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mpc_two_robot.py
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mpc_two_robot.py
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import time
import casadi as ca
import numpy as np
from matplotlib import pyplot as plt
from matplotlib.animation import FFMpegWriter
from vehicle import Vehicle
def shift(u, x_n):
u_end = np.concatenate((u[1:], u[-1:]))
x_n = np.concatenate((x_n[1:], x_n[-1:]))
return u_end, x_n
class MPCController:
def __init__(self, car: Vehicle, T=0.2, N=10, Q=np.diag([1.0, 1.0, 0.001, 0.01, 0.01]), R=np.diag([0.01, 0.01])):
self.car = car
self.T = T # time step
self.N = N # horizon length
# weight matrix
self.Q = Q
self.R = R
# The history states and controls
self.next_states = np.zeros((self.N + 1, 5))
self.u0 = np.zeros((self.N, 2))
def setupController(self, obs, dynamic_car_trajectories=None):
self.opti = ca.Opti()
# Control signal
self.U = self.opti.variable(self.N, 2)
self.u_opt = np.zeros((self.N, 2))
self.x_opt = np.zeros((self.N + 1, 5))
control_a = self.U[:, 0]
control_omega = self.U[:, 1]
# State system
self.X = self.opti.variable(self.N + 1, 5)
state_x = self.X[:, 0]
state_y = self.X[:, 1]
state_psi = self.X[:, 2]
state_v = self.X[:, 3]
state_delta = self.X[:, 4]
# Create model
f = lambda x, u: ca.vertcat(*[
x[3] * ca.cos(x[2]),
x[3] * ca.sin(x[2]),
x[3] / self.car.L * ca.tan(x[4]),
u[0],
u[1]
])
# Define target state
self.x_ref = self.opti.parameter(2, 5)
# Define control reference N
self.u_ref = self.opti.parameter(self.N, 2)
# Define k obstacles
num_obs = len(obs)
self.x_obs = self.opti.parameter(num_obs)
self.y_obs = self.opti.parameter(num_obs)
self.r_obs = self.opti.parameter(num_obs)
# Define multiple dynamic cars predicted trajectories
num_dynamic_cars = 0
if dynamic_car_trajectories is not None:
num_dynamic_cars = len(dynamic_car_trajectories)
self.dynamic_cars_x = []
self.dynamic_cars_y = []
self.dynamic_cars_psi = []
self.dynamic_cars_v = []
self.dynamic_cars_delta = []
for _ in range(num_dynamic_cars):
self.dynamic_cars_x.append(self.opti.parameter(self.N + 1))
self.dynamic_cars_y.append(self.opti.parameter(self.N + 1))
self.dynamic_cars_psi.append(self.opti.parameter(self.N + 1))
self.dynamic_cars_v.append(self.opti.parameter(self.N + 1))
self.dynamic_cars_delta.append(self.opti.parameter(self.N + 1))
# Initial constraints x0 = self.x_ref[0]
self.opti.subject_to(self.X[0, :] == self.x_ref[0, :])
for i in range(self.N):
x_next = self.X[i, :] + self.T * f(self.X[i, :], self.U[i, :]).T
self.opti.subject_to(self.X[i + 1, :] == x_next)
# Cost function
obj = 0
goal_state = self.x_ref[-1, :]
for i in range(self.N):
obj += ca.mtimes([(self.X[i, :] - goal_state), self.Q, (self.X[i, :] - goal_state).T]) + ca.mtimes(
[self.U[i, :], self.R, self.U[i, :].T])
# Add dynamic cars avoidance cost
for j in range(num_dynamic_cars):
self.opti.subject_to((state_x - self.dynamic_cars_x[j]) ** 2 + (state_y - self.dynamic_cars_y[j]) ** 2 >= (0.5 + self.car.d) ** 2)
for i in range(self.N):
dx = state_x[i] - self.dynamic_cars_x[j][i]
dy = state_y[i] - self.dynamic_cars_y[j][i]
# obj += ca.exp(-0.01 * (dx ** 2 + dy ** 2)) # Add cost term to avoid dynamic car
# Define horizon factor
distance = ca.sqrt(dx ** 2 + dy ** 2)
