implemented obstacle avoidance
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b755173c6b
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b54c2d565c
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@ -4,13 +4,15 @@ 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=10, T=2.0):
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def __init__(self, N=20, T=4.0):
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self.T = T
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self.N = N
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self.opti_x0 = None
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self.opti_lam_g0 = None
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self.use_warmstart = True
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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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@ -135,6 +137,8 @@ class OpenLoopSolver:
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#plt.show()
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#return
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def solve(self, x0, target, obstacles):
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# alternative solution using multiple shooting (way faster!)
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self.opti = Opti() # Optimization problem
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@ -143,6 +147,8 @@ class OpenLoopSolver:
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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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self.slack = self.opti.variable(1,1)
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#T = self.opti.variable() # final time
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# ---- objective ---------
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@ -158,7 +164,7 @@ class OpenLoopSolver:
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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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@ -205,12 +211,12 @@ class OpenLoopSolver:
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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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self.opti.minimize(self.Q[:, self.N] + 1.0e5 * self.slack**2)
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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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maxcontrol = 0.950
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maxcontrol = 0.95
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self.opti.subject_to(self.opti.bounded(-maxcontrol, self.U, maxcontrol)) # control is limited
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# ---- boundary conditions --------
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@ -227,10 +233,11 @@ class OpenLoopSolver:
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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)
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# for k in range(self.N):
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# self.opti.subject_to((X[0,k]-p[0])**2 + (X[1,k]-p[1])**2 > r**2)
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for o in obstacles:
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p = obstacles[o].pos
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r = obstacles[o].radius
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for k in range(1,self.N):
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self.opti.subject_to((self.X[0,k]-p[0])**2 + (self.X[1,k]-p[1])**2 + self.slack > r**2)
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# pass
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posx = self.X[0, :]
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posy = self.X[1, :]
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@ -241,12 +248,15 @@ class OpenLoopSolver:
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self.opti.subject_to(angle[0] == x0[2]) # finish line at position 1
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tend = time.time()
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print("setting up problem took {} seconds".format(tend - tstart))
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print("setting up problem took {} seconds".format(tend - tstart))
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if self.opti_x0 is not None:
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tstart = time.time()
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if self.use_warmstart and self.opti_x0 is not None:
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self.opti.set_initial(self.opti.lam_g, self.opti_lam_g0)
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self.opti.set_initial(self.opti.x, self.opti_x0)
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sol = self.opti.solve() # actual solve
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tend = time.time()
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print("solving the problem took {} seconds".format(tend - tstart))
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self.opti_x0 = sol.value(self.opti.x)
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self.opti_lam_g0 = sol.value(self.opti.lam_g)
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@ -256,7 +266,7 @@ class OpenLoopSolver:
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u_opt_1 = sol.value(self.U[0,:])
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u_opt_2 = sol.value(self.U[1,:])
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return (u_opt_1, u_opt_2)
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return (u_opt_1, u_opt_2, sol.value(posx), sol.value(posy))
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#lam_g0 = sol.value(self.opti.lam_g)
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@ -18,6 +18,7 @@ from copy import deepcopy
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import matplotlib.pyplot as plt
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import matplotlib.animation as anim
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import matplotlib.patches as patch
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import time
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@ -37,6 +38,12 @@ class Robot:
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self.ip = ip
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class Obstacle:
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def __init__(self, id, radius):
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self.id = id
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self.pos = None
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self.radius = radius
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def f_ode(t, x, u):
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# dynamical model of the two-wheeled robot
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# TODO: find exact values for these parameters
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@ -62,19 +69,28 @@ def f_ode(t, x, u):
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class RemoteController:
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def __init__(self):
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self.robots = [Robot(3)]
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self.robots = [Robot(3, '192.168.1.103')]
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self.robot_ids = {}
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for r in self.robots:
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self.robot_ids[r.id] = r
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obst = [Obstacle(6, 0.2), Obstacle(5, 0.2), Obstacle(8, 0.2)]
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self.obstacles = {}
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for r in obst:
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self.obstacles[r.id] = r
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# connect to robot
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self.rc_socket = socket.socket()
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#self.rc_socket = None
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try:
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pass
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self.rc_socket.connect(('192.168.1.103', 1234)) # connect to robot
