mirror of https://github.com/ArduPilot/ardupilot
335 lines
10 KiB
Python
Executable File
335 lines
10 KiB
Python
Executable File
#!/usr/bin/python
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from math import *
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from pymavlink.rotmat import Vector3, Matrix3
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from numpy import linspace
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from visual import *
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class Quat:
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def __init__(self,w=1.0,x=0.0,y=0.0,z=0.0):
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self.w = w
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self.x = x
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self.y = y
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self.z = z
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def to_euler(self):
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roll = (atan2(2.0*(self.w*self.x + self.y*self.z), 1 - 2.0*(self.x*self.x + self.y*self.y)))
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pitch = asin(2.0*(self.w*self.y - self.z*self.x))
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yaw = atan2(2.0*(self.w*self.z + self.x*self.y), 1 - 2.0*(self.y*self.y + self.z*self.z))
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return Vector3(roll,pitch,yaw)
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def from_euler(self,euler):
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#(roll,pitch,yaw)
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cr2 = cos(euler[0]*0.5)
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cp2 = cos(euler[1]*0.5)
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cy2 = cos(euler[2]*0.5)
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sr2 = sin(euler[0]*0.5)
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sp2 = sin(euler[1]*0.5)
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sy2 = sin(euler[2]*0.5)
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self.w = cr2*cp2*cy2 + sr2*sp2*sy2
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self.x = sr2*cp2*cy2 - cr2*sp2*sy2
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self.y = cr2*sp2*cy2 + sr2*cp2*sy2
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self.z = cr2*cp2*sy2 - sr2*sp2*cy2
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return self
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def from_axis_angle(self, vec):
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theta = vec.length()
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if theta == 0:
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self.w = 1.0
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self.x = 0.0
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self.y = 0.0
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self.z = 0.0
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return
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vec_normalized = vec.normalized()
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st2 = sin(theta/2.0)
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self.w = cos(theta/2.0)
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self.x = vec_normalized.x * st2
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self.y = vec_normalized.y * st2
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self.z = vec_normalized.z * st2
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def rotate(self, vec):
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r = Quat()
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r.from_axis_angle(vec)
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q = self * r
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self.w = q.w
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self.x = q.x
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self.y = q.y
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self.z = q.z
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def to_axis_angle(self):
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l = sqrt(self.x**2+self.y**2+self.z**2)
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(x,y,z) = (self.x,self.y,self.z)
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if l != 0:
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temp = 2.0*atan2(l,self.w)
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if temp > pi:
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temp -= 2*pi
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elif temp < -pi:
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temp += 2*pi
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(x,y,z) = (temp*x/l,temp*y/l,temp*z/l)
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return Vector3(x,y,z)
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def to_rotation_matrix(self):
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m = Matrix3()
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yy = self.y**2
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yz = self.y * self.z
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xx = self.x**2
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xy = self.x * self.y
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xz = self.x * self.z
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wx = self.w * self.x
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wy = self.w * self.y
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wz = self.w * self.z
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zz = self.z**2
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m.a.x = 1.0-2.0*(yy + zz)
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m.a.y = 2.0*(xy - wz)
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m.a.z = 2.0*(xz + wy)
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m.b.x = 2.0*(xy + wz)
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m.b.y = 1.0-2.0*(xx + zz)
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m.b.z = 2.0*(yz - wx)
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m.c.x = 2.0*(xz - wy)
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m.c.y = 2.0*(yz + wx)
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m.c.z = 1.0-2.0*(xx + yy)
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return m
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def inverse(self):
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return Quat(self.w,-self.x,-self.y,-self.z)
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def __mul__(self,operand):
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ret = Quat()
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w1=self.w
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x1=self.x
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y1=self.y
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z1=self.z
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w2=operand.w
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x2=operand.x
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y2=operand.y
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z2=operand.z
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ret.w = w1*w2 - x1*x2 - y1*y2 - z1*z2
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ret.x = w1*x2 + x1*w2 + y1*z2 - z1*y2
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ret.y = w1*y2 - x1*z2 + y1*w2 + z1*x2
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ret.z = w1*z2 + x1*y2 - y1*x2 + z1*w2
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return ret