relative_velocity_x = state_v[i] * ca.cos(state_psi[i]) - self.dynamic_cars_v[j][i] * ca.cos(
self.dynamic_cars_psi[j][i])
relative_velocity_y = state_v[i] * ca.sin(state_psi[i]) - self.dynamic_cars_v[j][i] * ca.sin(
self.dynamic_cars_psi[j][i])
relative_velocity = ca.sqrt(relative_velocity_x ** 2 + relative_velocity_y ** 2)
horizon_factor = (self.N - i) / self.N
alpha_combined = (0.1 * ca.exp(-0.01 * distance)) * \
(0.1 * ca.exp(-0.1 * relative_velocity)) * \
(0.01 * horizon_factor)
adaptive_cost_combined = ca.exp(-alpha_combined * distance)
obj += adaptive_cost_combined
self.opti.subject_to((dx ** 2 + dy ** 2) >= (0.5 + self.car.d) ** 2) # Avoid collision
# add constraints for car1 2
# for i in range(num_dynamic_cars):
self.opti.minimize(obj)
# Define boundaries
self.opti.subject_to(self.opti.bounded(self.car.min_v, state_v, self.car.max_v))
self.opti.subject_to(self.opti.bounded(self.car.min_delta, state_delta, self.car.max_delta))
self.opti.subject_to(self.opti.bounded(self.car.min_a, control_a, self.car.max_a))
self.opti.subject_to(self.opti.bounded(self.car.min_omega, control_omega, self.car.max_omega))
# Define obstacles
for i in range(num_obs):
ob_x = self.x_obs[i]
ob_y = self.y_obs[i]
ob_r = self.r_obs[i]
self.opti.subject_to((state_x - ob_x) ** 2 + (state_y - ob_y) ** 2 >= (ob_r + self.car.d) ** 2)
opts_setting = {'ipopt.max_iter': 1000,
'ipopt.print_level': 1,
'print_time': 0,
'ipopt.acceptable_tol': 1e-8,
'ipopt.acceptable_obj_change_tol': 1e-8}
self.opti.solver('ipopt', opts_setting)
def solve(self, x_ref, u_ref, obs, dynamic_car_trajectories=None):
self.opti.set_value(self.x_ref, x_ref)
self.opti.set_value(self.u_ref, u_ref)
self.opti.set_value(self.x_obs, obs[:, 0])
self.opti.set_value(self.y_obs, obs[:, 1])
self.opti.set_value(self.r_obs, obs[:, 2])
if dynamic_car_trajectories is not None:
for j, trajectory in enumerate(dynamic_car_trajectories):
self.opti.set_value(self.dynamic_cars_x[j], trajectory[:, 0])
self.opti.set_value(self.dynamic_cars_y[j], trajectory[:, 1])
self.opti.set_value(self.dynamic_cars_psi[j], trajectory[:, 2])
self.opti.set_value(self.dynamic_cars_v[j], trajectory[:, 3])
self.opti.set_value(self.dynamic_cars_delta[j], trajectory[:, 4])
x0 = x_ref[0, :]
self.opti.set_initial(self.X, np.tile(x0, (self.N + 1, 1)))
self.opti.set_initial(self.U, np.zeros((self.N, 2)))
try:
self.opti.solve()
self.u_opt = self.opti.value(self.U)
self.x_opt = self.opti.value(self.X)
self.u0, self.next_states = shift(self.u_opt, self.x_opt)
return self.x_opt, self.u_opt
# run with exception
except RuntimeError as e:
print(f"Optimization failed: {e}")
print("Solver stats:", self.opti.stats())
print("Current state guess:", self.opti.debug.value(self.X))
print("Current control guess:", self.opti.debug.value(self.U))
# Handle failure case
self.u_opt = np.zeros((self.N, 2))
self.x_opt = np.tile(x_ref, (self.N + 1, 1))
return self.x_opt, self.u_opt
def planning(self, x_ref, u_ref, obs, dynamic_car_trajectory=None):
self.setupController(obs, dynamic_car_trajectory)
return self.solve(x_ref, u_ref, obs, dynamic_car_trajectory)
# update the car state
def update_car(self, a, omega):
self.car.update_state(a, omega, self.T)
return self.car.x, self.car.y, self.car.psi, self.car.v, self.car.delta
def distance(p1, p2):
return np.sqrt((p1[0] - p2[0]) ** 2 + (p1[1] - p2[1]) ** 2)