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for r in self.robots:
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self.rc_socket.connect((r.ip, 1234)) # connect to robot
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except socket.error:
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print("could not connect to socket")
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self.rc_socket = None
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self.t = time.time()
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@ -89,6 +105,10 @@ class RemoteController:
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self.tms = None
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self.xms = None
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# variable for mpc open loop
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self.ol_x = None
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self.ol_y = None
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self.mutex = threading.Lock()
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marker_sub = rospy.Subscriber("/marker_id_pos_angle", id_pos_angle, self.measurement_callback)
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@ -113,10 +133,19 @@ class RemoteController:
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self.fig = plt.figure()
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self.ax = self.fig.add_subplot(1,1,1)
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self.xdata, self.ydata = [], []
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self.line, = self.ax.plot([],[])
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self.line, = self.ax.plot([],[], color='grey', linestyle=':')
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self.line_sim, = self.ax.plot([], [])
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self.line_ol, = self.ax.plot([],[], color='green', linestyle='--')
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self.dirm, = self.ax.plot([], [])
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self.dirs, = self.ax.plot([], [])
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self.circles = []
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for o in self.obstacles:
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self.circles.append(patch.Circle((0.0, 0.0), radius=0.1, fill=False, color='red', linestyle='--'))
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for s in self.circles:
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self.ax.add_artist(s)
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plt.xlabel('x-position')
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plt.ylabel('y-position')
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plt.grid()
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@ -136,7 +165,7 @@ class RemoteController:
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self.ax.set_ylim(-2, 2)
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self.ax.set_aspect('equal', adjustable='box')
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return self.line, self.line_sim, self.dirm, self.dirs,
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return self.line, self.line_sim, self.dirm, self.dirs, self.line_ol, self.circles[0], self.circles[1],self.circles[2],
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def ani_update(self, frame):
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#print("plotting")
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@ -155,8 +184,8 @@ class RemoteController:
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a = xm_local[-1, 0]
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b = xm_local[-1, 1]
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a2 = a + np.cos(xm_local[-1, 2]) * 1.0
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b2 = b + np.sin(xm_local[-1, 2]) * 1.0
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a2 = a + np.cos(xm_local[-1, 2]) * 0.2
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b2 = b + np.sin(xm_local[-1, 2]) * 0.2
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self.dirm.set_data(np.array([a, a2]), np.array([b, b2]))
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@ -171,14 +200,34 @@ class RemoteController:
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a = xs_local[-1, 0]
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b = xs_local[-1, 1]
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a2 = a + np.cos(xs_local[-1, 2]) * 1.0
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b2 = b + np.sin(xs_local[-1, 2]) * 1.0
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a2 = a + np.cos(xs_local[-1, 2]) * 0.2
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b2 = b + np.sin(xs_local[-1, 2]) * 0.2
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self.dirs.set_data(np.array([a, a2]), np.array([b, b2]))
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ol_x_local = deepcopy(self.ol_x)
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ol_y_local = deepcopy(self.ol_y)
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if ol_x_local is not None:
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self.line_ol.set_data(ol_x_local, ol_y_local)
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else:
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self.line_ol.set_data([],[])
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i = 0
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obst_keys = self.obstacles.keys()
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for s in self.circles:
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o = self.obstacles[obst_keys[i]]
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i = i + 1
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if o.pos is not None:
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s.center = o.pos
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s.radius = o.radius
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finally:
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self.mutex.release()
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return self.line, self.line_sim, self.dirm, self.dirs,
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return self.line, self.line_sim, self.dirm, self.dirs, self.line_ol, self.circles[0], self.circles[1],self.circles[2],
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def measurement_callback(self, data):
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#print("data = {}".format(data))
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@ -211,6 +260,10 @@ class RemoteController:
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finally:
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self.mutex.release()
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if data.id in self.obstacles.keys():
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obst = (data.x, data.y)
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self.obstacles[data.id].pos = obst
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def controller(self):
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tgrid = None
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us1 = None
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@ -348,54 +401,6 @@ class RemoteController:
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#print("speed = {}".format(self.speed))
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elif pid:
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# pid controller
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events = pygame.event.get()
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for event in events:
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if event.type == pygame.KEYDOWN:
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if event.key == pygame.K_LEFT:
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self.ii = self.ii / np.sqrt(np.sqrt(np.sqrt(10.0)))
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print("ii = {}".format(self.pp))
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elif event.key == pygame.K_RIGHT:
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self.ii = self.ii * np.sqrt(np.sqrt(np.sqrt(10.0)))
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print("ii = {}".format(self.pp))
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elif event.key == pygame.K_UP:
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self.controlling = True
