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ball.py
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ball.py
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# -*- coding: utf-8 -*-
"""
Created on Sat Jul 5 16:07:29 2014
@author: rlabbe
"""
import numpy as np
from KalmanFilter import KalmanFilter
from math import radians, sin, cos, sqrt, exp
import numpy.random as random
import matplotlib.markers as markers
import matplotlib.pyplot as plt
from RungeKutta import *
class BallPath(object):
def __init__(self, x0, y0, omega_deg, velocity, g=9.8, noise=[1.0,1.0]):
omega = radians(omega_deg)
self.vx0 = velocity * cos(omega)
self.vy0 = velocity * sin(omega)
self.x0 = x0
self.y0 = y0
self.g = g
self.noise = noise
def pos_at_t(self, t):
""" returns (x,y) tuple of ball position at time t"""
x = self.vx0*t + self.x0
y = -0.5*self.g*t**2 + self.vy0*t + self.y0
return (x +random.randn()*self.noise[0], y +random.randn()*self.noise[1])
def ball_kf(x, y, omega, v0, dt, r=0.5, q=0.02):
g = 9.8 # gravitational constant
f1 = KalmanFilter(dim_x=5, dim_z=2)
ay = .5*dt**2
f1.F = np.mat ([[1, dt, 0, 0, 0], # x = x0+dx*dt
[0, 1, 0, 0, 0], # dx = dx
[0, 0, 1, dt, ay], # y = y0 +dy*dt+1/2*g*dt^2
[0, 0, 0, 1, dt], # dy = dy0 + ddy*dt
[0, 0, 0, 0, 1]]) # ddy = -g.
f1.H = np.mat([
[1, 0, 0, 0, 0],
[0, 0, 1, 0, 0]])
f1.R *= r
f1.Q *= q
omega = radians(omega)
vx = cos(omega) * v0
vy = sin(omega) * v0
f1.x = np.mat([x,vx,y,vy,-9.8]).T
return f1
def ball_kf_noay(x, y, omega, v0, dt, r=0.5, q=0.02):
g = 9.8 # gravitational constant
f1 = KalmanFilter(dim_x=5, dim_z=2)
ay = .5*dt**2
f1.F = np.mat ([[1, dt, 0, 0, 0], # x = x0+dx*dt
[0, 1, 0, 0, 0], # dx = dx
[0, 0, 1, dt, 0], # y = y0 +dy*dt
[0, 0, 0, 1, dt], # dy = dy0 + ddy*dt
[0, 0, 0, 0, 1]]) # ddy = -g.
f1.H = np.mat([
[1, 0, 0, 0, 0],
[0, 0, 1, 0, 0]])
f1.R *= r
f1.Q *= q
omega = radians(omega)
vx = cos(omega) * v0
vy = sin(omega) * v0
f1.x = np.mat([x,vx,y,vy,-9.8]).T
return f1
def test_kf():
dt = 0.1
t = 0
f1 = ball_kf (0,1, 35, 50, 0.1)
f2 = ball_kf_noay (0,1, 35, 50, 0.1)
path = BallPath( 0, 1, 35, 50, noise=(0,0))
path_rk = BallRungeKutta(0, 1, 50, 35)
xs = []
ys = []
while f1.x[2,0]>= 0:
t += dt
f1.predict()
f2.predict()
#x,y = path.pos_at_t(t)
x,y = path_rk.step(dt)
xs.append(x)
ys.append(y)
plt.scatter (f1.x[0,0], f1.x[2,0], color='blue',alpha=0.6)
plt.scatter (f2.x[0,0], f2.x[2,0], color='red', alpha=0.6)
plt.plot(xs, ys, c='g')
class BaseballPath(object):
def __init__(self, x0, y0, launch_angle_deg, velocity_ms, noise=(1.0,1.0)):
""" Create baseball path object in 2D (y=height above ground)
x0,y0 initial position
launch_angle_deg angle ball is travelling respective to ground plane
velocity_ms speeed of ball in meters/second
noise amount of noise to add to each reported position in (x,y)
"""
omega = radians(launch_angle_deg)
self.v_x = velocity_ms * cos(omega)
self.v_y = velocity_ms * sin(omega)
self.x = x0
self.y = y0
self.noise = noise
def drag_force (self, velocity):
""" Returns the force on a baseball due to air drag at
the specified velocity. Units are SI
"""
B_m = 0.0039 + 0.0058 / (1. + exp((velocity-35.)/5.))
return B_m * velocity
def update(self, dt, vel_wind=0.):
""" compute the ball position based on the specified time step and
wind velocity. Returns (x,y) position tuple.