def test_multi_car():
car = Vehicle(0, 0, np.pi / 4)
Xcar = Vehicle(0, 0, np.pi / 4)
mpc_controller = MPCController(car, T=0.2, N=20)
x_ref = np.array([[0, 0, np.pi / 4, 0, 0], [10, 10, 0, 0, 0]])
u_ref = np.zeros((mpc_controller.N, 2))
car9 = Vehicle(10, 10, np.pi / 4)
Xcar9 = Vehicle(10, 10, np.pi / 4)
mpc_controller9 = MPCController(car9, T=0.2, N=20)
x_ref9 = np.array([[10, 10, np.pi / 4, 0, 0], [0, 0, np.pi / 4, 0, 0]])
u_ref9 = np.zeros((mpc_controller9.N, 2))
obs = np.array([[5, 5, 1.0]])
# Plot the paths
plt.ion() # Turn on interactive mode
fig, ax = plt.subplots()
ax.set_xlim(-1, 13)
ax.set_ylim(-1, 13)
line, = ax.plot([], [], 'b:', label='Trajectory', linewidth=2)
line9, = ax.plot([], [], 'r:', label='Trajectory', linewidth=2)
# plot line for car 1 and 2
line1, = ax.plot([], [], 'g:', label='Trajectory', linewidth=2)
line2, = ax.plot([], [], 'y:', label='Trajectory', linewidth=2)
line3, = ax.plot([], [], 'y:', label='Trajectory', linewidth=2)
line4, = ax.plot([], [], 'y:', label='Trajectory', linewidth=2)
# Draw obstacles
for ob in obs:
circle = plt.Circle((ob[0], ob[1]), ob[2], color='c', fill=True, alpha=0.2)
ax.add_artist(circle)
# Plot start and goal markers
ax.plot(x_ref[0, 0], x_ref[0, 1], 'g*', label='Start') # Green star for start
ax.plot(x_ref[-1, 0], x_ref[-1, 1], 'ro', label='Goal') # Red circle for goal
# Plot current car position
rect = plt.Rectangle((0, 0), 0.5, 1, angle=0, color='r', fill=True, label='Robot Pose', alpha=0.5)
ax.add_patch(rect)
rect1 = plt.Rectangle((0, 0), 0.5, 1, angle=0, color='g', fill=True, label='Robot Pose', alpha=0.2)
ax.add_patch(rect1)
rect2 = plt.Rectangle((0, 0), 0.5, 1, angle=0, color='g', fill=True, label='Robot Pose', alpha=0.2)
ax.add_patch(rect2)
rect3 = plt.Rectangle((0, 0), 0.5, 1, angle=0, color='g', fill=True, label='Robot Pose', alpha=0.2)
ax.add_patch(rect3)
rect4 = plt.Rectangle((0, 0), 0.5, 1, angle=0, color='g', fill=True, label='Robot Pose', alpha=0.2)
ax.add_patch(rect4)
rect9 = plt.Rectangle((0, 0), 0.5, 1, angle=0, color='y', fill=True, label='Robot Pose', alpha=0.5)
ax.add_patch(rect9)
car1 = Vehicle(2, 5, 0.0, 0.5, -0.0)
car2 = Vehicle(5, 8, 0, -0.5, 0.0)
car3 = Vehicle(9, 8, 0.0, -0.5, -0.0)
car4 = Vehicle(6, 6, -np.pi / 2, 0.5, -0.0)
metadata = dict(title='MPC Path Planning', artist='Matplotlib', comment='MPC simulation')
writer = FFMpegWriter(fps=2, metadata=metadata)
# save a, w for car1
a1 = []
w1 = []
vel1 = []
a99 = []
w99 = []
vel99 = []
u_ref_car1 = np.zeros((mpc_controller.N, 2))
u_ref_car2 = np.zeros((mpc_controller.N, 2))
u_ref_car3 = np.zeros((mpc_controller.N, 2))
u_ref_car4 = np.zeros((mpc_controller.N, 2))
# traj
opt_traj = np.zeros((mpc_controller.N + 1, 5))
opt_traj9 = np.zeros((mpc_controller.N + 1, 5))
# add current state to opt_traj with the same state
for i in range(mpc_controller.N + 1):
opt_traj[i] = x_ref[0]
opt_traj9[i] = x_ref[0]
with writer.saving(fig, "multi_car_animation.mp4", 600):
while not mpc_controller.car.is_goal_reached(mpc_controller.car.path[-1], x_ref[-1]) or \
not mpc_controller9.car.is_goal_reached(mpc_controller9.car.path[-1], x_ref9[-1]):
# Example dynamic car trajectories (replace with actual predicted trajectories)
dynamic_car_trajectories1 = []
# check distance car1, car2. car3 , car4 to car
if (distance([car1.x, car1.y], [car.x, car.y]) < 4):
