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passivity_control.py
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passivity_control.py
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#!/usr/bin/env python
import numpy as np
import scipy as sci
import pandas as pd
import sys
import csv
import rospy
from numpy import linalg
from scipy import linalg
from scipy.integrate import odeint
from matplotlib import pyplot as plt
np.set_printoptions(threshold=sys.maxsize)
np.set_printoptions(precision=6)
class Adaptive_Control:
def __init__(self):
self.m1 = 4.0
self.m2 = 4.0
self.L1 = 2.5
self.L2 = 1.5
self.J1 = (1.0/12.0)*self.m1*self.L1**2
self.J2 = (1.0/12.0)*self.m2*self.L2**2
self.Lc1 = self.L1/2
self.Lc2 = self.L2/2
self.k = 1 #signal amplitude
self.ke = 1 #passivity gain
self.k_gamma = 1 #adaptive gain
self.kD = 1 #Controller gain
self.k_S = 1
self.w = 1
self.gamma = self.k_gamma*np.identity(5)
self.K = self.kD*np.identity(2)
self.L = self.ke*np.identity(2)
self.g_const = 9.81
self.Ks = self.k_S*np.identity(2)
self.theta_star = np.array([[self.m1*self.Lc1**2 + self.m2*(self.L1**2 + self.Lc2**2) + self.J1 + self.J2,
self.m2*self.Lc2**2 + self.J2,
self.m2*self.L1*self.Lc2,
self.m1*self.Lc1 + self.m2*self.L1,
self.m2*self.L2]]).T
print(self.theta_star)
def computed_torque_ode(self, w, t, i):
'''
Defines the differential equations for the coupled spring-mass system.
w : vector of the state variables:
w[0] = q_dot_1 (joint velocity)
w[1] = q_dot_2
w[2] = q_1 (joint position)
w[3] = q_2
'''
z = 0.5
a = self.k*np.sin(self.w*t)
b = self.k*np.sin(0.5*self.w*t)
c = self.k*np.sin(0.3*self.w*t)
d = self.k*np.sin(0.4*self.w*t)
dz = 0
da = self.k*self.w*np.cos(self.w*t)
db = 0.5*self.k*self.w*np.cos(0.5*self.w*t)
dc = 0.3*self.k*self.w*np.cos(0.3*self.w*t)
dd = 0.4*self.k*self.w*np.cos(0.4*self.w*t)
ddz = 0
dda = -self.k*(self.w**2)*np.sin(self.w*t)
ddb = -0.25*self.k*(self.w**2)*np.sin(0.5*self.w*t)
ddc = -0.09*self.k*(self.w**2)*np.sin(0.3*self.w*t)
ddd = -0.16*self.k*(self.w**2)*np.sin(0.4*self.w*t)
traj = np.array([z, a, a+b, a+b+c, a+b+c+d])
dtraj = np.array([dz, da, da+db, da+db+dc, da+db+dc+dd])
ddtraj = np.array([ddz, dda, dda+ddb, dda+ddb+ddc, dda+ddb+ddc+ddd])
q_d = np.array([[traj[i], traj[i]]]).T
q_dot_d = np.array([[dtraj[i], dtraj[i]]]).T
q_ddot_d = np.array([[ddtraj[i], ddtraj[i]]]).T
q = np.array([[w[2],w[3]]]).T
q_dot = np.array([[w[0],w[1]]]).T
e = q - q_d
e_dot = q_dot - q_dot_d
s = e_dot + self.Ks.dot(e)
v = q_dot_d - self.L.dot(e)
a = q_ddot_d - self.L.dot(e_dot)
#True Dynamic Model
d11 = self.Lc1**2 + self.m2*(self.L1**2+self.Lc2**2+2*self.L1*self.Lc2*np.cos(q[1,0])) + self.J1 + self.J2
d12 = self.m2*(self.Lc2**2+self.L1*self.Lc2*np.cos(q[1,0])) + self.J2
d21 = d12
d22 = self.m2*self.Lc2**2 + self.J2
h = -self.m2*self.L1*self.Lc2*np.sin(q[1,0])
c11 = h*q_dot[1,0]
c12 = h*(q_dot[1,0]+q_dot[0,0])
c21 = -h*q_dot[0,0]
c22 = 0
g1 = (self.m1*self.Lc1 + self.m2*self.L1)*self.g_const*np.cos(q[0,0]) + self.m2*self.Lc2*self.g_const*np.cos(q[0,0]+q[1,0])
g2 = self.m2*self.Lc2*self.g_const*np.cos(q[0,0]+q[1,0])
M = np.array([[d11,d12],[d21,d22]])
C = np.array([[c11,c12],[c21,c22]])
G = np.array([[g1,g2]]).T
#Compute Torque
tau = M.dot(a) + C.dot(v) + G - self.K.dot(s)
#Input to Robot
q_ddot = np.linalg.inv(M).dot(tau - C.dot(q_dot) - G)
dwdt = [q_ddot[0,0], q_ddot[1,0], q_dot[0,0], q_dot[1,0]]
return dwdt
def adaptive_ode(self, w, t, i, th):
'''
Defines the differential equations for the coupled spring-mass system.
w : vector of the state variables:
w[0] = theta_1,
w[1] = theta_2,
w[2] = theta_3,
w[3] = theta_4,
w[4] = theta_5,
w[5] = q_dot_1 (joint velocity)
w[6] = q_dot_2
w[7] = q_1 (joint position)
w[8] = q_2
'''
z = 0.5
a = self.k*np.sin(self.w*t)
b = self.k*np.sin(0.5*self.w*t)
c = self.k*np.sin(0.3*self.w*t)
d = self.k*np.sin(0.4*self.w*t)
dz = 0
da = self.k*self.w*np.cos(self.w*t)
db = 0.5*self.k*self.w*np.cos(0.5*self.w*t)
dc = 0.3*self.k*self.w*np.cos(0.3*self.w*t)
dd = 0.4*self.k*self.w*np.cos(0.4*self.w*t)
ddz = 0
dda = -self.k*(self.w**2)*np.sin(self.w*t)
ddb = -0.25*self.k*(self.w**2)*np.sin(0.5*self.w*t)
ddc = -0.09*self.k*(self.w**2)*np.sin(0.3*self.w*t)
ddd = -0.16*self.k*(self.w**2)*np.sin(0.4*self.w*t)
traj = np.array([z, a, a+b, a+b+c, a+b+c+d])
dtraj = np.array([dz, da, da+db, da+db+dc, da+db+dc+dd])
ddtraj = np.array([ddz, dda, dda+ddb, dda+ddb+ddc, dda+ddb+ddc+ddd])
q_d = np.array([[traj[i], traj[i]]]).T
q_dot_d = np.array([[dtraj[i], dtraj[i]]]).T
q_ddot_d = np.array([[ddtraj[i], ddtraj[i]]]).T
q = np.array([[w[7],w[8]]]).T
q_dot = np.array([[w[5],w[6]]]).T
e = q - q_d
e_dot = q_dot - q_dot_d
s = e_dot + self.Ks.dot(e)
v = q_dot_d - self.L.dot(e)
a = q_ddot_d - self.L.dot(e_dot)
#Parameter Adaptation
theta_hat = np.array([[w[0], w[1], w[2], w[3], w[4]]]).T
Y = np.array([[a[0,0], a[1,0], np.cos(q[1,0])*(2*a[0,0]+a[1,0]) - q_dot[1,0]*np.sin(q[1,0])*v[0,0] - (q_dot[0,0]+q_dot[1,0])*np.sin(q[1,0])*v[0,0] , self.g_const*np.cos(q[0,0]), self.g_const*np.cos(q[0,0]+q[1,0])],
[0, a[0,0]+a[1,0] , np.cos(q[1,0])*a[0,0]+np.sin(q[1,0])*q_dot[0,0]*v[0,0] , 0, self.g_const*np.cos(q[0,0]+q[1,0]) ]])
theta_hat_dot = -(np.linalg.inv(self.gamma).dot(Y.T)).dot(s)
tau = Y.dot(theta_hat) - self.K.dot(s)
#True Dynamic Model
d11 = self.Lc1**2 + self.m2*(self.L1**2+self.Lc2**2+2*self.L1*self.Lc2*np.cos(q[1,0])) + self.J1 + self.J2
d12 = self.m2*(self.Lc2**2+self.L1*self.Lc2*np.cos(q[1,0])) + self.J2
d21 = d12
d22 = self.m2*self.Lc2**2 + self.J2
h = -self.m2*self.L1*self.Lc2*np.sin(q[1,0])
c11 = h*q_dot[1,0]
c12 = h*(q_dot[1,0]+q_dot[0,0])
c21 = -h*q_dot[0,0]
c22 = 0
g1 = (self.m1*self.Lc1 + self.m2*self.L1)*self.g_const*np.cos(q[0,0]) + self.m2*self.Lc2*self.g_const*np.cos(q[0,0]+q[1,0])
g2 = self.m2*self.Lc2*self.g_const*np.cos(q[0,0]+q[1,0])
M = np.array([[d11,d12],[d21,d22]])
C = np.array([[c11,c12],[c21,c22]])
G = np.array([[g1,g2]]).T
#Input to Robot
q_ddot = np.linalg.inv(M).dot(tau - C.dot(q_dot) - G)
dwdt = [theta_hat_dot[0,0], theta_hat_dot[1,0], theta_hat_dot[2,0], theta_hat_dot[3,0], theta_hat_dot[4,0],
q_ddot[0,0], q_ddot[1,0], q_dot[0,0], q_dot[1,0]]
return dwdt
def adaptive_simulation(self):
theta_1 = 0.0
theta_2 = 0.0
theta_3 = 0.0
theta_4 = 0.0
theta_5 = 0.0
q_dot_1 = 0.0
q_dot_2 = 0.0
q_1 = 0.0
q_2 = 0.0
