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kalman_syde750.py
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kalman_syde750.py
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import nengo
import numpy as np
nengo.rc.set('progress', 'progress_bar', 'nengo.utils.progress.TerminalProgressBar')
class mass_dyn(object):
def __init__(self, mass=1.0, xo=0,yo=0,dt=0.001, seed=None):
self.mass = mass
self.dt = dt
self.xo=xo
self.yo=yo
self.x=np.zeros([4,1])
self.u=np.zeros([2,1])
self.reset(seed)
self.A = np.matrix([[1, 0, self.dt, 0],
[0, 1, 0, self.dt],
[0, 0, 1, 0],
[0, 0, 0 ,1]]); #change to expm(A)
self.B = np.matrix([[0,0],
[0,0],
[self.dt/self.mass,0],
[0,self.dt/self.mass]]);
def reset(self, seed):
self.rng = np.random.RandomState(seed=seed)
self.x[0,0] = self.xo
self.x[1,0] = self.yo
self.x[2,0] = 0
self.x[3,0] = 0
def step(self, ux,uy):
self.u[0,0],self.u[1,0] = ux, uy
self.x = self.A*self.x + self.B* self.u
def generate_html(self, xd,yd):
x=50+self.x[0,0]
y=50-self.x[1,0]
xd_plot=50+xd
yd_plot=50-yd
return '''
<svg width="100%" height="100%" viewbox="30 30 40 40">
<line x1="0" y1="50" x2="100" y2="50" style="stroke:grey;stroke-width:0.25" />
<line x1="50" y1="0" x2="50" y2="100" style="stroke:grey;stroke-width:0.25" />
<circle cx="{x}" cy="{y}" r="1" style="stroke:blue;stroke-width:0.25"" fill="blue"/>
<circle cx="{xd_plot}" cy="{yd_plot}" r="1" style="stroke:black;stroke-width:0.25"" fill="none"/>
</svg>
'''.format(**locals())
class CtrlNetwork(nengo.Network):
def __init__(self, label=None, **kwargs):
super(CtrlNetwork, self).__init__(label=label)
with self:
tau=0.001
self.xd = nengo.Ensemble(n_neurons=1000, dimensions=1, radius=10)
self.yd = nengo.Ensemble(n_neurons=1000, dimensions=1, radius=10)
self.xdot_d = nengo.Node(None, size_in=1)
self.ydot_d = nengo.Node(None, size_in=1)
self.u = nengo.Ensemble(n_neurons=8000, dimensions=2, radius=20)
#nengo.Connection(self.uy, self.mass_dyn[3], synapse=0.0)
self.x = nengo.Ensemble(n_neurons=1000, dimensions=1, radius=10)
self.y = nengo.Ensemble(n_neurons=1000, dimensions=1, radius=10)
self.x_diff = nengo.Ensemble(n_neurons=1000, dimensions=1, radius=10)
nengo.Connection(self.xd, self.x_diff, synapse=tau)
nengo.Connection(self.x, self.x_diff, synapse=tau, transform=-1)
self.y_diff = nengo.Ensemble(n_neurons=1000, dimensions=1, radius=10)
nengo.Connection(self.yd, self.y_diff, synapse=tau)
nengo.Connection(self.y, self.y_diff, synapse=tau, transform=-1)
Kp = 1.5
nengo.Connection(self.x_diff, self.u[0], transform=Kp, synapse=tau)
nengo.Connection(self.y_diff, self.u[1], transform=Kp, synapse=tau)
self.dx = nengo.Ensemble(n_neurons=1000, dimensions=1, radius=10)
self.dy = nengo.Ensemble(n_neurons=1000, dimensions=1, radius=10)
self.xd_diff = nengo.Ensemble(n_neurons=1000, dimensions=1,radius=10)