dynamic_car_trajectories1.append(car1.prediction_traj(mpc_controller.N, u_ref_car1, mpc_controller.T))
if (distance([car2.x, car2.y], [car.x, car.y]) < 4):
dynamic_car_trajectories1.append(car2.prediction_traj(mpc_controller.N, u_ref_car2, mpc_controller.T))
if (distance([car3.x, car3.y], [car.x, car.y]) < 4):
dynamic_car_trajectories1.append(car3.prediction_traj(mpc_controller.N, u_ref_car3, mpc_controller.T))
if (distance([car4.x, car4.y], [car.x, car.y]) < 4):
dynamic_car_trajectories1.append(car4.prediction_traj(mpc_controller.N, u_ref_car4, mpc_controller.T))
if (distance([Xcar9.x, Xcar9.y], [car.x, car.y]) < 4):
dynamic_car_trajectories1.append(Xcar9.prediction_traj(mpc_controller.N, u_ref_car4, mpc_controller.T))
x_opt, u_opt = mpc_controller.planning(x_ref, u_ref, obs, dynamic_car_trajectories1)
a, omega = u_opt[0]
# add opt traj
# add car 9
dynamic_car_trajectories2 = []
if (distance([car1.x, car1.y], [car9.x, car9.y]) < 4):
dynamic_car_trajectories2.append(car1.prediction_traj(mpc_controller.N, u_ref_car1, mpc_controller.T))
if (distance([car2.x, car2.y], [car9.x, car9.y]) < 4):
dynamic_car_trajectories2.append(car2.prediction_traj(mpc_controller.N, u_ref_car2, mpc_controller.T))
if (distance([car3.x, car3.y], [car9.x, car9.y]) < 4):
dynamic_car_trajectories2.append(car3.prediction_traj(mpc_controller.N, u_ref_car3, mpc_controller.T))
if (distance([car4.x, car4.y], [car9.x, car9.y]) < 4):
dynamic_car_trajectories2.append(car4.prediction_traj(mpc_controller.N, u_ref_car4, mpc_controller.T))
if (distance([Xcar.x, Xcar.y], [car9.x, car9.y]) < 4):
dynamic_car_trajectories2.append(Xcar.prediction_traj(mpc_controller.N, u_ref_car4, mpc_controller.T))
x_opt9, u_opt9 = mpc_controller9.planning(x_ref9, u_ref9, obs, dynamic_car_trajectories2)
a9, omega9 = u_opt9[0]
# save a and omega
a1.append(a)
w1.append(omega)
vel1.append(mpc_controller.car.v)
a99.append(a9)
w99.append(omega9)
vel99.append(mpc_controller9.car.v)
x, y, psi, v, delta = mpc_controller.update_car(a, omega)
x9, y9, psi9, v9, delta9 = mpc_controller9.update_car(a9, omega9)
# Update x_ref for the next iteration
x_ref[0, :] = [x, y, psi, v, delta]
u_ref = np.concatenate((mpc_controller.u0, u_ref[mpc_controller.N:]))
x_ref9[0, :] = [x9, y9, psi9, v9, delta9]
u_ref9 = np.concatenate((mpc_controller9.u0, u_ref9[mpc_controller9.N:]))
traj1 = car1.prediction_traj(mpc_controller.N, u_ref_car1, mpc_controller.T)
traj2 = car2.prediction_traj(mpc_controller.N, u_ref_car2, mpc_controller.T)
traj3 = car3.prediction_traj(mpc_controller.N, u_ref_car3, mpc_controller.T)
traj4 = car4.prediction_traj(mpc_controller.N, u_ref_car4, mpc_controller.T)
line1.set_data(traj1[:, 0], traj1[:, 1])
line2.set_data(traj2[:, 0], traj2[:, 1])
line3.set_data(traj3[:, 0], traj3[:, 1])
line4.set_data(traj4[:, 0], traj4[:, 1])
# Update dynamic cars' state
car1.update_state(0.0, 0.0, 1 * mpc_controller.T)
car2.update_state(-0.0, 0.0, 1 * mpc_controller.T)
car3.update_state(-0.0, -0.0, 1 * mpc_controller.T)
car4.update_state(0.0, -0.0, 1 * mpc_controller.T)
Xcar.update_state(a, omega, mpc_controller.T)
Xcar9.update_state(a9, omega9, mpc_controller.T)
# Set line data from x_opt, take the current state
line.set_data(x_opt[:, 0], x_opt[:, 1])
line9.set_data(x_opt9[:, 0], x_opt9[:, 1])
