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robot_mpc_obs_DLCBF.py
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robot_mpc_obs_DLCBF.py
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import casadi as ca
import numpy as np
from matplotlib.patches import Rectangle, Circle
import matplotlib.pyplot as plt
from Car import Car
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: Car, T=0.1, N=50, Q=np.diag([100.0, 100.0, 1.0, 1.0, 1.0]), R=np.diag([0.1, 0.1])):
self.car = car
self.T = T # time step
self.N = N # horizon length
self.Q = Q
self.R = R
self.next_states = np.zeros((self.N + 1, 5))
self.u0 = np.zeros((self.N, 2))
def control_barrier_function(self, x, y, obs_x, obs_y, obs_r):
safety_margin = 0.1 # Additional safety margin
return (x - obs_x)**2 + (y - obs_y)**2 - (obs_r + self.car.d + safety_margin)**2
def lyapunov_function(self, x, x_ref):
# Simple quadratic Lyapunov function
return ca.sum1((x - x_ref)**2)
def setupController(self, obs, gamma=0.2, alpha=0.1, use_cbf=True, use_lyapunov=False):
self.opti = ca.Opti()
self.U = self.opti.variable(self.N, 2)
control_a = self.U[:, 0]
control_omega = self.U[:, 1]
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]
# Lyapunov relaxation variable
if use_lyapunov:
delta = self.opti.variable()
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]
])
self.x_ref = self.opti.parameter(2, 5)
self.u_ref = self.opti.parameter(self.N, 2)
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)
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)
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 Lyapunov relaxation term to objective if use_lyapunov is True
if use_lyapunov:
l = 1000 # Weight for Lyapunov relaxation
obj += l * delta**2
self.opti.minimize(obj)
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))
# CBF constraints
if use_cbf:
for i in range(self.N):
for j in range(num_obs):
h = self.control_barrier_function(state_x[i], state_y[i], self.x_obs[j], self.y_obs[j], self.r_obs[j])
h_next = self.control_barrier_function(state_x[i+1], state_y[i+1], self.x_obs[j], self.y_obs[j], self.r_obs[j])
self.opti.subject_to(h_next - h + gamma * h >= 0)
else:
for i in range(self.N):
for k in range(num_obs):
ob_x = self.x_obs[k]
ob_y = self.y_obs[k]
ob_r = self.r_obs[k]
self.opti.subject_to((state_x[i] - ob_x)**2 + (state_y[i] - ob_y)**2 >= (ob_r + self.car.d)**2)
# Lyapunov constraint
if use_lyapunov:
for i in range(self.N):
V = self.lyapunov_function(self.X[i, :], goal_state)
V_next = self.lyapunov_function(self.X[i+1, :], goal_state)
self.opti.subject_to(V_next - V + alpha * V <= delta)
opts_setting = {'ipopt.max_iter': 2000,
'ipopt.print_level': 0,
'print_time': 0,
'ipopt.acceptable_tol': 1e-8,
'ipopt.acceptable_obj_change_tol': 1e-6}
self.opti.solver('ipopt', opts_setting)
def solve(self, x_ref, u_ref, obs):
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])
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)))
self.opti.solve()
u_opt = self.opti.value(self.U)
x_opt = self.opti.value(self.X)
self.u0, self.next_states = shift(u_opt, x_opt)
return u_opt[:, 0], u_opt[:, 1]
def solve_obs(self, x_ref, u_ref, x_obs, y_obs, r_obs):
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, x_obs)
