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

$$\begin{array}{r}\begin{array}{l}\ddot{p}(t)=2c_2+6c_3(t-t_0)+12c_4{(t-t_0)}^2+20c_5{(t-t_0)}^3\end{array}\end{array}$$

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

$$\begin{array}{r}\{\begin{array}{l}t=t_1-t_0\\ p=p_1-p_0\\ c_0=p_0\\ c_1=v_0\\ c_2=\frac{a_0}{2}\\ c_3=\frac{(a_1-3a_0)t^2+(-12v_0-8v_1)t+20p}{2t^3}\\ c_4=\frac{(3a_0-2a_1)t^2+(16v_0+14v_1)t-30p}{2t^4}\\ c_5=\frac{(a_1-a_0)t^2+(-6v_0-6v_1)t+12p}{2t^5}\end{array}\end{array}$$

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

$$\begin{array}{r}\begin{array}{l}p(t)=c_0+c_1(t-t_0)+c_2{(t-t_0)}^2+c_3{(t-t_0)}^3+c_4{(t-t_0)}^4+c_5{(t-t_0)}^5\end{array}\end{array}$$

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

$$\begin{array}{r}\begin{array}{l}\dot{p}(t)=c_1+2c_2(t-t_0)+3c_3{(t-t_0)}^2+4c_4{(t-t_0)}^3+5c_5{(t-t_0)}^4\end{array}\end{array}$$

Parameters

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

Returns

velocity output