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cart.py
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import casadi as ca
import numpy as np
from matplotlib import pyplot as plt
import cv2
from PIL import Image
class cart():
def __init__(self):
self.opti = ca.Opti()
self.N = 200
self.d = 2.0
self.dmax = 20.0
self.umax = 20.0
self.pi = -np.pi
self.l = 0.5
self.m1 = 0.5
self.m2 = 0.1
self.g = -9.81
self.T = 2.0
self.h = self.T/self.N
goal1 = self.opti.parameter()
goal2 = self.opti.parameter()
goal3 = self.opti.parameter()
goal4 = self.opti.parameter()
self.opti.set_value(goal1,self.d)
self.opti.set_value(goal2,self.pi)
self.opti.set_value(goal3,0)
self.opti.set_value(goal4,0)
self.goal = [goal1,goal2,goal3,goal4]
self.q1 = self.opti.variable(self.N)
self.q2 = self.opti.variable(self.N)
self.q1_dot = self.opti.variable(self.N)
self.q2_dot = self.opti.variable(self.N)
self.u = self.opti.variable(self.N)
self.q1_ddot = (((self.l*self.m2*ca.sin(self.q2)*(self.q2**2))
+ (self.u) + (self.m2*self.g*ca.cos(self.q2)*ca.sin(self.q2)))
/(self.m1 + self.m2*(ca.sin(self.q2)**2)))
self.q2_ddot = (((self.l*self.m2*ca.cos(self.q2)*ca.sin(self.q2)*(self.q2_dot**2))
+ (self.u*ca.cos(self.q2)) + ((self.m1+self.m2)*self.g*ca.sin(self.q2)))
/(self.m1*self.l + self.l*self.m2*(ca.sin(self.q2)**2)))
self.state = ca.horzcat(self.q1,self.q2,self.q1_dot,self.q2_dot)
self.model = ca.horzcat(self.q1_dot,self.q2_dot,self.q1_ddot,self.q2_ddot)
class nlp_cart(cart):
def __init__(self,cart):
# self.x = ca.horzcat(cart.state,cart.u)#ca.vertcat(cart.state,cart.u)
cart.opti.minimize(self.getCost(cart.u,cart.N,cart.h))
cart.opti.subject_to(self.getConstraints(cart))
cart.opti.subject_to(self.getBounds(cart))
p_opts = {"expand":True}
s_opts = {"max_iter": 1000}
cart.opti.solver("ipopt",p_opts,s_opts)
self.initial = self.initalGuess(cart)
def initalGuess(self,cart):
ini = np.zeros((cart.N,5))
for i in range(cart.N):
cart.opti.set_initial(cart.state[i,0],(i/(cart.N - 1))*cart.d)
ini[i,0] = (i/(cart.N - 1))*cart.d
cart.opti.set_initial(cart.state[i,1],(i/(cart.N - 1))*cart.pi)
ini[i,1]=(i/(cart.N - 1))*cart.pi
cart.opti.set_initial(cart.state[i,2],cart.d/(cart.N - 1))
ini[i,2] = cart.d/(cart.N - 1)
cart.opti.set_initial(cart.state[i,3],cart.pi/(cart.N - 1))
ini[i,3] = cart.pi/(cart.N - 1)
cart.opti.set_initial(cart.u[i],0)
return ini
def getCost(self,u,N,h):
result = 0
for i in range(N-1): result += (h/2)*(u[i]**2 + u[i+1]**2)
return result
def getConstraints(self,cart):
ceq = []
for i in range(cart.N - 1):
ceq.append(self.getCollocationConstraints(cart.state[i,:],cart.state[i+1,:]
,cart.model[i,:],cart.model[i+1,:]
,cart.h))
ceq.extend(self.getBoundaryConstrainsts(cart.goal,cart.state[0,:],cart.state[-1,:]))
return ceq
def getCollocationConstraints(self,state1,state2,model1,model2,h):
return (((h/2)*(model2 + model1)) - (state2 - state1)==0)
def getBoundaryConstrainsts(self,goal,state1,state2):
ceq = []
for i in range(4): ceq.extend([(state1[i] == 0),((state2[i] - goal[i]) ==0)])
return ceq
def getBounds(self,cart):
c = []
c.extend([cart.opti.bounded(-cart.dmax,cart.state[:,0],cart.dmax),
cart.opti.bounded(cart.pi,cart.state[:,1],-cart.pi),
# cart.opti.bounded(-cart.d,cart.state[:,0],cart.d),
# cart.opti.bounded(-cart.d,cart.state[:,0],cart.d),
cart.opti.bounded(-cart.umax,cart.u[:],cart.umax)])
return c
mycart = cart()
ini = nlp_cart(mycart)
sol1 = mycart.opti.solve()
# # print(sol1.stats()["iter_count"])
pos = sol1.value(mycart.state[:,0])
ang = sol1.value(mycart.state[:,1])
u = sol1.value(mycart.u[:])
time = np.arange(0.0, mycart.T, mycart.h)
ball = 3
box = 1
rod = 2
d = {1: (255,175,0), #BGR format
2: (0,255,0),
3: (0,0,255)}
SIZE = 300
for i in range(len(pos)):
env = np.ones((SIZE,SIZE,3), dtype=np.uint8)
p1= pos[i]*50
ax= mycart.l*np.sin(ang[i])*100
ay = mycart.l*np.cos(ang[i])*100
ax = -ax.astype(np.int)
ay = ay.astype(np.int)
p = p1.astype(np.int)
# print(ang[i])
image = cv2.rectangle(env, (p+50 - 10,SIZE//2 - 3), (p+50+10 ,SIZE//2 + 3), d[box], -1)
image1 = cv2.line(image, (p+50,SIZE//2), (p+50 + ax, SIZE//2 + ay), d[rod], 1)
image2 = cv2.circle(image1, (p+50+ax,SIZE//2 +ay), 5, d[ball], -1)
img = Image.fromarray(image2, "RGB")
# img = img.resize((300,300))
cv2.imshow("", np.array(img))
status = cv2.imwrite(f'/home/shitwalker/PycharmProjects/Biped/animate/image-{i}.png', image2)
print(status)
if cv2.waitKey(10) & 0xFF == ord("q"):
break
fourcc = cv2.VideoWriter_fourcc('M','J','P','G')
out = cv2.VideoWriter('cartpole.avi', fourcc, 60.0, (300, 300))
for i in range(len(pos)):
img_path = f"/home/shitwalker/PycharmProjects/Biped/animate/image-{i}.png"
print(img_path)
frame = cv2.imread(img_path)
out.write(frame)
out.release()
name = ['position : x', 'angle : theta', 'controlForce : u']
plt.subplot(322)
plt.title('Optimised Solution')
plt.plot(time,pos)
plt.subplot(321)
plt.title('Initial Guess')
plt.plot(time,ini.initial[:,0],'r')
plt.ylabel(name[0])
plt.subplot(324)
plt.plot(time,ang)
plt.subplot(323)
plt.plot(time,ini.initial[:,1],'r')
plt.ylabel(name[1])
plt.subplot(326)
plt.plot(time,u)
plt.subplot(325)
plt.plot(time,ini.initial[:,4],'r')
plt.ylabel(name[2])
plt.suptitle('CartPole')
plt.show()