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def __str__(self):
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return "Quat(%f, %f, %f, %f)" % (self.w,self.x,self.y,self.z)
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def vpy_vec(vec):
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return vector(vec.y, -vec.z, -vec.x)
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def update_arrows(q,x,y,z):
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m = q.to_rotation_matrix().transposed()
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x.axis = vpy_vec(m*Vector3(1,0,0))
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x.up = vpy_vec(m*Vector3(0,1,0))
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y.axis = vpy_vec(m*Vector3(0,1,0))
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y.up = vpy_vec(m*Vector3(1,0,0))
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z.axis = vpy_vec(m*Vector3(0,0,1))
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z.up = vpy_vec(m*Vector3(1,0,0))
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class Attitude:
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def __init__(self,reference=False):
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self.labels = []
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self.xarrows = []
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self.yarrows = []
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self.zarrows = []
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self.q = Quat()
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self.reference = reference
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self.update_arrows()
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def add_arrows(self, arrowpos = Vector3(0,0,0), labeltext=None):
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if labeltext is not None:
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self.labels.append(label(pos = vpy_vec(arrowpos), text=labeltext))
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sw = .005 if self.reference else .05
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self.xarrows.append(arrow(pos=vpy_vec(arrowpos),color=color.red,opacity=1,shaftwidth=sw))
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self.yarrows.append(arrow(pos=vpy_vec(arrowpos),color=color.green,opacity=1,shaftwidth=sw))
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self.zarrows.append(arrow(pos=vpy_vec(arrowpos),color=color.blue,opacity=1,shaftwidth=sw))
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self.update_arrows()
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def rotate(self, vec):
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self.q.rotate(vec)
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def update_arrows(self):
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m = self.q.to_rotation_matrix().transposed()
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sl = 1.1 if self.reference else 1.0
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for i in self.xarrows:
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i.axis = vpy_vec(m*Vector3(sl,0,0))
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i.up = vpy_vec(m*Vector3(0,1,0))
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for i in self.yarrows:
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i.axis = vpy_vec(m*Vector3(0,sl,0))
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i.up = vpy_vec(m*Vector3(1,0,0))
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for i in self.zarrows:
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i.axis = vpy_vec(m*Vector3(0,0,sl))
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i.up = vpy_vec(m*Vector3(1,0,0))
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for i in self.labels:
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i.xoffset = scene.width*0.07
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i.yoffset = scene.width*0.1
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class Tian_integrator:
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def __init__(self, integrate_separately=True):
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self.alpha = Vector3(0,0,0)
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self.beta = Vector3(0,0,0)
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self.last_alpha = Vector3(0,0,0)
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self.last_delta_alpha = Vector3(0,0,0)
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self.last_sample = Vector3(0,0,0)
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self.integrate_separately = integrate_separately
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def add_sample(self, sample, dt):
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delta_alpha = (self.last_sample+sample)*0.5*dt
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self.alpha += delta_alpha
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delta_beta = 0.5 * (self.last_alpha + (1.0/6.0)*self.last_delta_alpha)%delta_alpha
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if self.integrate_separately:
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self.beta += delta_beta
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else:
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self.alpha += delta_beta
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self.last_alpha = self.alpha
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self.last_delta_alpha = delta_alpha
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self.last_sample = sample
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def pop_delta_angles(self):
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ret = self.alpha + self.beta
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self.alpha.zero()
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self.beta.zero()
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return ret
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filter2p_1khz_30hz_data = {}
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def filter2p_1khz_30hz(sample, key):
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global filter2p_1khz_30hz_data
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if not key in filter2p_1khz_30hz_data:
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filter2p_1khz_30hz_data[key] = (0.0,0.0)
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(delay_element_1, delay_element_2) = filter2p_1khz_30hz_data[key]
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sample_freq = 1000
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cutoff_freq = 30
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fr = sample_freq/cutoff_freq
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ohm = tan(pi/fr)
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c = 1.0+2.0*cos(pi/4.0)*ohm + ohm**2
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b0 = ohm**2/c
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b1 = 2.0*b0
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b2 = b0
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a1 = 2.0*(ohm**2-1.0)/c
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a2 = (1.0-2.0*cos(pi/4.0)*ohm+ohm**2)/c
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delay_element_0 = sample - delay_element_1 * a1 - delay_element_2 * a2
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output = delay_element_0 * b0 + delay_element_1 * b1 + delay_element_2 * b2
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filter2p_1khz_30hz_data[key] = (delay_element_0, delay_element_1)