self.opti.set_value(self.y_obs, y_obs)
self.opti.set_value(self.r_obs, r_obs)
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)))
self.opti.solve()
u_opt = self.opti.value(self.U)
x_opt = self.opti.value(self.X)
self.u0, self.next_states = shift(u_opt, x_opt)
return u_opt[:, 0], u_opt[:, 1]
def is_goal_reached(self, current_state, goal_state, tolerance=0.1):
distance = np.linalg.norm(current_state[:2] - goal_state[:2])
return distance < tolerance
def run_until_goal(self, x_ref, u_ref, obs, tolerance=0.1, use_cbf=True, use_lyapunov=False):
# compute gamma based on distance to obs
dis = np.linalg.norm(x_ref[0, :2] - obs[0, :2])
# gamma linear from 0.1 to 0.5 based on distance to obs ( dis = 1, gamma = 0.1; dis = 10, gamma = 0.5)
gamma_dis = 0.1 + 0.04 * dis
self.setupController(obs, 0.1, 0.5, use_cbf=use_cbf, use_lyapunov=use_lyapunov)
current_state = x_ref[0, :]
goal_state = x_ref[-1, :]
trajectory = [current_state]
control_inputs = []
plt.ion() # Turn on interactive mode
fig, ax = plt.subplots()
ax.set_xlim(-1, 13)
ax.set_ylim(-1, 13)
# Initialize plot elements
actual_line, = ax.plot([], [], 'b-', label='Actual Trajectory', linewidth=2)
predict_line, = ax.plot([], [], 'r--', label='Predicted Trajectory', linewidth=1)
rect = Rectangle((0, 0), 1, 1, angle=0, color='g', fill=True, label='Robot Pose', alpha=0.2)
ax.add_patch(rect)
obs_circles = [plt.Circle((obs[i, 0], obs[i, 1]), obs[i, 2], color='r', fill=True, alpha=0.2) for i in range(len(obs))]
for circle in obs_circles:
ax.add_artist(circle)
# Plot start and goal markers
ax.plot(x_ref[0, 0], x_ref[0, 1], 'g*', label='Start')
ax.plot(x_ref[-1, 0], x_ref[-1, 1], 'ro', label='Goal')
ax.legend()
def update_plot():
trajectory_np = np.array(trajectory)
actual_line.set_data(trajectory_np[:, 0], trajectory_np[:, 1])
# Update predicted trajectory
predicted_trajectory = self.next_states
predict_line.set_data(predicted_trajectory[:, 0], predicted_trajectory[:, 1])
# Update rectangle to represent the robot pose
x, y, psi = current_state[0], current_state[1], current_state[2]
robot_width, robot_length = 0.5, 1.0
rear_axle_x = robot_length / 4
rect.set_width(robot_length)
rect.set_height(robot_width)
rect.angle = np.degrees(psi)
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)
rx = center_x + rear_axle_x * np.cos(psi)
ry = center_y + rear_axle_x * np.sin(psi)
rect.set_xy((rx, ry))
ax.relim()
ax.autoscale_view()
plt.draw()
# Function to handle key press events
def on_key(event):
if event.key == 'escape':
plt.close(fig)
# Connect the key press event to the figure
fig.canvas.mpl_connect('key_press_event', on_key)
simulation_running = True
while simulation_running and not self.is_goal_reached(current_state, goal_state, tolerance):
u_a, u_omega = self.solve(x_ref, u_ref, obs)
current_state = self.next_states[1]
trajectory.append(current_state)
control_inputs.append([u_a[0], u_omega[0]]) # Store only the first control input
x_ref = np.concatenate(([current_state], x_ref[1:]))
u_ref = np.concatenate((self.u0, u_ref[self.N:]))
update_plot()
plt.pause(0.1)
if not plt.get_fignums(): # Check if the figure has been closed
simulation_running = False
plt.ioff()
plt.close(fig)
return np.array(trajectory), np.array(control_inputs)
