hepta polynomial trajectory

Collaboration diagram for hepta polynomial trajectory:

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

Typedefs
typedef struct a_trajpoly7	a_trajpoly7

Functions
void	a_trajpoly7_gen (a_trajpoly7 *ctx, a_real ts, a_real p0, a_real p1, a_real v0, a_real v1, a_real a0, a_real a1, a_real j0, a_real j1)
	generate for hepta polynomial trajectory
void	a_trajpoly7_c0 (a_trajpoly7 const *ctx, a_real c[8])
	compute coefficients of position for hepta polynomial trajectory
void	a_trajpoly7_c1 (a_trajpoly7 const *ctx, a_real c[7])
	compute coefficients of velocity for hepta polynomial trajectory
void	a_trajpoly7_c2 (a_trajpoly7 const *ctx, a_real c[6])
	compute coefficients of acceleration for hepta polynomial trajectory
void	a_trajpoly7_c3 (a_trajpoly7 const *ctx, a_real c[5])
	compute coefficients of jerk for hepta polynomial trajectory
a_real	a_trajpoly7_pos (a_trajpoly7 const *ctx, a_real x)
	compute position for hepta polynomial trajectory
a_real	a_trajpoly7_vel (a_trajpoly7 const *ctx, a_real x)
	compute velocity for hepta polynomial trajectory
a_real	a_trajpoly7_acc (a_trajpoly7 const *ctx, a_real x)
	compute acceleration for hepta polynomial trajectory
a_real	a_trajpoly7_jer (a_trajpoly7 const *ctx, a_real x)
	compute jerk for hepta polynomial trajectory

Detailed Description

Function Documentation

a_trajpoly7_acc()

a_real a_trajpoly7_acc	(	a_trajpoly7 const *	ctx,
		a_real	x )

compute 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_c0()

void a_trajpoly7_c0	(	a_trajpoly7 const *	ctx,
		a_real	c[8] )

compute coefficients of position for hepta polynomial trajectory

Parameters

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

a_trajpoly7_c1()

void a_trajpoly7_c1	(	a_trajpoly7 const *	ctx,
		a_real	c[7] )

compute coefficients of velocity for hepta polynomial trajectory

Parameters

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

a_trajpoly7_c2()

void a_trajpoly7_c2	(	a_trajpoly7 const *	ctx,
		a_real	c[6] )

compute coefficients of acceleration for hepta polynomial trajectory

Parameters

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

a_trajpoly7_c3()

void a_trajpoly7_c3	(	a_trajpoly7 const *	ctx,
		a_real	c[5] )

compute coefficients of jerk for hepta polynomial trajectory

Parameters

[in]	ctx	points to an instance of hepta polynomial trajectory
[out]	c	coefficients of jerk

a_trajpoly7_gen()

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

a_real a_trajpoly7_jer	(	a_trajpoly7 const *	ctx,
		a_real	x )

compute 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()

a_real a_trajpoly7_pos	(	a_trajpoly7 const *	ctx,
		a_real	x )

compute 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()

a_real a_trajpoly7_vel	(	a_trajpoly7 const *	ctx,
		a_real	x )

compute 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