working version of MPC controller
This commit is contained in:
parent
f100f21162
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b8927cf1c5
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@ -54,46 +54,64 @@ class Robot:
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print("connected!")
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listening = True
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while listening:
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# expected data: '(u1, u2)'\n"
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# expected data: '(t, u1, u2)'\n"
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# where ui = control for motor i
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# ui \in [-1.0, 1.0]
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try:
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data = comm_socket.readline()
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data_str = data.decode()
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#print("Data received: {}".format(data_str))
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#print("processing data = {}".format(data_str))
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print("Data received: {}".format(data_str))
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print("processing data = {}".format(data_str))
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l = data_str.strip('()\n').split(',')
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#print("l = {}".format(l))
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u1 = int(float(l[0])*100)
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#print("u1 = {}".format(u1))
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u2 = int(float(l[1])*100)
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#print("u2 = {}".format(u2))
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print("l = {}".format(l))
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t = float(l[0])
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print("t = {}".format(t))
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u1 = int(float(l[1])*100)
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print("u1 = {}".format(u1))
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u2 = int(float(l[2])*100)
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print("u2 = {}".format(u2))
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except ValueError:
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print("ValueError: Data has wrong format.")
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print("Data received: {}".format(data_str))
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print("Shutting down ...")
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u1 = u2 = 0
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t = 0.0
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listening = False
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comm_socket.close()
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socket.close()
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del comm_socket
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del socket
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print("disconnected!")
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except IndexError:
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print("IndexError: Data has wrong format.")
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print("Data received: {}".format(data_str))
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print("Shutting down ...")
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u1 = u2 = 0
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t = 0.0
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listening = False
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comm_socket.close()
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socket.close()
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del comm_socket
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del socket
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print("disconnected!")
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except Exception as e:
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print("Some other error occured")
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print("Exception: {}".format(e))
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print("Shutting down ...")
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u1 = u2 = 0
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t = 0.0
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listening = False
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comm_socket.close()
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socket.close()
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del comm_socket
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del socket
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print("disconnected!")
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finally:
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self.m1.speed(u1)
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self.m2.speed(u2)
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comm_socket.close()
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socket.close()
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del comm_socket
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del socket
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print("disconnected!")
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time.sleep(t)
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self.m1.speed(0)
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self.m2.speed(0)
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wall_e = Robot()
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wall_e.remote_control()
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@ -1,13 +1,14 @@
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from casadi import *
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import time
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# look at: https://github.com/casadi/casadi/blob/master/docs/examples/python/vdp_indirect_multiple_shooting.py
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class OpenLoopSolver:
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def __init__(self, N=60, T=6.0):
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def __init__(self, N=20, T=2.0):
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self.T = T
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self.N = N
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def solve(self, x0):
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def setup(self):
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x = SX.sym('x')
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y = SX.sym('y')
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theta = SX.sym('theta')
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@ -15,29 +16,31 @@ class OpenLoopSolver:
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r = 0.03
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R = 0.05
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d = 0.02
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omega_max = 13.32
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omegar = SX.sym('omegar')
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omegal = SX.sym('omegal')
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control = vertcat(omegar, omegal)
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# model equation
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f1 = (r / 2 * cos(theta) - r * d / (2 * R) * sin(theta)) * omegar + (r / 2 * cos(theta) + r * d / (2 * R) * sin(
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theta)) * omegal
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f2 = (r / 2 * sin(theta) + r * d / (2 * R) * cos(theta)) * omegar + (r / 2 * sin(theta) - r * d / (2 * R) * cos(
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theta)) * omegal
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f3 = r / (2 * R) * omegar - r / (2 * R) * omegal
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f1 = (r / 2 * cos(theta) - r * d / (2 * R) * sin(theta)) * omegar * omega_max + (r / 2 * cos(theta) + r * d / (2 * R) * sin(
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theta)) * omegal * omega_max
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f2 = (r / 2 * sin(theta) + r * d / (2 * R) * cos(theta)) * omegar * omega_max + (r / 2 * sin(theta) - r * d / (2 * R) * cos(
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theta)) * omegal * omega_max
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f3 = -(r / (2 * R) * omegar - r / (2 * R) * omegal) * omega_max
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xdot = vertcat(f1, f2, f3)
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f = Function('f', [x, y, theta, omegar, omegal], [f1, f2, f3])
