cubic polynomial trajectory

Collaboration diagram for cubic polynomial trajectory:

Data Structures
struct	a_trajpoly3
	instance structure for cubic polynomial trajectory More...

Typedefs
typedef struct a_trajpoly3	a_trajpoly3

Functions
void	a_trajpoly3_gen (a_trajpoly3 *ctx, a_real ts, a_real p0, a_real p1, a_real v0, a_real v1)
	generate for cubic polynomial trajectory
void	a_trajpoly3_c0 (a_trajpoly3 const *ctx, a_real c[4])
	compute coefficients of position for cubic polynomial trajectory
void	a_trajpoly3_c1 (a_trajpoly3 const *ctx, a_real c[3])
	compute coefficients of velocity for cubic polynomial trajectory
void	a_trajpoly3_c2 (a_trajpoly3 const *ctx, a_real c[2])
	compute coefficients of acceleration for cubic polynomial trajectory
a_real	a_trajpoly3_pos (a_trajpoly3 const *ctx, a_real x)
	compute position for cubic polynomial trajectory
a_real	a_trajpoly3_vel (a_trajpoly3 const *ctx, a_real x)
	compute velocity for cubic polynomial trajectory
a_real	a_trajpoly3_acc (a_trajpoly3 const *ctx, a_real x)
	compute acceleration for cubic polynomial trajectory

Detailed Description

Function Documentation

a_trajpoly3_acc()

a_real a_trajpoly3_acc	(	a_trajpoly3 const *	ctx,
		a_real	x )

compute acceleration for cubic polynomial trajectory

$$\begin{array}{r}\begin{array}{l}\ddot{p}(t)=2c_2+6c_3(t-t_0)\end{array}\end{array}$$

Parameters

[in]	ctx	points to an instance of cubic polynomial trajectory
[in]	x	difference between current time and initial time

Returns

acceleration output

a_trajpoly3_c0()

void a_trajpoly3_c0	(	a_trajpoly3 const *	ctx,
		a_real	c[4] )

compute coefficients of position for cubic polynomial trajectory

Parameters

[in]	ctx	points to an instance of cubic polynomial trajectory
[out]	c	coefficients of position

a_trajpoly3_c1()

void a_trajpoly3_c1	(	a_trajpoly3 const *	ctx,
		a_real	c[3] )

compute coefficients of velocity for cubic polynomial trajectory

Parameters

[in]	ctx	points to an instance of cubic polynomial trajectory
[out]	c	coefficients of velocity

a_trajpoly3_c2()

void a_trajpoly3_c2	(	a_trajpoly3 const *	ctx,
		a_real	c[2] )

compute coefficients of acceleration for cubic polynomial trajectory

Parameters

[in]	ctx	points to an instance of cubic polynomial trajectory
[out]	c	coefficients of acceleration

a_trajpoly3_gen()

void a_trajpoly3_gen	(	a_trajpoly3 *	ctx,
		a_real	ts,
		a_real	p0,
		a_real	p1,
		a_real	v0,
		a_real	v1 )

generate for cubic polynomial trajectory

$$\begin{array}{r}\{\begin{array}{l}t=t_1-t_0\\ p=p_1-p_0\\ c_0=p_0\\ c_1=v_0\\ c_2=\frac{(-2v_0-v_1)t+3p}{t^2}\\ c_3=\frac{(v_0+v_1)t-2p}{t^3}\end{array}\end{array}$$

Parameters

[in,out]	ctx	points to an instance of cubic polynomial trajectory
[in]	ts	difference between final time and initial time
[in]	p0	initial position
[in]	p1	final position
[in]	v0	initial velocity
[in]	v1	final velocity

a_trajpoly3_pos()

a_real a_trajpoly3_pos	(	a_trajpoly3 const *	ctx,
		a_real	x )

compute position for cubic polynomial trajectory

$$\begin{array}{r}\begin{array}{l}p(t)=c_0+c_1(t-t_0)+c_2{(t-t_0)}^2+c_3{(t-t_0)}^3\end{array}\end{array}$$

Parameters

[in]	ctx	points to an instance of cubic polynomial trajectory
[in]	x	difference between current time and initial time

Returns

position output

a_trajpoly3_vel()

a_real a_trajpoly3_vel	(	a_trajpoly3 const *	ctx,
		a_real	x )

compute velocity for cubic polynomial trajectory

$$\begin{array}{r}\begin{array}{l}\dot{p}(t)=c_1+2c_2(t-t_0)+3c_3{(t-t_0)}^2\end{array}\end{array}$$

Parameters

[in]	ctx	points to an instance of cubic polynomial trajectory
[in]	x	difference between current time and initial time

Returns

velocity output