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sim_mpc_forklift.py
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sim_mpc_forklift.py
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#!/usr/bin/env python
# coding=UTF-8
"""
Author: Wei Luo
Date: 2023-05-30 21:34:39
LastEditors: Wei Luo
LastEditTime: 2023-05-31 10:35:57
Note: Note
"""
import casadi as ca
from draw import Draw_FolkLift
import numpy as np
import time
# define a movement at next time step
def shift_movement(T, t0, x0, u, x_f, f):
f_value = f(x0, u[:, 0])
st = x0 + T * f_value.full()
t = t0 + T
u_end = np.concatenate((u[:, 1:], u[:, -1:]), axis=1)
x_f = np.concatenate((x_f[:, 1:], x_f[:, -1:]), axis=1)
return t, st, u_end, x_f
if __name__ == "__main__":
T = 0.2
N = 100
l = 1.0
v_max = 0.6
omega_max = np.pi / 4.0
x = ca.MX.sym("x")
y = ca.MX.sym("y")
theta = ca.MX.sym("theta")
alpha = ca.MX.sym("alpha")
states = ca.vertcat(x, y, theta, alpha)
n_states = states.size()[0]
v = ca.MX.sym("v")
omega = ca.MX.sym("omega")
controls = ca.vertcat(v, omega)
n_controls = controls.size()[0]
# rhs
rhs = ca.vertcat(
v * ca.cos(theta) * ca.cos(alpha),
v * ca.sin(theta) * ca.cos(alpha),
v / l * ca.sin(alpha),
omega,
)
# function
f = ca.Function(
"f", [states, controls], [rhs], ["input_state", "control_input"], ["rhs"]
)
# for MPC
U = ca.MX.sym("U", n_controls, N)
X = ca.MX.sym("X", n_states, N + 1)
P = ca.MX.sym("P", n_states + n_states)
# define
Q = np.array(
[
[5.0, 0.0, 0.0, 0.0],
[0.0, 5.0, 0.0, 0.0],
[0.0, 0.0, 2., 0.0],
[0.0, 0.0, 0.0, 0.1],
]
)
R = np.array([[0.5, 0.0], [0.0, .4]])
# cost function
obj = 0 # cost
g = [] # equal constrains
g.append(X[:, 0] - P[:n_states])
for i in range(N):
obj = (
obj
+ ca.mtimes([(X[:, i] - P[n_states:]).T, Q, X[:, i] - P[n_states:]])
+ ca.mtimes([U[:, i].T, R, U[:, i]])
)
x_next_ = f(X[:, i], U[:, i]) * T + X[:, i]
g.append(X[:, i + 1] - x_next_)
opt_variables = ca.vertcat(ca.reshape(U, -1, 1), ca.reshape(X, -1, 1))
nlp_prob = {"f": obj, "x": opt_variables, "p": P, "g": ca.vertcat(*g)}
opts_setting = {
"ipopt.max_iter": 100,
"ipopt.print_level": 0,
"print_time": 0,
"ipopt.acceptable_tol": 1e-8,
"ipopt.acceptable_obj_change_tol": 1e-6,
}
solver = ca.nlpsol("solver", "ipopt", nlp_prob, opts_setting)
lbg = 0.0
ubg = 0.0
lbx = []
ubx = []
for _ in range(N):
lbx.append(-v_max)
lbx.append(-omega_max)
ubx.append(v_max)
ubx.append(omega_max)
for _ in range(
N + 1
): # note that this is different with the method using structure
lbx.append(-16.0)
lbx.append(-16.0)
lbx.append(-np.pi)
lbx.append(-np.pi / 2.0)
ubx.append(7.01)
ubx.append(7.01)
ubx.append(np.pi)
ubx.append(np.pi / 2.0)
# simulation
t0 = 0.0
x_init = np.array([0.0, 0.0, 0.0, 0.0])
x_current = x_init.copy().reshape(-1, 1)
x_target = np.array([7, 7, 0.0, 0.0]).reshape(-1, 1)
u_guess = np.array([0.0, 0.0] * N).reshape(-1, 2)
x_guess = np.zeros((n_states, N + 1))
start_time = time.time()
cal_time_list = []
state_results = []
control_results = []
time_step_list = []
final_state_results = []
mpc_iter = 0
while np.linalg.norm(x_target - x_init) > 1e-3 and mpc_iter < 100:
# parameters
c_p = np.concatenate((x_current, x_target))
# guessing optimization states
init_opt_state = np.concatenate(
(u_guess.T.reshape(-1, 1), x_guess.T.reshape(-1, 1))
)
t_ = time.time()
opt_result = solver(
x0=init_opt_state, p=c_p, lbg=lbg, ubg=ubg, lbx=lbx, ubx=ubx
)
cal_time_list.append(time.time() - t_)
estimated_result = opt_result["x"].full()
u_guess = estimated_result[: n_controls * N].reshape(N, n_controls).T
x_guess = estimated_result[n_controls * N :].reshape(N + 1, n_states).T
# print(x_guess.T)
state_results.append(x_guess.T)
final_state_results.append(x_guess.T[0])
control_results.append(u_guess[:, 0])
time_step_list.append(t0)
t0, x_current, u_guess, x_guess = shift_movement(
T, t0, x_current, u_guess, x_guess, f
)
mpc_iter += 1
Draw_FolkLift(final_state_results, x_init, False)