hepta polynomial trajectory

Collaboration diagram for hepta polynomial trajectory:

Data Structures
struct	a_trajpoly7
	instance structure for hepta polynomial trajectory More...

Macros
#define	A_TRAJPOLY7   4

Typedefs
typedef struct a_trajpoly7	a_trajpoly7

Functions
void	a_trajpoly7_gen (a_trajpoly7 *ctx, double ts, double p0, double p1, double v0, double v1, double a0, double a1, double j0, double j1)
	generate for hepta polynomial trajectory
void	a_trajpoly7_gen0 (a_trajpoly7 *ctx, double ts, double p0, double p1, double v0, double v1, double a0, double a1, double j0, double j1)
void	a_trajpoly7_gen1 (a_trajpoly7 *ctx)
void	a_trajpoly7_gen2 (a_trajpoly7 *ctx)
void	a_trajpoly7_gen3 (a_trajpoly7 *ctx)
double	a_trajpoly7_pos (a_trajpoly7 const *ctx, double x)
	calculate position for hepta polynomial trajectory
double	a_trajpoly7_vel (a_trajpoly7 const *ctx, double x)
	calculate velocity for hepta polynomial trajectory
double	a_trajpoly7_acc (a_trajpoly7 const *ctx, double x)
	calculate acceleration for hepta polynomial trajectory
double	a_trajpoly7_jer (a_trajpoly7 const *ctx, double x)
	calculate jerk for hepta polynomial trajectory

Detailed Description

Function Documentation

a_trajpoly7_acc()

double a_trajpoly7_acc	(	a_trajpoly7 const *	ctx,
		double	x )

calculate acceleration for hepta 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}+30 c_{6}\left(t-t_{0}\right)^{4}+42 c_{7}\left(t-t_{0}\right)^{5}\\ \end{array} \end{aligned}

Parameters

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

Returns

acceleration output

a_trajpoly7_gen()

void a_trajpoly7_gen	(	a_trajpoly7 *	ctx,
		double	ts,
		double	p0,
		double	p1,
		double	v0,
		double	v1,
		double	a0,
		double	a1,
		double	j0,
		double	j1 )

generate for hepta 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{j_{0}}{6}\\ c_{4}=\cfrac{\left(-4\,j_{0}-j_{1}\right)\,t^3+\left(15\,a_{1}-30\,a_{0}\right)\,t^2+\left(-120\,v_{0}-90\,v_{1}\right)\,t+210\,p}{6\,t^4}\\ c_{5}=\cfrac{\left(2\,j_{0}+j_{1}\right)\,t^3+\left(20\,a_{0}-14\,a_{1}\right)\,t^2+\left(90\,v_{0}+78\,v_{1}\right)\,t-168\,p}{2\,t^5}\\ c_{6}=\cfrac{\left(-4\,j_{0}-3\,j_{1}\right)\,t^3+\left(39\,a_{1}-45\,a_{0}\right)\,t^2+\left(-216\,v_{0}-204\,v_{1}\right)\,t+420\,p}{6\,t^6}\\ c_{7}=\cfrac{\left(j_{0}+j_{1}\right)\,t^3+\left(12\,a_{0}-12\,a_{1}\right)\,t^2+\left(60\,v_{0}+60\,v_{1}\right)\,t-120\,p}{6\,t^7} \end{array}\right. \end{aligned}

Parameters

[in,out]	ctx	points to an instance of hepta 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
[in]	j0	initial jerk
[in]	j1	final jerk

a_trajpoly7_jer()

double a_trajpoly7_jer	(	a_trajpoly7 const *	ctx,
		double	x )

calculate jerk for hepta polynomial trajectory

\begin{aligned} \begin{array}{l} p^{(3)}(t)=6 c_{3}+24 c_{4}\left(t-t_{0}\right)+60 c_{5}\left(t-t_{0}\right)^{2}+120 c_{6}\left(t-t_{0}\right)^{3}+210 c_{7}\left(t-t_{0}\right)^{4} \end{array} \end{aligned}

Parameters

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

Returns

jerk output

a_trajpoly7_pos()

double a_trajpoly7_pos	(	a_trajpoly7 const *	ctx,
		double	x )

calculate position for hepta 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}+c_{6}\left(t-t_{0}\right)^{6}+c_{7}\left(t-t_{0}\right)^{7}\\ \end{array} \end{aligned}

Parameters

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

Returns

position output

a_trajpoly7_vel()

double a_trajpoly7_vel	(	a_trajpoly7 const *	ctx,
		double	x )

calculate velocity for hepta 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}+6 c_{6}\left(t-t_{0}\right)^{5}+7 c_{7}\left(t-t_{0}\right)^{6}\\ \end{array} \end{aligned}

Parameters

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

Returns

velocity output