cubic polynomial trajectory

Collaboration diagram for cubic polynomial trajectory:

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

Macros
#define	A_TRAJPOLY3   3

Typedefs
typedef struct a_trajpoly3	a_trajpoly3

Functions
void	a_trajpoly3_gen (a_trajpoly3 *ctx, double ts, double p0, double p1, double v0, double v1)
	generate for cubic polynomial trajectory
void	a_trajpoly3_gen0 (a_trajpoly3 *ctx, double ts, double p0, double p1, double v0, double v1)
void	a_trajpoly3_gen1 (a_trajpoly3 *ctx)
void	a_trajpoly3_gen2 (a_trajpoly3 *ctx)
double	a_trajpoly3_pos (a_trajpoly3 const *ctx, double x)
	calculate position for cubic polynomial trajectory
double	a_trajpoly3_vel (a_trajpoly3 const *ctx, double x)
	calculate velocity for cubic polynomial trajectory
double	a_trajpoly3_acc (a_trajpoly3 const *ctx, double x)
	calculate acceleration for cubic polynomial trajectory

Detailed Description

Function Documentation

a_trajpoly3_acc()

double a_trajpoly3_acc	(	a_trajpoly3 const *	ctx,
		double	x )

calculate acceleration for cubic polynomial trajectory

\begin{aligned} \begin{array}{l} \ddot{p}(t)=2 c_{2}+6 c_{3}\left(t-t_{0}\right) \end{array} \end{aligned}

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_gen()

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

generate for cubic polynomial trajectory

\begin{aligned} \left\{\begin{array}{l} t=t_{1}-t_{0}\\ p=p_{1}-p_{0}\\ c_{0}=p_{0}\\ c_{1}=v_{0}\\ c_{2}=\cfrac{\left(-2\,v_{0}-v_{1}\right)\,t+3\,p}{t^2}\\ c_{3}=\cfrac{\left(v_{0}+v_{1}\right)\,t-2\,p}{t^3} \end{array}\right. \end{aligned}

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()

double a_trajpoly3_pos	(	a_trajpoly3 const *	ctx,
		double	x )

calculate position for cubic polynomial trajectory

\begin{aligned} \begin{array}{l} p(t)=c_{0}+c_{1}\left(t-t_{0}\right)+c_{2}\left(t-t_{0}\right)^{2}+c_{3}\left(t-t_{0}\right)^{3} \\ \end{array} \end{aligned}

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()

double a_trajpoly3_vel	(	a_trajpoly3 const *	ctx,
		double	x )

calculate velocity for cubic polynomial trajectory

\begin{aligned} \begin{array}{l} \dot{p}(t)=c_{1}+2 c_{2}\left(t-t_{0}\right)+3 c_{3}\left(t-t_{0}\right)^{2} \\ \end{array} \end{aligned}

Parameters

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

Returns

velocity output