mpc_python_learn/mpc_pybullet_demo/mpc_demo_nosim.py

299 lines
8.1 KiB
Python
Executable File

#! /usr/bin/env python
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import animation
from scipy.integrate import odeint
from mpcpy.utils import compute_path_from_wp
import mpcpy
import sys
import time
# Robot Starting position
SIM_START_X = 0.0
SIM_START_Y = 0.5
SIM_START_V = 0.0
SIM_START_H = 0.0
L = 0.3
params = mpcpy.Params()
# Params
VEL = 1.0 # m/s
# Classes
class MPCSim:
def __init__(self):
# State for the robot mathematical model [x,y,heading]
self.state = np.array([SIM_START_X, SIM_START_Y, SIM_START_V, SIM_START_H])
# starting guess
self.action = np.zeros(params.M)
self.action[0] = params.MAX_ACC / 2 # a
self.action[1] = 0.0 # delta
self.K = int(params.T / params.DT)
self.opt_u = np.zeros((params.M, self.K))
# Cost Matrices
Q = [20, 20, 10, 20] # state error cost
Qf = [30, 30, 30, 30] # state final error cost
R = [10, 10] # input cost
P = [10, 10] # input rate of change cost
self.mpc = mpcpy.MPC(Q, Qf, R, P)
# Interpolated Path to follow given waypoints
self.path = compute_path_from_wp(
[0, 3, 4, 6, 10, 12, 13, 13, 6, 1, 0],
[0, 0, 2, 4, 3, 3, -1, -2, -6, -2, -2],
0.05,
)
# Sim help vars
self.sim_time = 0
self.x_history = []
self.y_history = []
self.v_history = []
self.h_history = []
self.a_history = []
self.d_history = []
self.predicted = None
# Initialise plot
plt.style.use("ggplot")
self.fig = plt.figure()
plt.ion()
plt.show()
def preview(self, mpc_out):
"""
[TODO:summary]
[TODO:description]
"""
predicted = np.zeros(self.opt_u.shape)
predicted[:, :] = mpc_out[0:2, 1:]
Rotm = np.array(
[
[np.cos(self.state[3]), np.sin(self.state[3])],
[-np.sin(self.state[3]), np.cos(self.state[3])],
]
)
predicted = (predicted.T.dot(Rotm)).T
predicted[0, :] += self.state[0]
predicted[1, :] += self.state[1]
self.predicted = predicted
def run(self):
"""
[TODO:summary]
[TODO:description]
"""
self.plot_sim()
input("Press Enter to continue...")
while 1:
if (
np.sqrt(
(self.state[0] - self.path[0, -1]) ** 2
+ (self.state[1] - self.path[1, -1]) ** 2
)
< 0.5
):
print("Success! Goal Reached")
input("Press Enter to continue...")
return
# optimization loop
# start=time.time()
# dynamycs w.r.t robot frame
curr_state = np.array([0, 0, self.state[2], 0])
# State Matrices
A, B, C = mpcpy.get_linear_model_matrices(curr_state, self.action)
# Get Reference_traj -> inputs are in worldframe
target, _ = mpcpy.get_ref_trajectory(self.state, self.path, VEL)
x_mpc, u_mpc = self.mpc.optimize_linearized_model(
A,
B,
C,
curr_state,
target,
verbose=False,
)
# NOTE: used only for preview purposes
self.opt_u = np.vstack(
(
np.array(u_mpc.value[0, :]).flatten(),
np.array(u_mpc.value[1, :]).flatten(),
)
)
self.action[:] = [u_mpc.value[0, 0], u_mpc.value[1, 0]]
# print("CVXPY Optimization Time: {:.4f}s".format(time.time()-start))
self.predict([self.action[0], self.action[1]])
self.preview(x_mpc.value)
self.plot_sim()
def predict(self, u):
def kinematics_model(x, t, u):
dxdt = x[2] * np.cos(x[3])