# ODE solver parameters
abserr = 1.0e-8
relerr = 1.0e-6
stoptime = 100
numpoints = 250
theta_0 = 1.2*self.theta_star
t = [stoptime * float(i) / (numpoints - 1) for i in range(numpoints)]
w0 = [theta_0[0], theta_0[1], theta_0[2], theta_0[3], theta_0[4], q_dot_1, q_dot_2, q_1, q_2]
j = 0
for i in range(3):
wsol = odeint(self.adaptive_ode, w0, t, args =(i,self.theta_star), atol=abserr, rtol=relerr)
time = np.asarray(t)
data = np.asarray(wsol)
z = 0.5
a = self.k*np.sin(self.w*time)
b = self.k*np.sin(0.5*self.w*time)
c = self.k*np.sin(0.3*self.w*time)
d = self.k*np.sin(0.4*self.w*time)
dz = 0
da = self.k*self.w*np.cos(self.w*time)
db = 0.5*self.k*self.w*np.cos(0.5*self.w*time)
dc = 0.3*self.k*self.w*np.cos(0.3*self.w*time)
dd = 0.4*self.k*self.w*np.cos(0.4*self.w*time)
traj_des = np.array([z, a, a+b, a+b+c, a+b+c+d])
dtraj_des = np.array([dz, da, da+db, da+db+dc, da+db+dc+dd])
e = data[:,7] - traj_des[i]
e_dot = data[:,5] - dtraj_des[i]
s = (e_dot + e)[:,np.newaxis]
data = np.column_stack((data,s))
self.plot_adaptive_results(time,data,j)
j += 1
plt.show()
def ct_simulation(self):
q_dot_1 = 0.0
q_dot_2 = 0.0
q_1 = 0.0
q_2 = 0.0
# ODE solver parameters
abserr = 1.0e-8
relerr = 1.0e-6
stoptime = 100
numpoints = 200
t = [stoptime * float(i) / (numpoints - 1) for i in range(numpoints)]
w0 = [q_dot_1, q_dot_2, q_1, q_2]
j = 0
for i in range(1,3):
wsol = odeint(self.computed_torque_ode, w0, t, args =(i,), atol=abserr, rtol=relerr)
time = np.asarray(t)
data = np.asarray(wsol)
z = 0.5
a = self.k*np.sin(self.w*time)
b = self.k*np.sin(0.5*self.w*time)
c = self.k*np.sin(0.3*self.w*time)
d = self.k*np.sin(0.4*self.w*time)
dz = 0
da = self.k*self.w*np.cos(self.w*time)
db = 0.5*self.k*self.w*np.cos(0.5*self.w*time)
dc = 0.3*self.k*self.w*np.cos(0.3*self.w*time)
dd = 0.4*self.k*self.w*np.cos(0.4*self.w*time)
traj_des = np.array([z, a, a+b, a+b+c, a+b+c+d])
dtraj_des = np.array([dz, da, da+db, da+db+dc, da+db+dc+dd])
e = data[:,2] - traj_des[i]
e_dot = data[:,0] - dtraj_des[i]
s = (e_dot + e)[:,np.newaxis]
data = np.column_stack((data,s))
self.plot_ct_results(time,data,j)
j += 1
plt.show()
def plot_adaptive_results(self, time, data, i):
plt.subplot(3,2,2*i+1)
plt.plot(time,data[:,9])
plt.xlabel('t')
plt.ylabel('s')
plt.subplot(3,2,2*i+2)
plt.plot(time,data[:,0])
plt.plot(time,data[:,1])
plt.plot(time,data[:,2])
plt.plot(time,data[:,3])
plt.plot(time,data[:,4])
plt.xlabel('t')
plt.legend(['theta_1', 'theta_2', 'theta_3', 'theta_4', 'theta_5'])
def plot_ct_results(self, time, data, i):
plt.subplot(2,1,i+1)
plt.plot(time,data[:,4])
plt.xlabel('t')
plt.ylabel('s')
if __name__ == '__main__':
rospy.init_node("test_node", anonymous=True,disable_signals=True)
adapt = Adaptive_Control()
adapt.ct_simulation()
adapt.adaptive_simulation()