quintic polynomial trajectory

Collaboration diagram for quintic polynomial trajectory:

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

Typedefs
typedef struct a_trajpoly5	a_trajpoly5

Functions
void	a_trajpoly5_gen (a_trajpoly5 *ctx, a_real ts, a_real p0, a_real p1, a_real v0, a_real v1, a_real a0, a_real a1)
	generate for quintic polynomial trajectory
void	a_trajpoly5_c0 (a_trajpoly5 const *ctx, a_real c[6])
	compute coefficients of position for quintic polynomial trajectory
void	a_trajpoly5_c1 (a_trajpoly5 const *ctx, a_real c[5])
	compute coefficients of velocity for quintic polynomial trajectory
void	a_trajpoly5_c2 (a_trajpoly5 const *ctx, a_real c[4])
	compute coefficients of acceleration for quintic polynomial trajectory
a_real	a_trajpoly5_pos (a_trajpoly5 const *ctx, a_real x)
	compute position for quintic polynomial trajectory
a_real	a_trajpoly5_vel (a_trajpoly5 const *ctx, a_real x)
	compute velocity for quintic polynomial trajectory
a_real	a_trajpoly5_acc (a_trajpoly5 const *ctx, a_real x)
	compute acceleration for quintic polynomial trajectory

Detailed Description

Function Documentation

a_trajpoly5_acc()

a_real a_trajpoly5_acc	(	a_trajpoly5 const *	ctx,
		a_real	x )

compute 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_c0()

void a_trajpoly5_c0	(	a_trajpoly5 const *	ctx,
		a_real	c[6] )

compute coefficients of position for quintic polynomial trajectory

Parameters

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

a_trajpoly5_c1()

void a_trajpoly5_c1	(	a_trajpoly5 const *	ctx,
		a_real	c[5] )

compute coefficients of velocity for quintic polynomial trajectory

Parameters

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

a_trajpoly5_c2()

void a_trajpoly5_c2	(	a_trajpoly5 const *	ctx,
		a_real	c[4] )

compute coefficients of acceleration for quintic polynomial trajectory

Parameters

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

a_trajpoly5_gen()

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

a_real a_trajpoly5_pos	(	a_trajpoly5 const *	ctx,
		a_real	x )

compute 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()

a_real a_trajpoly5_vel	(	a_trajpoly5 const *	ctx,
		a_real	x )

compute 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