dydt = x[2] * np.sin(x[3])
dvdt = u[0]
dtheta0dt = x[2] * np.tan(u[1]) / params.L
dqdt = [dxdt, dydt, dvdt, dtheta0dt]
return dqdt
# solve ODE
tspan = [0, params.DT]
self.state = odeint(kinematics_model, self.state, tspan, args=(u[:],))[1]
def plot_sim(self):
"""
[TODO:summary]
[TODO:description]
"""
self.sim_time = self.sim_time + params.DT
self.x_history.append(self.state[0])
self.y_history.append(self.state[1])
self.v_history.append(self.state[2])
self.h_history.append(self.state[3])
self.a_history.append(self.opt_u[0, 1])
self.d_history.append(self.opt_u[1, 1])
plt.clf()
grid = plt.GridSpec(2, 3)
plt.subplot(grid[0:2, 0:2])
plt.title(
"MPC Simulation \n" + "Simulation elapsed time {}s".format(self.sim_time)
)
plt.plot(
self.path[0, :],
self.path[1, :],
c="tab:orange",
marker=".",
label="reference track",
)
plt.plot(
self.x_history,
self.y_history,
c="tab:blue",
marker=".",
alpha=0.5,
label="vehicle trajectory",
)
if self.predicted is not None:
plt.plot(
self.predicted[0, :],
self.predicted[1, :],
c="tab:green",
marker="+",
alpha=0.5,
label="mpc opt trajectory",
)
# plt.plot(self.x_history[-1], self.y_history[-1], c='tab:blue',
# marker=".",
# markersize=12,
# label="vehicle position")
# plt.arrow(self.x_history[-1],
# self.y_history[-1],
# np.cos(self.h_history[-1]),
# np.sin(self.h_history[-1]),
# color='tab:blue',
# width=0.2,
# head_length=0.5,
# label="heading")
plot_car(self.x_history[-1], self.y_history[-1], self.h_history[-1])
plt.ylabel("map y")
plt.yticks(
np.arange(min(self.path[1, :]) - 1.0, max(self.path[1, :] + 1.0) + 1, 1.0)
)
plt.xlabel("map x")
plt.xticks(
np.arange(min(self.path[0, :]) - 1.0, max(self.path[0, :] + 1.0) + 1, 1.0)
)
plt.axis("equal")
# plt.legend()
plt.subplot(grid[0, 2])
# plt.title("Linear Velocity {} m/s".format(self.v_history[-1]))
plt.plot(self.a_history, c="tab:orange")
locs, _ = plt.xticks()
plt.xticks(locs[1:], locs[1:] * params.DT)
plt.ylabel("a(t) [m/ss]")
plt.xlabel("t [s]")
plt.subplot(grid[1, 2])
# plt.title("Angular Velocity {} m/s".format(self.w_history[-1]))
plt.plot(np.degrees(self.d_history), c="tab:orange")
plt.ylabel("gamma(t) [deg]")
locs, _ = plt.xticks()
plt.xticks(locs[1:], locs[1:] * params.DT)
plt.xlabel("t [s]")
plt.tight_layout()
plt.draw()
plt.pause(0.1)
def plot_car(x, y, yaw):
"""
[TODO:summary]
[TODO:description]
Parameters
----------
x : [TODO:type]
[TODO:description]
y : [TODO:type]
[TODO:description]
yaw : [TODO:type]
[TODO:description]
"""
LENGTH = 0.5 # [m]
WIDTH = 0.25 # [m]
OFFSET = LENGTH # [m]
outline = np.array(
[
[-OFFSET, (LENGTH - OFFSET), (LENGTH - OFFSET), -OFFSET, -OFFSET],
[WIDTH / 2, WIDTH / 2, -WIDTH / 2, -WIDTH / 2, WIDTH / 2],
]
)
Rotm = np.array([[np.cos(yaw), np.sin(yaw)], [-np.sin(yaw), np.cos(yaw)]])
outline = (outline.T.dot(Rotm)).T
outline[0, :] += x
outline[1, :] += y
plt.plot(
np.array(outline[0, :]).flatten(), np.array(outline[1, :]).flatten(), "tab:blue"
)
def do_sim():
sim = MPCSim()
try:
sim.run()
except Exception as e:
sys.exit(e)
if __name__ == "__main__":
do_sim()