

Member Function Documentation

◆ latency_compensate()

◆ reset()

◆ update()