working version of MPC controller

This commit is contained in:
Simon Pirkelmann 2019-06-13 13:18:46 +02:00
parent f100f21162
commit b8927cf1c5
3 changed files with 267 additions and 126 deletions

View File

@ -54,46 +54,64 @@ class Robot:
print("connected!")
listening = True
while listening:
# expected data: '(u1, u2)'\n"
# expected data: '(t, u1, u2)'\n"
# where ui = control for motor i
# ui \in [-1.0, 1.0]
try:
data = comm_socket.readline()
data_str = data.decode()
#print("Data received: {}".format(data_str))
#print("processing data = {}".format(data_str))
print("Data received: {}".format(data_str))
print("processing data = {}".format(data_str))
l = data_str.strip('()\n').split(',')
#print("l = {}".format(l))
u1 = int(float(l[0])*100)
#print("u1 = {}".format(u1))
u2 = int(float(l[1])*100)
#print("u2 = {}".format(u2))
print("l = {}".format(l))
t = float(l[0])
print("t = {}".format(t))
u1 = int(float(l[1])*100)
print("u1 = {}".format(u1))
u2 = int(float(l[2])*100)
print("u2 = {}".format(u2))
except ValueError:
print("ValueError: Data has wrong format.")
print("Data received: {}".format(data_str))
print("Shutting down ...")
u1 = u2 = 0
t = 0.0
listening = False
except IndexError:
print("IndexError: Data has wrong format.")
print("Data received: {}".format(data_str))
print("Shutting down ...")
u1 = u2 = 0
listening = False
except Exception as e:
print("Some other error occured")
print("Exception: {}".format(e))
print("Shutting down ...")
u1 = u2 = 0
listening = False
finally:
self.m1.speed(u1)
self.m2.speed(u2)
comm_socket.close()
socket.close()
del comm_socket
del socket
print("disconnected!")
except IndexError:
print("IndexError: Data has wrong format.")
print("Data received: {}".format(data_str))
print("Shutting down ...")
u1 = u2 = 0
t = 0.0
listening = False
comm_socket.close()
socket.close()
del comm_socket
del socket
print("disconnected!")
except Exception as e:
print("Some other error occured")
print("Exception: {}".format(e))
print("Shutting down ...")
u1 = u2 = 0
t = 0.0
listening = False
comm_socket.close()
socket.close()
del comm_socket
del socket
print("disconnected!")
finally:
self.m1.speed(u1)
self.m2.speed(u2)
time.sleep(t)
self.m1.speed(0)
self.m2.speed(0)
wall_e = Robot()
wall_e.remote_control()

View File

@ -1,13 +1,14 @@
from casadi import *
import time
# look at: https://github.com/casadi/casadi/blob/master/docs/examples/python/vdp_indirect_multiple_shooting.py
class OpenLoopSolver:
def __init__(self, N=60, T=6.0):
def __init__(self, N=20, T=2.0):
self.T = T
self.N = N
def solve(self, x0):
def setup(self):
x = SX.sym('x')
y = SX.sym('y')
theta = SX.sym('theta')
@ -15,29 +16,31 @@ class OpenLoopSolver:
r = 0.03
R = 0.05
d = 0.02
omega_max = 13.32
omegar = SX.sym('omegar')
omegal = SX.sym('omegal')
control = vertcat(omegar, omegal)
# model equation
f1 = (r / 2 * cos(theta) - r * d / (2 * R) * sin(theta)) * omegar + (r / 2 * cos(theta) + r * d / (2 * R) * sin(
theta)) * omegal
f2 = (r / 2 * sin(theta) + r * d / (2 * R) * cos(theta)) * omegar + (r / 2 * sin(theta) - r * d / (2 * R) * cos(
theta)) * omegal
f3 = r / (2 * R) * omegar - r / (2 * R) * omegal