nengo.Connection(self.xdot_d, self.xd_diff, synapse=tau)
nengo.Connection(self.dx, self.xd_diff, synapse=tau, transform=-1)
self.yd_diff = nengo.Ensemble(n_neurons=1000, dimensions=1,radius=10)
nengo.Connection(self.ydot_d, self.yd_diff, synapse=tau)
nengo.Connection(self.dy, self.yd_diff, synapse=tau, transform=-1)
Kd = 1
nengo.Connection(self.xd_diff, self.u[0], transform=Kd, synapse=tau)
nengo.Connection(self.yd_diff, self.u[1], transform=Kd, synapse=tau)
class MassNetwork(nengo.Network):
def __init__(self, label=None, **kwargs):
super(MassNetwork, self).__init__(label=label)
self.env = mass_dyn(**kwargs)
with self:
def func(t, x):
self.env.step(x[2],x[3])
func._nengo_html_ = self.env.generate_html(x[0],x[1])
return (self.env.x[0,0],self.env.x[1,0], self.env.x[2,0],self.env.x[3,0])
self.mass_dyn = nengo.Node(func, size_in=4)
self.xd = nengo.Node(None, size_in=1)
nengo.Connection(self.xd, self.mass_dyn[0], synapse=0.0)
self.yd = nengo.Node(None, size_in=1)
nengo.Connection(self.yd, self.mass_dyn[1], synapse=0.0)
self.ux = nengo.Ensemble(n_neurons=500, dimensions=1, radius=20)
nengo.Connection(self.ux, self.mass_dyn[2], synapse=0.0)
self.uy = nengo.Ensemble(n_neurons=500, dimensions=1, radius=20)
nengo.Connection(self.uy, self.mass_dyn[3], synapse=0.0)
self.x = nengo.Node(None, size_in=1)
self.y = nengo.Node(None, size_in=1)
self.dx = nengo.Node(None, size_in=1)
self.dy = nengo.Node(None, size_in=1)
nengo.Connection(self.mass_dyn[0], self.x, synapse=0.0)
nengo.Connection(self.mass_dyn[1], self.y, synapse=0.0)
nengo.Connection(self.mass_dyn[2], self.dx, synapse=0.00)
nengo.Connection(self.mass_dyn[3], self.dy, synapse=0.0)
class Estimate_Network(nengo.Network):
def __init__(self, label=None, **kwargs):
super(Estimate_Network, self).__init__(label=label)
tau=0.001; taup = 0.1; dt=0.001
with self:
self.mass=1
self.u = nengo.Ensemble(n_neurons=6000, dimensions=2, radius=10) #u
self.y = nengo.Ensemble(n_neurons=6000, dimensions=4, radius=10)
self.pred = nengo.Ensemble(n_neurons=12000,dimensions=4,radius=10)
self.Q_est=0.1
self.R_est=0.1
A =[[1, 0, taup, 0],[0, 1, 0, taup],[0, 0, 1, 0],[0, 0, 0 ,1]]
B=[[0,0],[0,0],[m_gain*taup/self.mass,0],[0,m_gain*taup/self.mass]]
nengo.Connection(self.u,self.pred,transform=B,synapse=taup)
nengo.Connection(self.pred,self.pred,transform=A,synapse=taup)
def gain_func(x):
return(x[0]+x[8]*(x[4]-x[0])+x[9]*(x[6]-x[2]),
x[1]+x[8]*(x[5]-x[1])+x[9]*(x[7]-x[3]),
x[2]+x[9]*(x[4]-x[0])+x[10]*(x[6]-x[2]),
x[3]+x[9]*(x[5]-x[1])+x[10]*(x[7]-x[3]))
self.upd2 = nengo.Ensemble(n_neurons=10000,dimensions=7,radius=10)
def gain_func3(x):
return(x[4]*x[0]+x[5]*x[2],
x[4]*x[1]+x[5]*x[3],
x[5]*x[0]+x[6]*x[2],
x[5]*x[1]+x[6]*x[3])
nengo.Connection(self.pred,self.upd2[:4],transform=-1,synapse=tau)
nengo.Connection(self.y,self.upd2[:4],synapse=tau)
def prod3(x):