# plot line for car 1 and 2, predict trajectory
# Plot the car
robot_width, robot_length = 0.5, 1.0 # Adjust size as necessary
rear_axle_x = robot_length / 4
rect.set_width(robot_length)
rect.set_height(robot_width)
rect.angle = np.degrees(psi)
# Compute the center of the rectangle with angle psi from traj1
x = x_opt[0, 0]
y = x_opt[0, 1]
center_x = x - robot_length / 2 * np.cos(psi) + robot_width / 2 * np.sin(psi)
center_y = y - robot_length / 2 * np.sin(psi) - robot_width / 2 * np.cos(psi)
# Adjust to rear center
rx = center_x + rear_axle_x * np.cos(psi)
ry = center_y + rear_axle_x * np.sin(psi)
rect.set_xy((rx, ry))
rect9.set_width(robot_length)
rect9.set_height(robot_width)
rect9.angle = np.degrees(psi9)
# Compute the center of the rectangle with angle psi from traj1
x9 = x_opt9[0, 0]
y9 = x_opt9[0, 1]
center_x9 = x9 - robot_length / 2 * np.cos(psi9) + robot_width / 2 * np.sin(psi9)
center_y9 = y9 - robot_length / 2 * np.sin(psi9) - robot_width / 2 * np.cos(psi9)
# Adjust to rear center
rx9 = center_x9 + rear_axle_x * np.cos(psi9)
ry9 = center_y9 + rear_axle_x * np.sin(psi9)
rect9.set_xy((rx9, ry9))
# plot car1, car2
x1, y1, psi1, v1, delta1, del1, om1 = car1.path[-1]
x2, y2, psi2, v2, delta2, del2, om2 = car2.path[-1]
x3, y3, psi3, v3, delta3, del3, om3 = car3.path[-1]
x4, y4, psi4, v4, delta4, del4, om4 = car4.path[-1]
rect1.set_width(robot_length)
rect1.set_height(robot_width)
rect1.angle = np.degrees(psi1)
center_x1 = x1 - robot_length / 2 * np.cos(psi1) + robot_width / 2 * np.sin(psi1)
center_y1 = y1 - robot_length / 2 * np.sin(psi1) - robot_width / 2 * np.cos(psi1)
rx1 = center_x1 + rear_axle_x * np.cos(psi1)
ry1 = center_y1 + rear_axle_x * np.sin(psi1)
rect1.set_xy((rx1, ry1))
rect2.set_width(robot_length)
rect2.set_height(robot_width)
rect2.angle = np.degrees(psi2)
center_x2 = x2 - robot_length / 2 * np.cos(psi2) + robot_width / 2 * np.sin(psi2)
center_y2 = y2 - robot_length / 2 * np.sin(psi2) - robot_width / 2 * np.cos(psi2)
rx2 = center_x2 + rear_axle_x * np.cos(psi2)
ry2 = center_y2 + rear_axle_x * np.sin(psi2)
rect2.set_xy((rx2, ry2))
rect3.set_width(robot_length)
rect3.set_height(robot_width)
rect3.angle = np.degrees(psi3)
center_x3 = x3 - robot_length / 2 * np.cos(psi3) + robot_width / 2 * np.sin(psi3)
center_y3 = y3 - robot_length / 2 * np.sin(psi3) - robot_width / 2 * np.cos(psi3)
rx3 = center_x3 + rear_axle_x * np.cos(psi3)
ry3 = center_y3 + rear_axle_x * np.sin(psi3)
rect3.set_xy((rx3, ry3))
rect4.set_width(robot_length)
rect4.set_height(robot_width)
rect4.angle = np.degrees(psi4)
center_x4 = x4 - robot_length / 2 * np.cos(psi4) + robot_width / 2 * np.sin(psi4)
center_y4 = y4 - robot_length / 2 * np.sin(psi4) - robot_width / 2 * np.cos(psi4)
rx4 = center_x4 + rear_axle_x * np.cos(psi4)
ry4 = center_y4 + rear_axle_x * np.sin(psi4)
rect4.set_xy((rx4, ry4))
ax.relim()
ax.autoscale_view()
plt.draw()
writer.grab_frame()
# save plt as gif
# Update the figure
plt.pause(0.01)
try:
writer.grab_frame()
except Exception as e:
print(f"Error grabbing frame: {e}")
time.sleep(0.01) # Simulate real-time update
plt.ioff() # Turn off interactive mode
plt.show()
# create new fig and plot a, w
fig, ax = plt.subplots()
ax.plot(a1, label='a')
ax.plot(w1, label='w')
ax.plot(vel1, label='v')
ax.legend()
plt.show()
if __name__ == '__main__':
test_multi_car()