f1 = (r / 2 * cos(theta) - r * d / (2 * R) * sin(theta)) * omegar * omega_max + (r / 2 * cos(theta) + r * d / (2 * R) * sin(
theta)) * omegal * omega_max
f2 = (r / 2 * sin(theta) + r * d / (2 * R) * cos(theta)) * omegar * omega_max + (r / 2 * sin(theta) - r * d / (2 * R) * cos(
theta)) * omegal * omega_max
f3 = -(r / (2 * R) * omegar - r / (2 * R) * omegal) * omega_max
xdot = vertcat(f1, f2, f3)
f = Function('f', [x, y, theta, omegar, omegal], [f1, f2, f3])
print("f = {}".format(f))
# cost functional
L = x ** 2 + y ** 2 + 1e-2 * theta ** 2 + 1e-4 * (omegar ** 2 + omegal ** 2)
target = (-0.0, 0.0)
L = (x-target[0]) ** 2 + (y-target[1]) ** 2 + 1e-2 * theta ** 2 + 1e-2 * (omegar ** 2 + omegal ** 2)
# Fixed step Runge-Kutta 4 integrator
M = 4 # RK4 steps per interval
DT = self.T / self.N / M
print("DT = {}".format(DT))
f = Function('f', [state, control], [xdot, L])
self.f = Function('f', [state, control], [xdot, L])
X0 = MX.sym('X0', 3)
U = MX.sym('U', 2)
X = X0
@ -45,10 +48,10 @@ class OpenLoopSolver:
runge_kutta = True
if runge_kutta:
for j in range(M):
k1, k1_q = f(X, U)
k2, k2_q = f(X + DT / 2 * k1, U)
k3, k3_q = f(X + DT / 2 * k2, U)
k4, k4_q = f(X + DT * k3, U)
k1, k1_q = self.f(X, U)
k2, k2_q = self.f(X + DT / 2 * k1, U)
k3, k3_q = self.f(X + DT / 2 * k2, U)
k4, k4_q = self.f(X + DT * k3, U)
X = X + DT / 6 * (k1 + 2 * k2 + 2 * k3 + k4)
Q = Q + DT / 6 * (k1_q + 2 * k2_q + 2 * k3_q + k4_q)
else:
@ -75,37 +78,38 @@ class OpenLoopSolver:
ubg = []
# Formulate the NLP
Xk = MX(x0)
for k in range(self.N):
# New NLP variable for the control
U1k = MX.sym('U1_' + str(k), 2)
# U2k = MX.sym('U2_' + str(k))
w += [U1k]
lbw += [-10, -10]
ubw += [10, 10]
w0 += [0, 0]
# Integrate till the end of the interval
Fk = F(x0=Xk, p=U1k)
Xk = Fk['xf']
J = J + Fk['qf']
# Add inequality constraint
# g += [Xk[1]]
# lbg += [-.0]
# ubg += [inf]
# Create an NLP solver
prob = {'f': J, 'x': vertcat(*w), 'g': vertcat(*g)}
self.solver = nlpsol('solver', 'ipopt', prob)
# Xk = MX(x0)
# for k in range(self.N):
# # New NLP variable for the control
# U1k = MX.sym('U1_' + str(k), 2)
# # U2k = MX.sym('U2_' + str(k))
# w += [U1k]
# lbw += [-0.5, -0.5]
# ubw += [0.5, 0.5]
# w0 += [0, 0]
#
# # Integrate till the end of the interval
# Fk = F(x0=Xk, p=U1k)
# Xk = Fk['xf']
# J = J + Fk['qf']
#
# # Add inequality constraint
# # g += [Xk[1]]
# # lbg += [-.0]
# # ubg += [inf]
#
# # Create an NLP solver
# prob = {'f': J, 'x': vertcat(*w), 'g': vertcat(*g)}
# self.solver = nlpsol('solver', 'ipopt', prob)
# Solve the NLP
if False:
sol = self.solver(x0=w0, lbx=lbw, ubx=ubw, lbg=lbg, ubg=ubg)
w_opt = sol['x']
# Plot the solution
u_opt = w_opt
x_opt = [x0]
x_opt = [self.x0]
for k in range(self.N):
Fk = F(x0=x_opt[-1], p=u_opt[2*k:2*k+2])
x_opt += [Fk['xf'].full()]
@ -114,88 +118,140 @@ class OpenLoopSolver:
x3_opt = [r[2] for r in x_opt]
tgrid = [self.T/self.N*k for k in range(self.N+1)]
import matplotlib.pyplot as plt
plt.figure(2)
plt.clf()
plt.plot(tgrid, x1_opt, '--')
plt.plot(tgrid, x2_opt, '-')
plt.plot(tgrid, x3_opt, '*')
#import matplotlib.pyplot as plt
#plt.figure(2)
#plt.clf()
#plt.plot(tgrid, x1_opt, '--')
#plt.plot(tgrid, x2_opt, '-')
#plt.plot(tgrid, x3_opt, '*')
#plt.step(tgrid, vertcat(DM.nan(1), u_opt), '-.')
