bicycle-obstacle-avoidance-mpc.py

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## @example mpc/python/bicycle/bicycle-obstacle-avoidance-mpc.py
# This example shows how to call the alpaqa solver from Python code, applied
# to a simple model predictive control problem.
 
#%% Import necessary libraries and generate the MPC problem
 
import casadi as cs
import numpy as np
import time
import matplotlib.pyplot as plt
from datetime import timedelta
import os
import sys
 
sys.path.append(os.path.dirname(__file__))
 
from bicycle_model import generate_problem
 
Ts = 0.05  # Sampling time
N_hor = 18  # Horizon length
N_sim = 80 # Length of the simulation
 
multipleshooting = False
R_obstacle = 2
 
f, nlp, bounds, n_states, n_inputs, first_input_idx = generate_problem(
    Ts, N_hor, R_obstacle, multipleshooting
)
 
# %% Build the problem for PANOC+ALM
 
import panocpy as pa
from tempfile import TemporaryDirectory
 
name = "mpcproblem"
f_prob = cs.Function("f", [nlp["x"], nlp["p"]], [nlp["f"]])
g_prob = cs.Function("g", [nlp["x"], nlp["p"]], [nlp["g"]])
prob = pa.generate_and_compile_casadi_problem(f_prob, g_prob, name=name)
 
prob.C.lowerbound = bounds["lbx"]
prob.C.upperbound = bounds["ubx"]
prob.D.lowerbound = bounds["lbg"]
prob.D.upperbound = bounds["ubg"]
 
#%% PANOC params
 
lbfgsmem = N_hor
tol = 1e-5
verbose = False
 
panocparams = {
    "max_iter": 1000,
    "max_time": timedelta(seconds=0.5),
    "print_interval": 10 if verbose else 0,
    "stop_crit": pa.PANOCStopCrit.ProjGradUnitNorm,
    "update_lipschitz_in_linesearch": True,
}
 
innersolver = pa.PANOCSolver(
    pa.PANOCParams(**panocparams),
    pa.LBFGSParams(memory=lbfgsmem),
)
 
almparams = pa.ALMParams(
    max_iter=20,
    max_time=timedelta(seconds=1),
    print_interval=1 if verbose else 0,
    preconditioning=False,
    ε=tol,
    δ=tol,
    Δ=5,
    Σ_0=4e5,
    Σ_max=1e12,
)
 
#%% Simulate MPC
 
solver = pa.ALMSolver(almparams, innersolver)
 
state = np.array([-5, 0, 0, 0])
dest = np.array([5, 0.1, 0, 0])
 
if multipleshooting:
    x_sol = np.concatenate((np.tile(state, N_hor), np.zeros((n_inputs * N_hor,))))
else:
    x_sol = np.zeros((prob.n,))
assert x_sol.size == prob.n
y_sol = np.zeros((prob.m,))
 
 
def solve_ocp(state, y_sol, x_sol):
    state = np.reshape(state, (n_states,))
    prob.param = np.concatenate((state, dest))
    t0 = time.perf_counter()
    x_sol, y_sol, stats = solver(problem=prob, x=x_sol, y=y_sol)
    t1 = time.perf_counter()
    return t1 - t0, stats, state, y_sol, x_sol
 
 
xs = np.zeros((N_sim, n_states))
times = np.zeros((N_sim,))
for k in range(N_sim):
    t, stats, state, y_sol, x_sol = solve_ocp(state, y_sol, x_sol)
    times[k] = t
    xs[k] = state
    print(
        stats["status"],
        stats["elapsed_time"],
        stats["outer_iterations"],
        stats["inner"]["iterations"],
    )
    input = x_sol[first_input_idx : first_input_idx + n_inputs]
    state += Ts * f(state, input)
 
#%% Plot
 
fig_trajectory, ax = plt.subplots(1, 1)
c = plt.Circle((0, 0), R_obstacle)
ax.set_aspect(1)
ax.add_artist(c)
ax.plot(xs[:, 0], xs[:, 1], "r.-")
ax.set_title('Trajectory')
 
fig_time, ax = plt.subplots(1, 1)
ax.plot(times)
ax.set_title("Run time")
ax.set_xlabel("MPC time step")
ax.set_ylabel("Run time [s]")
 
plt.show()
 
# %%