Created
August 3, 2021 21:25
-
-
Save jgillis/cc8b6ab7f1d174955dedd8ea7ab94a98 to your computer and use it in GitHub Desktop.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
import casadi | |
from casadi import * | |
from casadi.casadi import OPTI_INEQUALITY, Opti_bounded | |
import matplotlib.pyplot as plt | |
# https://epubs.siam.org/doi/pdf/10.1137/16M1062569 | |
m1 = 1 | |
m2 = 0.3 | |
g = 9.81 | |
l = 0.5 #pendulum length | |
dmax = 2.0 #max horiz distance | |
umax = 20.0 #max force | |
T = 2 #total time | |
d = 1 #horizontal distance | |
t0 = 0 | |
tf = 2 | |
plt.figure(1) | |
opti = casadi.Opti() | |
N = 25 # number of collocation points | |
h = (tf-t0) / (N-1) #step size | |
#states | |
x = opti.variable(4,N) #col vector of 4 vars | |
y1 = x[0,:] #cart pos | |
y2 = x[1,:] #pendulum position | |
ydot1 = x[2,:] | |
ydot2 = x[3,:] | |
u = opti.variable(1,N-1) | |
def f(x,u): | |
[y1,y2,ydot1,ydot2] =vertsplit(x) | |
dy1 = ydot1 | |
dy2 = ydot2 | |
dydot1 = ((l*m2*sin(y2)*ydot2**2) + u + (m2*g*cos(y2)*sin(y2))) / (m1 + m2*(1-cos(y2)**2)) | |
dydot2 = -1*((l*m2*cos(y2)*sin(y2)*ydot2**2) + u*cos(y2) + ((m1+m2)*g*sin(y2))) / (l*m1 + l*m2*(1-cos(y2)**2)) | |
return vertcat(dy1,dy2,dydot1,dydot2) | |
for k in range(N-1): | |
f1 = f(x[:,k+1],u[:,k]) | |
f0 = f(x[:,k],u[:,k]) | |
opti.subject_to(h/2*(f1+f0)==x[:,k+1]-x[:,k]) | |
#path | |
opti.subject_to(Opti_bounded(-dmax,y1,dmax)) | |
opti.subject_to(Opti_bounded(-umax,u,umax)) | |
x_goal = vertcat(d,pi,0,0) | |
# Bound Constraints | |
opti.subject_to(x[:,0] == 0) | |
opti.subject_to(x[:,-1] == x_goal) | |
print(repmat(x_goal,1,N)*repmat(linspace(0,1,N).T,4,1)) | |
#Guess | |
opti.set_initial(x,repmat(x_goal,1,N)*repmat(linspace(0,1,N).T,4,1)) #initial guess | |
sol = opti.minimize(sumsqr(u)) | |
s_opts = {"ipopt.tol": 1e-6, "expand":True} | |
opti.solver('ipopt',s_opts); # set numerical backend | |
sol = opti.solve(); #actual solve | |
plt.figure(1) | |
t1 = linspace(t0,tf,N-1) | |
print(sol) | |
plt.plot(t1,sol.value(u)) | |
plt.figure(2) | |
t1 = linspace(t0,tf,N) | |
print(sol.value(x).T) | |
plt.plot(t1,sol.value(x).T) | |
plt.show() | |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment