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demo_buoys.py
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demo_buoys.py
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from __future__ import division
import numpy as np
import numpy.linalg as npl
from matplotlib import pyplot as plt
import matplotlib.animation as ani
import alqr
# Hmm let's try a linear system with two positional
# states [position1, position2, velocity1, velocity2]
# and with damping but no springs.
# One "thruster" is available on each axis.
# Remember that xDOT = Ax + Bu.
nstates = 4
ncontrols = 2
drag = 3
def linearize(x):
A = np.array([
[ 0, 0, 1, 0],
[ 0, 0, 0, 1],
[ 0, 0, -drag/1.5, 0],
[ 0, 0, 0, -drag]
])
B = np.array([
[0, 0],
[0, 0],
[1, 0],
[0, 1]
])
return (A, B)
def dynamics(x, u):
# Truly linear system!
A, B = linearize(x)
return A.dot(x) + B.dot(u)
# Set up a cost field
goal = [1, 1, 0, 0]
cost_field = alqr.Cost_Field(nstates, ncontrols, goal,
goal_weight=2, obstacle_weight=1, effort_weight=0.3)
# Noised grid of obstacles
obs_grid_x, obs_grid_y = np.mgrid[slice(0.3, 1+0.2, 0.2), slice(0.3, 1+0.2, 0.2)]
obs_grid_x = obs_grid_x.reshape(obs_grid_x.size)
obs_grid_y = obs_grid_y.reshape(obs_grid_y.size)
obs = [np.zeros(2)] * obs_grid_x.size
for i in range(len(obs)):
obs[i] = np.round([obs_grid_x[i], obs_grid_y[i]] + 0.1*(np.random.rand(2)-0.5), 2)
name = 'buoy' + str(i)
cost_field.add_obstacle(name, obs[i], 0.1)
# Associate an alqr planner
planning_horizon = 10 # s
planning_resolution = 0.03 # s
planner = alqr.Planner(dynamics, linearize, cost_field,
planning_horizon, planning_resolution,
demo_plots=True)
# Initial condition and time
x = [0, 0.05, 0, 0]
dt = planning_resolution # convenient to use in sim testing too
t_arr = np.arange(0, planning_horizon, dt)
framerate = 30
show_cost_field = True
# Plan a path from these initial conditions
planner.update_plan(x)
# Preallocate results memory
x_history = np.zeros((len(t_arr), nstates))
goal_history = np.zeros((len(t_arr), nstates))
u_history = np.zeros((len(t_arr), ncontrols))
c_history = np.zeros(len(t_arr))
# Integrate dynamics
for i, t in enumerate(t_arr):
# Planner's decision
u = planner.u_seq[i, :]
# u = planner.get_effort(t)
# Record this instant
x_history[i, :] = x
goal_history[i, :] = goal
u_history[i, :] = u
c_history[i] = cost_field.state_cost(x)
# First-order integrate
xdot = dynamics(x, u)
x = x + xdot*dt
# Plot results
fig1 = plt.figure()
fig1.suptitle('Results', fontsize=20)
ax1 = fig1.add_subplot(2, 3, 1)
ax1.set_ylabel('Position 1', fontsize=16)
ax1.plot(t_arr, x_history[:, 0], 'k',
t_arr, goal_history[:, 0], 'g--')
ax1.grid(True)
ax1 = fig1.add_subplot(2, 3, 2)
ax1.set_ylabel('Position 2', fontsize=16)
ax1.plot(t_arr, x_history[:, 1], 'k',
t_arr, goal_history[:, 1], 'g--')
ax1.grid(True)
ax1 = fig1.add_subplot(2, 3, 3)
ax1.set_ylabel('Efforts', fontsize=16)
ax1.plot(t_arr, u_history[:, 0], 'b',
t_arr, u_history[:, 1], 'g')
ax1.grid(True)
ax1 = fig1.add_subplot(2, 3, 4)
ax1.set_ylabel('Velocity 1', fontsize=16)
ax1.plot(t_arr, x_history[:, 2], 'k',
t_arr, goal_history[:, 2], 'g--')
ax1.set_xlabel('Time')
ax1.grid(True)
ax1 = fig1.add_subplot(2, 3, 5)
ax1.set_ylabel('Velocity 2', fontsize=16)
ax1.plot(t_arr, x_history[:, 3], 'k',
t_arr, goal_history[:, 3], 'g--')
ax1.set_xlabel('Time')
ax1.grid(True)
ax1 = fig1.add_subplot(2, 3, 6)
ax1.set_ylabel('State Cost', fontsize=16)
ax1.plot(t_arr, c_history, 'k')
ax1.grid(True)
ax1.set_xlabel('Time')
print("\nClose the plot window to continue to animation.")
plt.show()
# Animation
fig2 = plt.figure()
fig2.suptitle('Evolution', fontsize=24)
plt.axis('equal')
ax2 = fig2.add_subplot(1, 1, 1)
ax2.set_xlabel('- Position 1 +')
ax2.set_ylabel('- Position 2 +')
ax2.grid(True)
radius = 0.02
xlim = (min(x_history[:, 0])*1.1 - radius, max(x_history[:, 0])*1.1 + radius)
ylim = (min(x_history[:, 1])*1.1 - radius, max(x_history[:, 1])*1.1 + radius)
ax2.set_xlim(xlim)
ax2.set_ylim(ylim)
# (color map of cost function over position space, zero velocity)
if show_cost_field:
# resolution
dX, dY = 0.01, 0.01
# grid
X, Y = np.mgrid[slice(xlim[0], xlim[1] + dX, dX),
slice(ylim[0], ylim[1] + dY, dY)]
Jmap = np.zeros_like(X)
# evaluate cost field
for i, xval in enumerate(X[:, 0]):
for j, yval in enumerate(Y[0, :]):
Jmap[i, j] = cost_field.state_cost([xval, yval, 0, 0])
if Jmap[i, j] < 0:
print "Negative cost! At ({0}, {1})".format(xval, yval)
Jmap = Jmap[:-1, :-1]
plt.pcolor(X, Y, Jmap, cmap='YlOrRd', vmin=np.min(Jmap), vmax=np.max(Jmap))
plt.colorbar()
graphic_robot = ax2.add_patch(plt.Circle((x_history[0, 0], x_history[0, 1]), radius=radius, fc='k'))
graphic_goal = ax2.add_patch(plt.Circle((goal_history[0, 0], goal_history[0, 1]), radius=radius, fc='g'))
for p in cost_field.obstacle_positions:
ax2.add_patch(plt.Circle((p[0], p[1]), radius=radius, fc='r'))
def ani_update(arg, ii=[0]):
i = ii[0] # don't ask...
if np.isclose(t_arr[i], np.around(t_arr[i], 1)):
fig2.suptitle('Evolution (Time: {})'.format(t_arr[i]), fontsize=24)
graphic_robot.center = ((x_history[i, 0], x_history[i, 1]))
ii[0] += int(1 / (dt * framerate))
if ii[0] >= len(t_arr):
print("Resetting animation!")
ii[0] = 0
return [graphic_robot]
# Run animation
print("\nStarting animation. \nBlack: robot \nRed: obstacles \nGreen: goal \nHeat Map: state cost\n")
animation = ani.FuncAnimation(fig2, func=ani_update, interval=dt*1000)
plt.show()