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elif event.key == pygame.K_DOWN:
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self.controlling = False
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self.rc_socket.send('({},{})\n'.format(0, 0))
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dt = 0.05
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if self.controlling:
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# test: turn robot such that angle is zero
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for r in self.robots:
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if r.euler is not None:
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self.k = self.k + 1
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alpha = r.euler
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self.alphas.append(alpha)
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# compute error
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e = alpha - 0
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# compute integral of error (approximately)
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self.inc += e * dt
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# PID
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p = self.pp * e
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i = self.ii * self.inc
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d = 0.0
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# compute controls for robot from PID
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u1 = p + i + d
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u2 = - p - i - d
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print("alpha = {}, u = ({}, {})".format(alpha, u1, u2))
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self.rc_socket.send('({},{})\n'.format(u1, u2))
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time.sleep(dt)
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elif open_loop_solve:
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# open loop controller
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@ -407,7 +412,8 @@ class RemoteController:
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self.t = time.time()
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elif event.key == pygame.K_DOWN:
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self.controlling = False
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self.rc_socket.send('(0.1, 0.0,0.0)\n')
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if self.rc_socket:
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self.rc_socket.send('(0.0,0.0)\n')
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elif event.key == pygame.K_0:
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self.target = (0.0, 0.0, 0.0)
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elif event.key == pygame.K_1:
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@ -419,7 +425,6 @@ class RemoteController:
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elif event.key == pygame.K_4:
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self.target = (-0.5,0.5, 0.0)
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if self.controlling:
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tmpc_start = time.time()
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# get measurement
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self.mutex.acquire()
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try:
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@ -428,24 +433,33 @@ class RemoteController:
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finally:
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self.mutex.release()
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print("current measurement (t, x) = ({}, {})".format(last_time, last_measurement))
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print("current control (u1, u2) = ({}, {})".format(u1, u2))
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#print("current measurement (t, x) = ({}, {})".format(last_time, last_measurement))
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#print("current control (u1, u2) = ({}, {})".format(u1, u2))
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# prediction of state at time the mpc will terminate
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r.set_f_params(np.array([u1 * omega_max, u2 * omega_max]))
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r.set_initial_value(last_measurement, last_time)
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dt = self.ols.T/self.ols.N
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print("integrating for {} seconds".format((dt)))
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#print("integrating for {} seconds".format((dt)))
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x_pred = r.integrate(r.t + (dt))
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print("predicted initial state x_pred = ({})".format(x_pred))
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#print("predicted initial state x_pred = ({})".format(x_pred))
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res = self.ols.solve(x_pred, self.target)
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tmpc_start = time.time()
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res = self.ols.solve(x_pred, self.target, self.obstacles)
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#tgrid = res[0]
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us1 = res[0]
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us2 = res[1]
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self.mutex.acquire()
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try:
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self.ol_x = res[2]
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self.ol_y = res[3]
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finally:
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self.mutex.release()
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# tt = 0
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# x = last_measurement
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# t_ol = np.array([tt])
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finally:
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self.mutex.release()
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print("(last_time, second_time, dt) = ({}, {}, {})".format(last_time, second_time, second_time - last_time))
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print("mismatch between predicted state and measured state: {}\n\n".format(second_measurement - last_measurement))
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#print("(last_time, second_time, dt) = ({}, {}, {})".format(last_time, second_time, second_time - last_time))
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#print("mismatch between predicted state and measured state: {}\n\n".format(second_measurement - last_measurement))
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for i in range(0, 1):
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u1 = us1[i]
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u2 = us2[i]
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#self.rc_socket.send('({},{},{})\n'.format(dt,u1, u2))
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self.rc_socket.send('({},{})\n'.format(u1, u2))
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if self.rc_socket:
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self.rc_socket.send('({},{})\n'.format(u1, u2))
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self.t = time.time()
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time.sleep(0.2)
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#time.sleep(0.2)
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#
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@ -506,7 +521,7 @@ def main(args):
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screenheight = 480
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screenwidth = 640
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screen = pygame.display.set_mode([screenwidth, screenheight])
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pygame.display.set_mode([screenwidth, screenheight])
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threading.Thread(target=rc.controller).start()
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