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return output
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def filter2p_1khz_30hz_vector3(sample, key):
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ret = Vector3()
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ret.x = filter2p_1khz_30hz(sample.x, "vec3f"+key+"x")
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ret.y = filter2p_1khz_30hz(sample.y, "vec3f"+key+"y")
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ret.z = filter2p_1khz_30hz(sample.z, "vec3f"+key+"z")
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return ret
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reference_attitude = Attitude(True)
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uncorrected_attitude_low = Attitude()
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uncorrected_attitude_high = Attitude()
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corrected_attitude = Attitude()
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corrected_attitude_combined = Attitude()
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corrected_attitude_integrator = Tian_integrator()
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corrected_attitude_integrator_combined = Tian_integrator(integrate_separately = False)
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reference_attitude.add_arrows(Vector3(0,-3,0))
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uncorrected_attitude_low.add_arrows(Vector3(0,-3,0), "no correction\nlow rate integration\n30hz software LPF @ 1khz\n(ardupilot 2015-02-18)")
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reference_attitude.add_arrows(Vector3(0,-1,0))
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uncorrected_attitude_high.add_arrows(Vector3(0,-1,0), "no correction\nhigh rate integration")
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reference_attitude.add_arrows(Vector3(0,1,0))
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corrected_attitude.add_arrows(Vector3(0,1,0), "Tian et al\nseparate integration")
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reference_attitude.add_arrows(Vector3(0,3,0))
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corrected_attitude_combined.add_arrows(Vector3(0,3,0), "Tian et al\ncombined_integration\n(proposed patch)")
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#scene.scale = (0.3,0.3,0.3)
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scene.fov = 0.001
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scene.forward = (-0.5, -0.5, -1)
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coning_frequency_hz = 50
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coning_magnitude_rad_s = 2
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label_text = (
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"coning motion frequency %f hz\n"
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"coning motion peak amplitude %f deg/s\n"
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"thin arrows are reference attitude"
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) % (coning_frequency_hz, degrees(coning_magnitude_rad_s))
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label(pos = vpy_vec(Vector3(0,0,2)), text=label_text)
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t = 0.0
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dt_10000 = 0.0001
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dt_1000 = 0.001
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dt_333 = 0.003
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accumulated_delta_angle = Vector3(0,0,0)
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last_gyro_10000 = Vector3(0,0,0)
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last_gyro_1000 = Vector3(0,0,0)
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last_filtered_gyro_333 = Vector3(0,0,0)
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filtered_gyro = Vector3(0,0,0)
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while True:
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rate(66)
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for i in range(5):
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for j in range(3):
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for k in range(10):
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#vvvvvvvvvv 10 kHz vvvvvvvvvv#
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#compute angular rate at current time
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gyro = Vector3(sin(t*coning_frequency_hz*2*pi), cos(t*coning_frequency_hz*2*pi),0)*coning_magnitude_rad_s
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#integrate reference attitude
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reference_attitude.rotate((gyro+last_gyro_10000) * dt_10000 * 0.5)
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#increment time
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t += dt_10000
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last_gyro_10000 = gyro
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#vvvvvvvvvv 1 kHz vvvvvvvvvv#
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#update filter for sim 1
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filtered_gyro = filter2p_1khz_30hz_vector3(gyro, "1")
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#update integrator for sim 2
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accumulated_delta_angle += (gyro+last_gyro_1000) * dt_1000 * 0.5
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#update integrator for sim 3
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corrected_attitude_integrator.add_sample(gyro, dt_1000)
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#update integrator for sim 4
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corrected_attitude_integrator_combined.add_sample(gyro, dt_1000)
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last_gyro_1000 = gyro
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#vvvvvvvvvv 333 Hz vvvvvvvvvv#
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#update sim 1 (leftmost)
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uncorrected_attitude_low.rotate((filtered_gyro+last_filtered_gyro_333) * dt_333 * 0.5)
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#update sim 2
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uncorrected_attitude_high.rotate(accumulated_delta_angle)
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accumulated_delta_angle.zero()
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#update sim 3
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corrected_attitude.rotate(corrected_attitude_integrator.pop_delta_angles())
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#update sim 4 (rightmost)
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corrected_attitude_combined.rotate(corrected_attitude_integrator_combined.pop_delta_angles())
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last_filtered_gyro_333 = filtered_gyro
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#vvvvvvvvvv 66 Hz vvvvvvvvvv#
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reference_attitude.update_arrows()
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corrected_attitude.update_arrows()
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corrected_attitude_combined.update_arrows()
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uncorrected_attitude_low.update_arrows()
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uncorrected_attitude_high.update_arrows()
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