plt.xlabel('t')
plt.legend(['x1','x2','x3','u'])
plt.grid()
#plt.xlabel('t')
#plt.legend(['x1','x2','x3','u'])
#plt.grid()
#plt.show()
#return
# alternative solution using multiple shooting (way faster!)
opti = Opti() # Optimization problem
self.opti = Opti() # Optimization problem
# ---- decision variables ---------
X = opti.variable(3,self.N+1) # state trajectory
Q = opti.variable(1,self.N+1) # state trajectory
posx = X[0,:]
posy = X[1,:]
angle = X[2,:]
U = opti.variable(2,self.N) # control trajectory (throttle)
#T = opti.variable() # final time
self.X = self.opti.variable(3,self.N+1) # state trajectory
self.Q = self.opti.variable(1,self.N+1) # state trajectory
self.U = self.opti.variable(2,self.N) # control trajectory (throttle)
#T = self.opti.variable() # final time
# ---- objective ---------
#opti.minimize(T) # race in minimal time
#self.opti.minimize(T) # race in minimal time
# ---- dynamic constraints --------
#f = lambda x,u: vertcat(f1, f2, f3) # dx/dt = f(x,u)
# ---- initial values for solver ---
#self.opti.set_initial(speed, 1)
#self.opti.set_initial(T, 1)
def solve(self, x0, target):
tstart = time.time()
x = SX.sym('x')
y = SX.sym('y')
theta = SX.sym('theta')
state = vertcat(x, y, theta)
r = 0.03
R = 0.05
d = 0.02
omega_max = 13.32
omegar = SX.sym('omegar')
omegal = SX.sym('omegal')
control = vertcat(omegar, omegal)
# model equation
f1 = (r / 2 * cos(theta) - r * d / (2 * R) * sin(theta)) * omegar * omega_max + (r / 2 * cos(theta) + r * d / (
2 * R) * sin(
theta)) * omegal * omega_max
f2 = (r / 2 * sin(theta) + r * d / (2 * R) * cos(theta)) * omegar * omega_max + (r / 2 * sin(theta) - r * d / (
2 * R) * cos(
theta)) * omegal * omega_max
f3 = -(r / (2 * R) * omegar - r / (2 * R) * omegal) * omega_max
xdot = vertcat(f1, f2, f3)
L = (x - target[0]) ** 2 + (y - target[1]) ** 2 + 1e-2 * theta ** 2 + 1e-2 * (omegar ** 2 + omegal ** 2)
self.f = Function('f', [state, control], [xdot, L])
# ---- solve NLP ------
# set numerical backend
# delete constraints
self.opti.subject_to()
# add new constraints
dt = self.T / self.N # length of a control interval
for k in range(self.N): # loop over control intervals
# Runge-Kutta 4 integration
k1, k1_q = f(X[:,k], U[:,k])
k2, k2_q = f(X[:,k]+dt/2*k1, U[:,k])
