ergodic_exploration::RungeKutta Class Reference

4th order Runge-Kutta integration More...

#include <integrator.hpp>

Public Member Functions
	RungeKutta (double dt)
	Constructor. More...
template<class ModelT >
mat	solve (const CoStateFunc &func, const ModelT &model, const vec &rhoT, const mat &xt, const mat &ut, const mat &edx, const mat &bdx, double horizon) const
	Solve the co-state variable backwards in time. More...
template<class ModelT >
mat	solve (const ModelT &model, const vec &x0, const mat &ut, double horizon) const
	Simulate the dynamics forward in time. More...
vec	step (const CoStateFunc &func, const vec &rho, const vec &gdx, const vec &dbar, const mat &fdx) const
	Performs one step of RK4 backwards in time. More...
template<class ModelT >
vec	step (const ModelT &model, const vec &x, const vec &u) const
	Performs one step of RK4 forward in time. More...

Private Attributes
double	dt_

Detailed Description

4th order Runge-Kutta integration

Definition at line 63 of file integrator.hpp.

Constructor & Destructor Documentation

RungeKutta()

ergodic_exploration::RungeKutta::RungeKutta

(

double

dt

)

Constructor.

Parameters

dt	- time step

Definition at line 131 of file integrator.hpp.

Member Function Documentation

solve() [1/2]

template<class ModelT >

mat ergodic_exploration::RungeKutta::solve	(	const CoStateFunc &	func,
		const ModelT &	model,
		const vec &	rhoT,
		const mat &	xt,
		const mat &	ut,
		const mat &	edx,
		const mat &	bdx,
		double	horizon
	)		const

Solve the co-state variable backwards in time.

Parameters

func	- time derivatve of co-state variable
model	- dynamic model
rhoT	- co-state variable terminal condition (zero vector)
xt	- forward porpagated dynamic model trajectory
ut	- control signal
edx	- gradient of the ergodic metric for each state in xt
bdx	- derivatve of barrier function for each state in xt
horizon	- length of trajectory in time

Returns

co-state variable solution

co-state is sorted from [t0 tf] no need to index backwards and the boundary condition is not added to the trajectory

Definition at line 155 of file integrator.hpp.

solve() [2/2]

template<class ModelT >

mat ergodic_exploration::RungeKutta::solve	(	const ModelT &	model,
		const vec &	x0,
		const mat &	ut,
		double	horizon
	)		const

Simulate the dynamics forward in time.

Parameters

model	- dynamic model
x0	- initial state
ut	- control signal (each column is applied at a single time step)
horizon	- length of trajectory in time

Returns

trajectory

the boundary condition is not added to the trajectory

Definition at line 136 of file integrator.hpp.

step() [1/2]

vec ergodic_exploration::RungeKutta::step	(	const CoStateFunc &	func,
		const vec &	rho,
		const vec &	gdx,
		const vec &	dbar,
		const mat &	fdx
	)		const

Performs one step of RK4 backwards in time.

Parameters

func	- time derivatve of the co-state variable
rho	- co-state variable
gdx	- gradient of the ergodic metric
dbar	- derivatve of barrier function for a state
fdx	- jacobian of the model with respect to the control

Returns

co-state variable

The robot model is used to compose A = D1[f(x,u)]. The columns of xt, ut, and edx correspond to the state, control, or derivative at a given time.

Definition at line 186 of file integrator.hpp.

step() [2/2]

template<class ModelT >

vec ergodic_exploration::RungeKutta::step	(	const ModelT &	model,
		const vec &	x,
		const vec &	u
	)		const

Performs one step of RK4 forward in time.

Parameters

model	- dynamic model
x	- state
u	- control

Returns

new state

Definition at line 177 of file integrator.hpp.

Member Data Documentation

dt_

double ergodic_exploration::RungeKutta::dt_

private

Definition at line 128 of file integrator.hpp.

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

• integrator.hpp