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vaj1d.go
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vaj1d.go
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package vaj
import (
"github.com/chewxy/math32"
"github.com/foxis/EasyRobot/pkg/core/math"
)
type VAJ1D struct {
maxV, maxA, maxJ float32
v1max, v2max, vamax float32
Velocity, Acceleration, j0 float32
Input, Output, Target float32
}
func New1D(maxVelocity, maxAcceleration, jerk float32) VAJ1D {
vamax := (maxAcceleration * maxAcceleration) / (jerk * 2)
v1max := maxVelocity / 2
v2max := maxVelocity / 2
if v1max > vamax {
v1max = vamax
}
if v2max < maxVelocity-vamax {
v2max = maxVelocity - vamax
}
return VAJ1D{
maxV: maxVelocity,
maxA: maxAcceleration,
maxJ: jerk,
v1max: v1max,
v2max: v2max,
vamax: vamax,
}
}
func (l *VAJ1D) Reset() *VAJ1D {
l.Velocity = 0
l.Acceleration = 0
return l
}
func (l *VAJ1D) Update(samplePeriod float32) *VAJ1D {
defer func() {
l.Input = l.Output
}()
x1 := l.Target - l.Input
var c float32 = 1
if x1 < 1 {
x1 = -x1
c = -1
}
if x1 < .001 {
l.Output = l.Input
l.j0 = 0
l.Velocity = 0
l.Acceleration = 0
return l
}
x0 := l.calculateKinematics(samplePeriod, x1)
l.Output = l.Input + x0*c
return l
}
func (l *VAJ1D) calculateKinematics(samplePeriod, x1 float32) float32 {
dt := samplePeriod
v0 := l.Velocity
a0 := l.Acceleration
// check the stage of the acceleration/deceleration part
x0, v0, a0, jC := l.calculateJerk(samplePeriod, x1, v0, a0, l.j0)
// check if we are able to stop in time
stopAt := l.calculateStoppingDistance(v0, a0)
if stopAt <= x1 {
if math32.Abs(v0) >= l.maxV-l.maxA*dt-0.5*l.maxJ*dt*dt-0.001 {
a0 = 0
jC = 0
v0 = l.maxV
}
} else if jC == 0 || (a0 < l.maxA && a0 >= 0) {
jC = -1
}
// integrate the step
x0 += (v0 + (0.5*a0*dt+(1/6)*l.j0*dt)*dt) * dt
l.Velocity += (a0 + .5*l.j0*dt) * dt
a0 += l.j0 * dt
l.Acceleration = math.Clamp(a0, -l.maxA, l.maxA)
l.j0 = jC * l.maxJ
return x0
}
func (l *VAJ1D) calculateJerk(dt, x1, v0, a0, j0 float32) (float32, float32, float32, float32) {
var x0, jC float32
v0x := v0 + a0*dt + .5*j0*dt*dt
if v0x >= 0 && v0x <= l.v1max {
if j0 == -l.maxJ {
_, t := math.Quad(.5*j0, a0, v0-l.v1max, 1e-6)
if t <= 2*dt {
x0 = (v0 + (0.5*a0+(1/6)*j0*t)*t) * t
v0 += (a0 + .5*j0*t) * t
a0 += j0 * t
}
}
jC = 1
} else if v0x < l.maxV && v0x > l.v2max {
if j0 == l.maxJ {
t, _ := math.Quad(.5*j0, a0, v0-l.v2max, 1e-6)
x0 = (v0 + (0.5*a0+(1/6)*j0*t)*t) * t
v0 += (a0 + .5*j0*t) * t
a0 += j0 * t
}
jC = -1
} else {
jC = 0
}
return x0, v0, a0, jC
}
func (l *VAJ1D) calculateStoppingDistance(v0, a0 float32) float32 {
var (
s, s1, s2, s3 float32
v1m, v2m float32
v1, v2, a1 float32
)
// Remove acceleration
if a0 > 0 {
t := a0 / l.maxJ
jt := .5 * l.maxJ * t
s = (v0 + (.5*a0-(1/3)*jt)*t) * t
v0 += (a0 - jt) * t
a0 = 0
}
if a0 == 0 {
v1m = math32.Min(v0/2, l.vamax)
v2m = math32.Max(v0/2, v0-l.vamax)
} else {
v1m = l.v1max
v2m = l.v2max
}
// decelerate
if v0 > v2m {
_, t := math.Quad(-.5*l.maxJ, a0, v0-v2m, 1e-6)
v2 = v2m
v1 = v2m
s1 = (v0 + (0.5*a0-(1/6)*l.maxJ*t)*t) * t
a1 = a0 - l.maxJ*t
} else {
v1 = v0
v2 = v0
a1 = a0
}
// coast
if v1 <= v2m && v1 > v1m {
t := (v1 - v1m) / (-a1)
v2 = v1m
s2 = (v1 + .5*a1*t) * t
}
// remove deceleration
if v2 > 0 {
t, _ := math.Quad(.5*l.maxJ, a1, v2, 1e-6)
s3 = (v2 + (.5*a1+(1/6)*l.maxJ*t)*t) * t
}
return s + s1 + s2 + s3
}