Proportional-Integral-Derivative controller for Lie groups. More...

#include <pid.hpp>

Public Types
using	TrajectoryReturnT = std::tuple< G, Tangent< G >, Tangent< G > >
	Desired trajectory consists of position, velocity, and acceleration. More...

Public Member Functions
	PID (const PIDParams &prm=PIDParams{}) noexcept
	Create a PID controller. More...

	PID (const PID &)=default
	Default copy constructor.

	PID (PID &&)=default
	Default move constructor.

PID &	operator= (const PID &)=default
	Default copy assignment.

PID &	operator= (PID &&)=default
	Default move assignment.

	~PID ()=default
	Default destructor.

Tangent< G >	operator() (const T &t, const G &x, const Tangent< G > &v)
	Calculate control input. More...

void	set_kp (double kp)
	Set all proportional gains to kp. More...

template<typename Derived >
void	set_kp (const Eigen::MatrixBase< Derived > &kp)
	Set proportional gains. More...

void	set_kd (double kd)
	Set all derivative gains to kd. More...

template<typename Derived >
void	set_kd (const Eigen::MatrixBase< Derived > &kd)
	Set derivative gains. More...

void	set_ki (double ki)
	Set all integral gains to ki. More...

template<typename Derived >
void	set_ki (const Eigen::MatrixBase< Derived > &ki)
	Set derivative gains. More...

void	reset_integral ()
	Reset integral state to zero. More...

template<int K>
void	set_xdes (T t0, const smooth::Spline< K, G > &c)
	Set desired trajectory as a smooth::Spline. More...

template<int K>
void	set_xdes (T t0, smooth::Spline< K, G > &&c)
	Set desired trajectory as a smooth::Spline (rvalue version) More...

void	set_xdes (const std::function< TrajectoryReturnT(T)> &f)
	Set desired trajectory. More...

void	set_xdes (std::function< TrajectoryReturnT(T)> &&f)
	Set desired trajectory (rvalue version). More...

Detailed Description

template<Time T, LieGroup G>
requires (Dof<G> > 0)
class smooth::feedback::PID< T, G >

Proportional-Integral-Derivative controller for Lie groups.

Template Parameters

T	Time type
G	LieGroup state space type

This controller is designed for a system

\[ \begin{aligned} \mathrm{d}^r \mathbf{x}_t & = \mathbf{v}, \quad \mathbf{x} \in \mathbb{G}, \mathbf{v} \in \mathbb{R}^{\dim \mathbb{G}} \\ \frac{\mathrm{d}}{\mathrm{d}t} {\mathbf{v}} & = \mathbf{u}, \quad \mathbf{u} \in \mathbb{R}^{\dim \mathbb{G}} \end{aligned} \]

i.e. the input is the body acceleration.

Definition at line 39 of file pid.hpp.

Member Typedef Documentation

◆ TrajectoryReturnT

template<Time T, LieGroup G>

using smooth::feedback::PID< T, G >::TrajectoryReturnT = std::tuple<G, Tangent<G>, Tangent<G> >

Desired trajectory consists of position, velocity, and acceleration.

Definition at line 43 of file pid.hpp.

Constructor & Destructor Documentation

◆ PID()

template<Time T, LieGroup G>

smooth::feedback::PID< T, G >::PID ( const PIDParams & prm = PIDParams{} )

inlinenoexcept

Create a PID controller.

Parameters

prm	parameters

At construction the proportional and derivative gains are set to 1, and the integral gains are set to 0.

Definition at line 53 of file pid.hpp.

Member Function Documentation

◆ operator()()

template<Time T, LieGroup G>

Tangent< G > smooth::feedback::PID< T, G >::operator()	(	const T &	t,
		const G &	x,
		const Tangent< G > &	v
	)

inline

Calculate control input.

Parameters

t	current time
x	current state
v	current body velocity

Returns: input proportional to desired body acceleration

Definition at line 74 of file pid.hpp.

◆ reset_integral()

template<Time T, LieGroup G>

void smooth::feedback::PID< T, G >::reset_integral ( )

inline

Reset integral state to zero.