def plot_results(self, trajectory, control_inputs, x_ref, obs):
time = np.arange(len(trajectory)) * self.T
fig = plt.figure(figsize=(20, 15))
grid = plt.GridSpec(3, 3, figure=fig)
# Trajectory plot
ax_traj = fig.add_subplot(grid[:, 0])
ax_traj.plot(trajectory[:, 0], trajectory[:, 1], 'b-', label='Actual Trajectory')
ax_traj.plot(x_ref[0, 0], x_ref[0, 1], 'g*', markersize=10, label='Start')
ax_traj.plot(x_ref[-1, 0], x_ref[-1, 1], 'r*', markersize=10, label='Goal')
# Plot obstacles
for ob in obs:
circle = Circle((ob[0], ob[1]), ob[2], fill=True, color='r')
ax_traj.add_artist(circle)
ax_traj.set_xlabel('X Position (m)')
ax_traj.set_ylabel('Y Position (m)')
ax_traj.set_title('Robot Trajectory')
ax_traj.legend()
ax_traj.grid(True)
ax_traj.axis('equal')
# X and Y positions over time
ax_x = fig.add_subplot(grid[0, 1])
ax_x.plot(time, trajectory[:, 0], 'b-')
ax_x.set_ylabel('X Position (m)')
ax_x.grid(True)
ax_y = fig.add_subplot(grid[0, 2])
ax_y.plot(time, trajectory[:, 1], 'r-')
ax_y.set_ylabel('Y Position (m)')
ax_y.grid(True)
# Orientation and velocity over time
ax_psi = fig.add_subplot(grid[1, 1])
ax_psi.plot(time, np.degrees(trajectory[:, 2]), 'g-')
ax_psi.set_ylabel('Orientation (degrees)')
ax_psi.grid(True)
ax_v = fig.add_subplot(grid[1, 2])
ax_v.plot(time, trajectory[:, 3], 'm-')
ax_v.set_ylabel('Velocity (m/s)')
ax_v.grid(True)
# Control inputs over time
ax_a = fig.add_subplot(grid[2, 1])
ax_a.plot(time[:-1], control_inputs[:, 0], 'c-')
ax_a.set_ylabel('Acceleration (m/s^2)')
ax_a.set_xlabel('Time (s)')
ax_a.grid(True)
ax_omega = fig.add_subplot(grid[2, 2])
ax_omega.plot(time[:-1], np.degrees(control_inputs[:, 1]), 'y-')
ax_omega.set_ylabel('Steering Rate (degrees/s)')
ax_omega.set_xlabel('Time (s)')
ax_omega.grid(True)
plt.tight_layout()
plt.show()
pass
def test_run():
car = Car()
mpc_controller = MPCController(car, T=0.2, N=10)
x_ref = np.array([[0, 0, 0, 0, 0], [10, 10, 0, 0, 0]])
u_ref = np.zeros((mpc_controller.N, 2))
obs = np.array([[5, 5, 2]])
# Run with Lyapunov constraint
trajectory_lyap, control_inputs_lyap = mpc_controller.run_until_goal(x_ref, u_ref, obs, tolerance=0.1, use_cbf=True,
use_lyapunov=True)
mpc_controller.plot_results(trajectory_lyap, control_inputs_lyap, x_ref, obs)
# Run without Lyapunov constraint
trajectory_no_lyap, control_inputs_no_lyap = mpc_controller.run_until_goal(x_ref, u_ref, obs, tolerance=0.1,
use_cbf=True, use_lyapunov=False)
mpc_controller.plot_results(trajectory_no_lyap, control_inputs_no_lyap, x_ref, obs)
# Compare results
plt.figure(figsize=(12, 8))
plt.plot(trajectory_lyap[:, 0], trajectory_lyap[:, 1], 'b-', label='With Lyapunov')
plt.plot(trajectory_no_lyap[:, 0], trajectory_no_lyap[:, 1], 'r--', label='Without Lyapunov')
plt.plot(x_ref[0, 0], x_ref[0, 1], 'g*', markersize=10, label='Start')
plt.plot(x_ref[-1, 0], x_ref[-1, 1], 'ro', markersize=10, label='Goal')
# Plot obstacle
obstacle = plt.Circle((obs[0, 0], obs[0, 1]), obs[0, 2], color='gray', fill=True, alpha=0.3)
plt.gca().add_artist(obstacle)
plt.xlabel('X Position (m)')
plt.ylabel('Y Position (m)')
plt.title('Comparison of Trajectories With and Without Lyapunov Constraint')
plt.legend()
plt.grid(True)
plt.axis('equal')
plt.show()
if __name__ == '__main__':
test_run()