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print("f = {}".format(f))
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# cost functional
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L = x ** 2 + y ** 2 + 1e-2 * theta ** 2 + 1e-4 * (omegar ** 2 + omegal ** 2)
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target = (-0.0, 0.0)
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L = (x-target[0]) ** 2 + (y-target[1]) ** 2 + 1e-2 * theta ** 2 + 1e-2 * (omegar ** 2 + omegal ** 2)
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# Fixed step Runge-Kutta 4 integrator
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M = 4 # RK4 steps per interval
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DT = self.T / self.N / M
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print("DT = {}".format(DT))
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f = Function('f', [state, control], [xdot, L])
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self.f = Function('f', [state, control], [xdot, L])
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X0 = MX.sym('X0', 3)
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U = MX.sym('U', 2)
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X = X0
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@ -45,10 +48,10 @@ class OpenLoopSolver:
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runge_kutta = True
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if runge_kutta:
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for j in range(M):
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k1, k1_q = f(X, U)
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k2, k2_q = f(X + DT / 2 * k1, U)
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k3, k3_q = f(X + DT / 2 * k2, U)
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k4, k4_q = f(X + DT * k3, U)
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k1, k1_q = self.f(X, U)
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k2, k2_q = self.f(X + DT / 2 * k1, U)
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k3, k3_q = self.f(X + DT / 2 * k2, U)
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k4, k4_q = self.f(X + DT * k3, U)
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X = X + DT / 6 * (k1 + 2 * k2 + 2 * k3 + k4)
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Q = Q + DT / 6 * (k1_q + 2 * k2_q + 2 * k3_q + k4_q)
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else:
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@ -75,127 +78,180 @@ class OpenLoopSolver:
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ubg = []
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# Formulate the NLP
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Xk = MX(x0)
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for k in range(self.N):
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# New NLP variable for the control
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U1k = MX.sym('U1_' + str(k), 2)
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# U2k = MX.sym('U2_' + str(k))
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w += [U1k]
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lbw += [-10, -10]
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ubw += [10, 10]
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w0 += [0, 0]
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# Integrate till the end of the interval
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Fk = F(x0=Xk, p=U1k)
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Xk = Fk['xf']
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J = J + Fk['qf']
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# Add inequality constraint
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# g += [Xk[1]]
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# lbg += [-.0]
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# ubg += [inf]
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# Create an NLP solver
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prob = {'f': J, 'x': vertcat(*w), 'g': vertcat(*g)}
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self.solver = nlpsol('solver', 'ipopt', prob)
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# Xk = MX(x0)
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# for k in range(self.N):
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# # New NLP variable for the control
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# U1k = MX.sym('U1_' + str(k), 2)
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# # U2k = MX.sym('U2_' + str(k))
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# w += [U1k]
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# lbw += [-0.5, -0.5]
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# ubw += [0.5, 0.5]
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# w0 += [0, 0]
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#
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# # Integrate till the end of the interval
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# Fk = F(x0=Xk, p=U1k)
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# Xk = Fk['xf']
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# J = J + Fk['qf']
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#
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# # Add inequality constraint
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# # g += [Xk[1]]
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# # lbg += [-.0]
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# # ubg += [inf]
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#
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# # Create an NLP solver
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# prob = {'f': J, 'x': vertcat(*w), 'g': vertcat(*g)}
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# self.solver = nlpsol('solver', 'ipopt', prob)
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# Solve the NLP
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sol = self.solver(x0=w0, lbx=lbw, ubx=ubw, lbg=lbg, ubg=ubg)
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w_opt = sol['x']
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if False:
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sol = self.solver(x0=w0, lbx=lbw, ubx=ubw, lbg=lbg, ubg=ubg)
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w_opt = sol['x']
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# Plot the solution
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u_opt = w_opt
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x_opt = [x0]
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for k in range(self.N):
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Fk = F(x0=x_opt[-1], p=u_opt[2*k:2*k+2])
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x_opt += [Fk['xf'].full()]
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x1_opt = [r[0] for r in x_opt]
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x2_opt = [r[1] for r in x_opt]
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x3_opt = [r[2] for r in x_opt]
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# Plot the solution
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u_opt = w_opt
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x_opt = [self.x0]
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for k in range(self.N):
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Fk = F(x0=x_opt[-1], p=u_opt[2*k:2*k+2])
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x_opt += [Fk['xf'].full()]
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x1_opt = [r[0] for r in x_opt]
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x2_opt = [r[1] for r in x_opt]
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x3_opt = [r[2] for r in x_opt]
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tgrid = [self.T/self.N*k for k in range(self.N+1)]
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import matplotlib.pyplot as plt
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plt.figure(2)
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plt.clf()
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plt.plot(tgrid, x1_opt, '--')
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plt.plot(tgrid, x2_opt, '-')
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plt.plot(tgrid, x3_opt, '*')
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#import matplotlib.pyplot as plt
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#plt.figure(2)
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#plt.clf()
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#plt.plot(tgrid, x1_opt, '--')
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#plt.plot(tgrid, x2_opt, '-')
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#plt.plot(tgrid, x3_opt, '*')
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#plt.step(tgrid, vertcat(DM.nan(1), u_opt), '-.')