"""
# Euler equations for x and y
self.x += self.v_x*dt
self.y += self.v_y*dt
# force due to air drag
v_x_wind = self.v_x - vel_wind
v = sqrt (v_x_wind**2 + self.v_y**2)
F = self.drag_force(v)
# Euler's equations for velocity
self.v_x = self.v_x - F*v_x_wind*dt
self.v_y = self.v_y - 9.81*dt - F*self.v_y*dt
return (self.x + random.randn()*self.noise[0],
self.y + random.randn()*self.noise[1])
def test_baseball_path():
ball = BaseballPath (0, 1, 35, 50)
while ball.y > 0:
ball.update (0.1, 0.)
plt.scatter (ball.x, ball.y)
def test_ball_path():
y = 15
x = 0
omega = 0.
noise = [1,1]
v0 = 100.
ball = BallPath (x0=x, y0=y, omega_deg=omega, velocity=v0, noise=noise)
dt = 1
f1 = KalmanFilter(dim_x=6, dim_z=2)
dt = 1/30. # time step
ay = -.5*dt**2
f1.F = np.mat ([[1, dt, 0, 0, 0, 0], # x=x0+dx*dt
[0, 1, dt, 0, 0, 0], # dx = dx
[0, 0, 0, 0, 0, 0], # ddx = 0
[0, 0, 0, 1, dt, ay], # y = y0 +dy*dt+1/2*g*dt^2
[0, 0, 0, 0, 1, dt], # dy = dy0 + ddy*dt
[0, 0, 0, 0, 0, 1]]) # ddy = -g
f1.H = np.mat([
[1, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0]])
f1.R = np.eye(2) * 5
f1.Q = np.eye(6) * 0.
omega = radians(omega)
vx = cos(omega) * v0
vy = sin(omega) * v0
f1.x = np.mat([x,vx,0,y,vy,-9.8]).T
f1.P = np.eye(6) * 500.
z = np.mat([[0,0]]).T
count = 0
markers.MarkerStyle(fillstyle='none')
np.set_printoptions(precision=4)
while f1.x[3,0] > 0:
count += 1
#f1.update (z)
f1.predict()
plt.scatter(f1.x[0,0],f1.x[3,0], color='green')
def drag_force (velocity):
""" Returns the force on a baseball due to air drag at
the specified velocity. Units are SI
"""
B_m = 0.0039 + 0.0058 / (1. + exp((velocity-35.)/5.))
return B_m * velocity
def update_drag(f, dt):
vx = f.x[1,0]
vy = f.x[3,0]
v = sqrt(vx**2 + vy**2)
F = -drag_force(v)
print F
f.u[0,0] = -drag_force(vx)
f.u[1,0] = -drag_force(vy)
#f.x[2,0]=F*vx
#f.x[5,0]=F*vy
def test_kf_drag():
y = 1
x = 0
omega = 35.
noise = [0,0]
v0 = 50.
ball = BaseballPath (x0=x, y0=y,
launch_angle_deg=omega,
velocity_ms=v0, noise=noise)
#ball = BallPath (x0=x, y0=y, omega_deg=omega, velocity=v0, noise=noise)
dt = 1
f1 = KalmanFilter(dim_x=6, dim_z=2)
dt = 1/30. # time step
ay = -.5*dt**2
ax = .5*dt**2
f1.F = np.mat ([[1, dt, ax, 0, 0, 0], # x=x0+dx*dt
[0, 1, dt, 0, 0, 0], # dx = dx
[0, 0, 1, 0, 0, 0], # ddx = 0
[0, 0, 0, 1, dt, ay], # y = y0 +dy*dt+1/2*g*dt^2
[0, 0, 0, 0, 1, dt], # dy = dy0 + ddy*dt
[0, 0, 0, 0, 0, 1]]) # ddy = -g
# We will inject air drag using Bu
f1.B = np.mat([[0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 1.]]).T
f1.u = np.mat([[0., 0.]]).T
f1.H = np.mat([
[1, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0]])
f1.R = np.eye(2) * 5
f1.Q = np.eye(6) * 0.
omega = radians(omega)
vx = cos(omega) * v0
vy = sin(omega) * v0
f1.x = np.mat([x,vx,0,y,vy,-9.8]).T
f1.P = np.eye(6) * 500.
z = np.mat([[0,0]]).T
markers.MarkerStyle(fillstyle='none')
np.set_printoptions(precision=4)
t=0
while f1.x[3,0] > 0:
t+=dt
#f1.update (z)
x,y = ball.update(dt)
#x,y = ball.pos_at_t(t)
update_drag(f1, dt)
f1.predict()
print f1.x.T
plt.scatter(f1.x[0,0],f1.x[3,0], color='red', alpha=0.5)
plt.scatter (x,y)
return f1
if __name__ == '__main__':
#test_baseball_path()
#test_ball_path()
#test_kf()
f1 = test_kf_drag()