k3, k3_q = f(X[:,k]+dt/2*k2, U[:,k])
k4, k4_q = f(X[:,k]+dt*k3, U[:,k])
x_next = X[:,k] + dt/6*(k1+2*k2+2*k3+k4)
q_next = Q[:,k] + dt/6*(k1_q + 2 * k2_q + 2 * k3_q + k4_q)
opti.subject_to(X[:,k+1]==x_next) # close the gaps
opti.subject_to(Q[:,k+1]==q_next) # close the gaps
opti.minimize(Q[:,self.N])
k1, k1_q = self.f(self.X[:, k], self.U[:, k])
k2, k2_q = self.f(self.X[:, k] + dt / 2 * k1, self.U[:, k])
k3, k3_q = self.f(self.X[:, k] + dt / 2 * k2, self.U[:, k])
k4, k4_q = self.f(self.X[:, k] + dt * k3, self.U[:, k])
x_next = self.X[:, k] + dt / 6 * (k1 + 2 * k2 + 2 * k3 + k4)
q_next = self.Q[:, k] + dt / 6 * (k1_q + 2 * k2_q + 2 * k3_q + k4_q)
self.opti.subject_to(self.X[:, k + 1] == x_next) # close the gaps
self.opti.subject_to(self.Q[:, k + 1] == q_next) # close the gaps
self.opti.minimize(self.Q[:, self.N])
# ---- path constraints -----------
# limit = lambda pos: 1-sin(2*pi*pos)/2
#opti.subject_to(speed<=limit(pos)) # track speed limit
opti.subject_to(opti.bounded(-10,U,10)) # control is limited
# self.opti.subject_to(speed<=limit(pos)) # track speed limit
self.opti.subject_to(self.opti.bounded(-0.5, self.U, 0.5)) # control is limited
# ---- boundary conditions --------
opti.subject_to(posx[0]==x0[0]) # start at position 0 ...
opti.subject_to(posy[0]==x0[1]) # ... from stand-still
opti.subject_to(angle[0]==x0[2]) # finish line at position 1
#opti.subject_to(speed[-1]==0) # .. with speed 0
opti.subject_to(Q[:,0]==0.0)
# self.opti.subject_to(speed[-1]==0) # .. with speed 0
self.opti.subject_to(self.Q[:, 0] == 0.0)
self.opti.solver("ipopt")
# ---- misc. constraints ----------
#opti.subject_to(X[1,:]>=0) # Time must be positive
#opti.subject_to(X[2,:]<=4) # Time must be positive
#opti.subject_to(X[2,:]>=-2) # Time must be positive
# self.opti.subject_to(X[1,:]>=0) # Time must be positive
# self.opti.subject_to(X[2,:]<=4) # Time must be positive
# self.opti.subject_to(X[2,:]>=-2) # Time must be positive
# avoid obstacle
# r = 0.25
# p = (0.5, 0.5)
# for k in range(self.N):
# opti.subject_to((X[0,k]-p[0])**2 + (X[1,k]-p[1])**2 > r**2)
# self.opti.subject_to((X[0,k]-p[0])**2 + (X[1,k]-p[1])**2 > r**2)
# pass
posx = self.X[0, :]
posy = self.X[1, :]
angle = self.X[2, :]
self.opti.subject_to(posx[0] == x0[0]) # start at position 0 ...
self.opti.subject_to(posy[0] == x0[1]) # ... from stand-still
self.opti.subject_to(angle[0] == x0[2]) # finish line at position 1
tend = time.time()
# ---- initial values for solver ---
#opti.set_initial(speed, 1)
#opti.set_initial(T, 1)
print("setting up problem took {} seconds".format(tend - tstart))
# ---- solve NLP ------
opti.solver("ipopt") # set numerical backend
sol = opti.solve() # actual solve
sol = self.opti.solve() # actual solve
#x0 = sol.value(opti.x)
#lam_g0 = sol.value(opti.lam_g)
#opti.set_initial(opti.lam_g, lam_g0)
#opti.set_initial(opti.x, x0)
#opti.solve()
#x0 = sol.value(self.opti.x)
#u_opt_1 = map(lambda x: float(x), [u_opt[i * 2] for i in range(0, 60)])
#u_opt_2 = map(lambda x: float(x), [u_opt[i * 2 + 1] for i in range(0, 60)])
u_opt_1 = sol.value(self.U[0,:])
u_opt_2 = sol.value(self.U[1,:])
return (u_opt_1, u_opt_2)
#lam_g0 = sol.value(self.opti.lam_g)
#self.opti.set_initial(self.opti.lam_g, lam_g0)
#self.opti.set_initial(self.opti.x, x0)
#self.opti.solve()
from pylab import plot, step, figure, legend, show, spy
@ -206,8 +262,8 @@ class OpenLoopSolver:
plt.figure(3)
plot(sol.value(posx), sol.value(posy))
ax = plt.gca()
circle = plt.Circle(p, r)
ax.add_artist(circle)
#circle = plt.Circle(p, r)
#ax.add_artist(circle)
#plot(limit(sol.value(pos)),'r--',label="speed limit")
#step(range(N),sol.value(U),'k',label="throttle")
legend(loc="upper left")

View File

@ -11,6 +11,7 @@ import pygame
import numpy as np
import socket
import scipy.integrate
import copy
import threading
from copy import deepcopy
@ -118,8 +119,12 @@ class RemoteController:
self.dirs, = self.ax.plot([], [])
plt.xlabel('x-position')
plt.ylabel('y-position')
plt.grid()
self.ols = OpenLoopSolver()
self.ols.setup()
self.target = (0.0, 0.0)
def ani(self):
self.ani = anim.FuncAnimation(self.fig, init_func=self.ani_init, func=self.ani_update, interval=10, blit=True)
@ -207,6 +212,9 @@ class RemoteController:
self.mutex.release()
def controller(self):
tgrid = None
us1 = None
us2 = None
print("starting control")
while True:
@ -342,7 +350,66 @@ class RemoteController:
for event in events:
if event.type == pygame.KEYDOWN:
if event.key == pygame.K_UP:
self.ols.solve(self.xms[-1])
self.controlling = True
elif event.key == pygame.K_DOWN:
self.controlling = False
self.rc_socket.send('(0.0,0.0)\n')
elif event.key == pygame.K_0:
self.target = (0.0, 0.0)
elif event.key == pygame.K_1:
self.target = (0.5,0.5)
elif event.key == pygame.K_2:
self.target = (0.5, -0.5)
elif event.key == pygame.K_3:
self.target = (-0.5,-0.5)
elif event.key == pygame.K_4:
self.target = (-0.5,0.5)
if self.controlling:
tmpc_start = time.time()
# get measurement
last_measurement = copy.deepcopy(self.xms[-1])
res = self.ols.solve(last_measurement, self.target)
#tgrid = res[0]
us1 = res[0]
us2 = res[1]
# tt = 0
# x = last_measurement
# t_ol = np.array([tt])
# x_ol = np.array([x])
# # compute open loop prediction
# for i in range(len(us1)):
# r = scipy.integrate.ode(f_ode)
# r.set_f_params(np.array([us1[i] * 13.32, us2[i] * 13.32]))
# r.set_initial_value(x, tt)
#
# tt = tt + 0.1
# x = r.integrate(tt)
#
# t_ol = np.vstack((t_ol, tt))
# x_ol = np.vstack((x_ol, x))
#plt.figure(4)
#plt.plot(x_ol[:,0], x_ol[:,1])
#if event.key == pygame.K_DOWN:
# if tgrid is not None:
tmpc_end = time.time()
print("---------------- mpc solution took {} seconds".format(tmpc_end-tmpc_start))
for i in range(0, 1):
u1 = us1[i]
u2 = us2[i]
dt_mpc = time.time() - self.t
#if dt_mpc < 0.1:
# time.sleep(0.1 - dt_mpc)
self.rc_socket.send('({},{},{})\n'.format(0.1,u1, u2))
self.t = time.time()
time.sleep(0.01)
#
pass
def main(args):
rospy.init_node('controller_node', anonymous=True)