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plt.xlabel('t')
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plt.legend(['x1','x2','x3','u'])
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plt.grid()
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#plt.xlabel('t')
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#plt.legend(['x1','x2','x3','u'])
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#plt.grid()
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#plt.show()
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#return
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# alternative solution using multiple shooting (way faster!)
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opti = Opti() # Optimization problem
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self.opti = Opti() # Optimization problem
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# ---- decision variables ---------
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X = opti.variable(3,self.N+1) # state trajectory
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Q = opti.variable(1,self.N+1) # state trajectory
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posx = X[0,:]
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posy = X[1,:]
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angle = X[2,:]
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U = opti.variable(2,self.N) # control trajectory (throttle)
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#T = opti.variable() # final time
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self.X = self.opti.variable(3,self.N+1) # state trajectory
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self.Q = self.opti.variable(1,self.N+1) # state trajectory
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self.U = self.opti.variable(2,self.N) # control trajectory (throttle)
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#T = self.opti.variable() # final time
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# ---- objective ---------
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#opti.minimize(T) # race in minimal time
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#self.opti.minimize(T) # race in minimal time
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# ---- dynamic constraints --------
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#f = lambda x,u: vertcat(f1, f2, f3) # dx/dt = f(x,u)
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dt = self.T/self.N # length of a control interval
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for k in range(self.N): # loop over control intervals
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# Runge-Kutta 4 integration
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k1, k1_q = f(X[:,k], U[:,k])
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k2, k2_q = f(X[:,k]+dt/2*k1, U[:,k])
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k3, k3_q = f(X[:,k]+dt/2*k2, U[:,k])
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k4, k4_q = f(X[:,k]+dt*k3, U[:,k])
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x_next = X[:,k] + dt/6*(k1+2*k2+2*k3+k4)
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q_next = Q[:,k] + dt/6*(k1_q + 2 * k2_q + 2 * k3_q + k4_q)
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opti.subject_to(X[:,k+1]==x_next) # close the gaps
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opti.subject_to(Q[:,k+1]==q_next) # close the gaps
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opti.minimize(Q[:,self.N])
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# ---- path constraints -----------
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#limit = lambda pos: 1-sin(2*pi*pos)/2
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#opti.subject_to(speed<=limit(pos)) # track speed limit
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opti.subject_to(opti.bounded(-10,U,10)) # control is limited
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# ---- boundary conditions --------
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opti.subject_to(posx[0]==x0[0]) # start at position 0 ...