l,m = x[0], x[1]; #Q's values
i,j = x[2], x[3]; #R's values
a,b,c=x[4],x[5],x[6] #P's elements
p = a + 2*b*dt + c*dt**2 + l ; #P_ = APA' +Q
q = b + c*dt
r = c + m
s = p + i #P_+R
t = q
u = r + j
l = -u/(t**2-s*u);
m = t/(t**2-s*u);
n = -s/(t**2-s*u) #inv(P+R)
k1 = l*p + m*q
k2 = m*p + n*q
k3 = m*q + n*r
return(k1,k2,k3)
def getP(x):
l,m = x[0], x[1]; #Q's values
i,j = x[2], x[3]; #R's values
a,b,c=x[4],x[5],x[6] #P's elements
p = a + 2*b*dt + c*dt**2 + l ; #P_ = APA' +Q
q = b + c*dt
r = c + m
s = p + i #P_+R
t = q
u = r + j
l = -u/(t**2-s*u);
m = t/(t**2-s*u);
n = -s/(t**2-s*u) #inv(P+R)
k1 = l*p + m*q
k2 = m*p + n*q
k3 = m*q + n*r
return(-q*k2+p*(1-k1), -r*k2+q*(1-k1), -q*k2+r*(1-k3))
# self.P = nengo.Ensemble(n_neurons=7000, dimensions=7, radius=0.5,neuron_type=nengo.Direct()) #This node works with direct mode
Peval=np.abs(np.random.normal(loc=0.0, scale=0.1, size=[3000,7]))
self.P = nengo.Ensemble(n_neurons=10000, dimensions=7, radius=0.5,eval_points=Peval)
self.Ex_n=nengo.Node(self.Q_est);self.Ez_n=nengo.Node(self.R_est);
self.ONE=nengo.Node(output=lambda t:[t<0.002,0,t<0.002]);
nengo.Connection(self.ONE,self.P[4:],synapse=None);
nengo.Connection(self.Ex_n,self.P[:2],transform=[[1],[1]],synapse=None);
nengo.Connection(self.Ez_n,self.P[2:4],transform=[[1],[1]],synapse=None);
nengo.Connection(self.P,self.P[4:],function=getP,synapse=taup)
nengo.Connection(self.P,self.upd2[4:],transform=30,function=prod3,synapse=taup)
nengo.Connection(self.upd2,self.pred,transform=(1/30)*np.eye(4),function=gain_func3,synapse=taup)
model = nengo.Network(seed=0)
model.config[nengo.Ensemble].neuron_type = nengo.Direct() # to run with direct mode
#model.config[nengo.Ensemble].neuron_type = nengo.LIFRate()
m_gain=2; #Scaling constant =2
with model:
tau=0.001
controller = CtrlNetwork(seed=2)
env = MassNetwork(mass=1,seed=1,xo=5,yo=0) #xo, yo are the initial values of the mass
x_target = nengo.Node(0.0) # Target x value
y_target = nengo.Node(7.0) # Target y value
nengo.Connection(x_target, controller.xd, synapse=None)
nengo.Connection(y_target, controller.yd, synapse=None)
xd_target = nengo.Node(None, size_in=1)
yd_target = nengo.Node(None, size_in=1)
nengo.Connection(xd_target,controller.xdot_d,synapse=tau)
nengo.Connection(yd_target,controller.ydot_d,synapse=tau)
nengo.Connection(x_target, env.xd, synapse=None)
nengo.Connection(y_target, env.yd, synapse=None)
nengo.Connection(controller.u[0],env.ux,transform=m_gain,synapse=None)
nengo.Connection(controller.u[1],env.uy,transform=m_gain,synapse=None)
nengo.Connection(env.x,controller.x,synapse=None)
nengo.Connection(env.y,controller.y,synapse=None)
nengo.Connection(env.dx,controller.dx,synapse=None)
nengo.Connection(env.dy,controller.dy,synapse=None)
#%% Kalman Filter
kf = Estimate_Network(seed=2)
noise = nengo.Node(nengo.processes.WhiteSignal(1, high=25,rms=0.25, seed=0), size_out=4)
nengo.Connection(noise,kf.y,synapse=tau);
nengo.Connection(controller.u,kf.u,synapse=None)
nengo.Connection(env.x, kf.y[0], synapse=tau)
nengo.Connection(env.y, kf.y[1], synapse=tau)
nengo.Connection(env.dx, kf.y[2], synapse=tau)
nengo.Connection(env.dy, kf.y[3], synapse=tau)
#%%
xp = nengo.Probe(env.x)
yp = nengo.Probe(env.y)
dxp = nengo.Probe(env.dx)
dyp = nengo.Probe(env.dy)
predp = nengo.Probe(kf.pred,synapse=0.01)
upp = nengo.Probe(kf.upd2,synapse=0.01)
obsp = nengo.Probe(kf.y,synapse=0.01)
ctrlp = nengo.Probe(controller.u,synapse=0.01)
ctrlkf = nengo.Probe(kf.u,synapse=0.01)
check = nengo.Probe(kf.P,synapse=0.01)
with nengo.Simulator(model) as sim:
sim.run(1.5)
#%%
import matplotlib.pyplot as plt
plt.figure()
plt.title('model probe')
plt.plot(sim.trange(),sim.data[xp],'b',alpha=0.5)
plt.plot(sim.trange(),sim.data[yp],'r',alpha=0.5)
plt.plot(sim.trange(),sim.data[dxp],'g',alpha=0.5)
plt.plot(sim.trange(),sim.data[dyp],'k',alpha=0.5)
plt.title('predict probe')
plt.plot(sim.trange(), sim.data[obsp][:,0],'b',alpha=0.5)
plt.plot(sim.trange(), sim.data[obsp][:,1],'r',alpha=0.5)
plt.plot(sim.trange(), sim.data[obsp][:,2],'g',alpha=0.5)
plt.plot(sim.trange(), sim.data[obsp][:,3],'k',alpha=0.5)
"""
"""
#plt.figure()
plt.title('States')
plt.plot(sim.trange(), sim.data[predp][:,0],'b',label='x')
plt.plot(sim.trange(), sim.data[predp][:,1],'r',label='y')
plt.plot(sim.trange(), sim.data[predp][:,2],'g',label='xvel')
plt.plot(sim.trange(), sim.data[predp][:,3],'k',label='yvel');
plt.legend();
plt.show()
#%%
plt.figure()
plt.title('Control')
plt.plot(sim.trange(), sim.data[ctrlp][:,0],'b')
plt.plot(sim.trange(), sim.data[ctrlp][:,1],'r')
plt.plot(sim.trange(), sim.data[ctrlkf][:,0],'b',alpha=0.5)
plt.plot(sim.trange(), sim.data[ctrlkf][:,1],'r',alpha=0.5)
plt.show()
#%%
"""
plt.figure()
plt.title('upd2')
plt.plot(sim.trange(), sim.data[upp][:,0],'b--')
plt.plot(sim.trange(), sim.data[upp][:,1],'r--')
plt.plot(sim.trange(), sim.data[upp][:,2],'g--')
plt.plot(sim.trange(), sim.data[upp][:,3],'k--')
plt.figure()
plt.title('Kgains')
plt.plot(sim.trange(), sim.data[upp][:,4],'b')
plt.plot(sim.trange(), sim.data[upp][:,5],'r')
plt.plot(sim.trange(), sim.data[upp][:,6],'g')
plt.figure()
plt.plot(sim.trange(), sim.data[check][:,4],'b')
plt.plot(sim.trange(), sim.data[check][:,5],'r')
plt.plot(sim.trange(), sim.data[check][:,6],'g')
plt.plot(sim.trange(), sim.data[check][:,:4],'b')
#"""
#%% XY prane trajectory plot
plt.figure(figsize=(6,6))
plt.plot(0,0,'ko')
plt.title("Initialized at origin")
plt.plot(sim.data[xp],sim.data[yp],label='Actual')
plt.plot(sim.data[obsp][:,0],sim.data[obsp][:,1],label='Observation')
plt.plot(sim.data[predp][:,0],sim.data[predp][:,1],label='Prediction')
plt.legend();plt.show();plt.axis('equal')