Definition at line 134 of file pid.hpp.

◆ set_kd() [1/2]

template<Time T, LieGroup G>

template<typename Derived >

void smooth::feedback::PID< T, G >::set_kd ( const Eigen::MatrixBase< Derived > & kd )

inline

Set derivative gains.

Definition at line 112 of file pid.hpp.

◆ set_kd() [2/2]

template<Time T, LieGroup G>

void smooth::feedback::PID< T, G >::set_kd ( double kd )

inline

Set all derivative gains to kd.

Definition at line 106 of file pid.hpp.

◆ set_ki() [1/2]

template<Time T, LieGroup G>

template<typename Derived >

void smooth::feedback::PID< T, G >::set_ki ( const Eigen::MatrixBase< Derived > & ki )

inline

Set derivative gains.

Definition at line 126 of file pid.hpp.

◆ set_ki() [2/2]

template<Time T, LieGroup G>

void smooth::feedback::PID< T, G >::set_ki ( double ki )

inline

Set all integral gains to ki.

Definition at line 120 of file pid.hpp.

◆ set_kp() [1/2]

template<Time T, LieGroup G>

template<typename Derived >

void smooth::feedback::PID< T, G >::set_kp ( const Eigen::MatrixBase< Derived > & kp )

inline

Set proportional gains.

Definition at line 98 of file pid.hpp.

◆ set_kp() [2/2]

template<Time T, LieGroup G>

void smooth::feedback::PID< T, G >::set_kp ( double kp )

inline

Set all proportional gains to kp.

Definition at line 92 of file pid.hpp.

◆ set_xdes() [1/4]

template<Time T, LieGroup G>

void smooth::feedback::PID< T, G >::set_xdes ( const std::function< TrajectoryReturnT(T)> & f )

inline

Set desired trajectory.

The trajectory is a function from time to (position, velocity, acceleration). To track a time-dependent trajectory consider using smooth::Spline and set_xdes(T, const smooth::Spline<K, G> &) to set the desired trajectory.

For a constant reference target the velocity and acceleration should be constantly zero.

Note: For best performance the trajectory should be dynamically consistent, i.e.
\[ \mathrm{d}^r \mathbf{x}_t = \mathbf{v}, \\ \frac{\mathrm{d}}{\mathrm{d}t} \mathbf{v} = \mathbf{a}, \]
where (x, v, a) is the (position, velocity, acceleration)-tuple returned by the trajectory.

Definition at line 177 of file pid.hpp.

◆ set_xdes() [2/4]

template<Time T, LieGroup G>

void smooth::feedback::PID< T, G >::set_xdes ( std::function< TrajectoryReturnT(T)> && f )

inline

Set desired trajectory (rvalue version).

Definition at line 186 of file pid.hpp.

◆ set_xdes() [3/4]

template<Time T, LieGroup G>

template<int K>

void smooth::feedback::PID< T, G >::set_xdes	(	T	t0,
		const smooth::Spline< K, G > &	c
	)

inline

Set desired trajectory as a smooth::Spline.

Parameters

c	desired trajectory as a smooth::Spline
t0	curve initial time s.t. the desired position at time t is equal to c(t - t0)

Definition at line 143 of file pid.hpp.

◆ set_xdes() [4/4]

template<Time T, LieGroup G>

template<int K>

void smooth::feedback::PID< T, G >::set_xdes	(	T	t0,
		smooth::Spline< K, G > &&	c
	)

inline

Set desired trajectory as a smooth::Spline (rvalue version)

Definition at line 152 of file pid.hpp.

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

include/smooth/feedback/pid.hpp

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ TrajectoryReturnT

Constructor & Destructor Documentation

◆ PID()

Member Function Documentation

◆ operator()()

◆ reset_integral()

◆ set_kd() [1/2]

◆ set_kd() [2/2]

◆ set_ki() [1/2]

◆ set_ki() [2/2]

◆ set_kp() [1/2]

◆ set_kp() [2/2]

◆ set_xdes() [1/4]

◆ set_xdes() [2/4]

◆ set_xdes() [3/4]

◆ set_xdes() [4/4]