quintic polynomial trajectory

Collaboration diagram for quintic polynomial trajectory:

Data Structures
struct	a_trajpoly5
	instance structure for quintic polynomial trajectory More...

Macros
#define	A_TRAJPOLY5   3

Typedefs
typedef struct a_trajpoly5	a_trajpoly5

Functions
void	a_trajpoly5_gen (a_trajpoly5 *ctx, double ts, double p0, double p1, double v0, double v1, double a0, double a1)
	generate for quintic polynomial trajectory
void	a_trajpoly5_gen0 (a_trajpoly5 *ctx, double ts, double p0, double p1, double v0, double v1, double a0, double a1)
void	a_trajpoly5_gen1 (a_trajpoly5 *ctx)
void	a_trajpoly5_gen2 (a_trajpoly5 *ctx)
double	a_trajpoly5_pos (a_trajpoly5 const *ctx, double x)
	calculate position for quintic polynomial trajectory
double	a_trajpoly5_vel (a_trajpoly5 const *ctx, double x)
	calculate velocity for quintic polynomial trajectory
double	a_trajpoly5_acc (a_trajpoly5 const *ctx, double x)
	calculate acceleration for quintic polynomial trajectory

Detailed Description

Function Documentation

a_trajpoly5_acc()

double a_trajpoly5_acc	(	a_trajpoly5 const *	ctx,
		double	x )

calculate acceleration for quintic polynomial trajectory

\begin{aligned} \begin{array}{l} \ddot{p}(t)=2 c_{2}+6 c_{3}\left(t-t_{0}\right)+12 c_{4}\left(t-t_{0}\right)^{2}+20 c_{5}\left(t-t_{0}\right)^{3} \end{array} \end{aligned}

Parameters

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

Returns

acceleration output

a_trajpoly5_gen()

void a_trajpoly5_gen	(	a_trajpoly5 *	ctx,
		double	ts,
		double	p0,
		double	p1,
		double	v0,
		double	v1,
		double	a0,
		double	a1 )

generate for quintic 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{a_{0}}{2}\\ c_{3}=\cfrac{\left(a_{1}-3\,a_{0}\right)\,t^2+\left(-12\,v_{0}-8\,v_{1}\right)\,t+20\,p}{2\,t^3}\\ c_{4}=\cfrac{\left(3\,a_{0}-2\,a_{1}\right)\,t^2+\left(16\,v_{0}+14\,v_{1}\right)\,t-30\,p}{2\,t^4}\\ c_{5}=\cfrac{\left(a_{1}-a_{0}\right)\,t^2+\left(-6\,v_{0}-6\,v_{1}\right)\,t+12\,p}{2\,t^5} \end{array}\right. \end{aligned}

Parameters

[in,out]	ctx	points to an instance of quintic 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
[in]	a0	initial acceleration
[in]	a1	final acceleration

a_trajpoly5_pos()

double a_trajpoly5_pos	(	a_trajpoly5 const *	ctx,
		double	x )

calculate position for quintic 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}+c_{4}\left(t-t_{0}\right)^{4}+c_{5}\left(t-t_{0}\right)^{5}\\ \end{array} \end{aligned}

Parameters

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

Returns

position output

a_trajpoly5_vel()

double a_trajpoly5_vel	(	a_trajpoly5 const *	ctx,
		double	x )

calculate velocity for quintic 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}+4 c_{4}\left(t-t_{0}\right)^{3}+5 c_{5}\left(t-t_{0}\right)^{4}\\ \end{array} \end{aligned}

Parameters

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

Returns

velocity output