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opti.subject_to(posy[0]==x0[1]) # ... from stand-still
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opti.subject_to(angle[0]==x0[2]) # finish line at position 1
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#opti.subject_to(speed[-1]==0) # .. with speed 0
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opti.subject_to(Q[:,0]==0.0)
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# ---- misc. constraints ----------
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#opti.subject_to(X[1,:]>=0) # Time must be positive
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#opti.subject_to(X[2,:]<=4) # Time must be positive
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#opti.subject_to(X[2,:]>=-2) # Time must be positive
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# avoid obstacle
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#r = 0.25
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#p = (0.5, 0.5)
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#for k in range(self.N):
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# opti.subject_to((X[0,k]-p[0])**2 + (X[1,k]-p[1])**2 > r**2)
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# pass
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# ---- initial values for solver ---
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#opti.set_initial(speed, 1)
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#opti.set_initial(T, 1)
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#self.opti.set_initial(speed, 1)
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#self.opti.set_initial(T, 1)
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def solve(self, x0, target):
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tstart = time.time()
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x = SX.sym('x')
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y = SX.sym('y')
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theta = SX.sym('theta')
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state = vertcat(x, y, theta)
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r = 0.03
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R = 0.05
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d = 0.02
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omega_max = 13.32
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omegar = SX.sym('omegar')
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omegal = SX.sym('omegal')
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control = vertcat(omegar, omegal)
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# model equation
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f1 = (r / 2 * cos(theta) - r * d / (2 * R) * sin(theta)) * omegar * omega_max + (r / 2 * cos(theta) + r * d / (
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2 * R) * sin(
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theta)) * omegal * omega_max
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f2 = (r / 2 * sin(theta) + r * d / (2 * R) * cos(theta)) * omegar * omega_max + (r / 2 * sin(theta) - r * d / (
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2 * R) * cos(
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theta)) * omegal * omega_max
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f3 = -(r / (2 * R) * omegar - r / (2 * R) * omegal) * omega_max
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xdot = vertcat(f1, f2, f3)
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L = (x - target[0]) ** 2 + (y - target[1]) ** 2 + 1e-2 * theta ** 2 + 1e-2 * (omegar ** 2 + omegal ** 2)
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self.f = Function('f', [state, control], [xdot, L])
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# ---- solve NLP ------
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opti.solver("ipopt") # set numerical backend
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sol = opti.solve() # actual solve
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#x0 = sol.value(opti.x)
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#lam_g0 = sol.value(opti.lam_g)
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#opti.set_initial(opti.lam_g, lam_g0)
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#opti.set_initial(opti.x, x0)
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#opti.solve()
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# set numerical backend
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# delete constraints
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self.opti.subject_to()
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# add new constraints
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dt = self.T / self.N # length of a control interval
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for k in range(self.N): # loop over control intervals
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# Runge-Kutta 4 integration
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k1, k1_q = self.f(self.X[:, k], self.U[:, k])
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k2, k2_q = self.f(self.X[:, k] + dt / 2 * k1, self.U[:, k])
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k3, k3_q = self.f(self.X[:, k] + dt / 2 * k2, self.U[:, k])
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k4, k4_q = self.f(self.X[:, k] + dt * k3, self.U[:, k])
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x_next = self.X[:, k] + dt / 6 * (k1 + 2 * k2 + 2 * k3 + k4)
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q_next = self.Q[:, k] + dt / 6 * (k1_q + 2 * k2_q + 2 * k3_q + k4_q)
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self.opti.subject_to(self.X[:, k + 1] == x_next) # close the gaps
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self.opti.subject_to(self.Q[:, k + 1] == q_next) # close the gaps
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self.opti.minimize(self.Q[:, self.N])
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# ---- path constraints -----------
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# limit = lambda pos: 1-sin(2*pi*pos)/2
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# self.opti.subject_to(speed<=limit(pos)) # track speed limit
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self.opti.subject_to(self.opti.bounded(-0.5, self.U, 0.5)) # control is limited
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# ---- boundary conditions --------
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# self.opti.subject_to(speed[-1]==0) # .. with speed 0
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self.opti.subject_to(self.Q[:, 0] == 0.0)
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self.opti.solver("ipopt")
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# ---- misc. constraints ----------
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# self.opti.subject_to(X[1,:]>=0) # Time must be positive
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# self.opti.subject_to(X[2,:]<=4) # Time must be positive
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# self.opti.subject_to(X[2,:]>=-2) # Time must be positive
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# avoid obstacle
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# r = 0.25
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# p = (0.5, 0.5)
|
||||
# for k in range(self.N):
|
||||
# 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()
|
||||
|
||||
print("setting up problem took {} seconds".format(tend - tstart))
|
||||
|
||||
sol = self.opti.solve() # actual 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")
|
||||
|
|
|
|||
|
|
@ -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)
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user