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multi_agent_rmp_centralized.py
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# A simple centralized multi-agent RMP example:
# exchange positions while avoiding collisions
# @author Anqi Li
# @date April 8, 2019
from rmp import RMPRoot, RMPNode
from rmp_leaf import CollisionAvoidanceCentralized, GoalAttractorUni
import numpy as np
from numpy.linalg import norm
from scipy.integrate import solve_ivp
import matplotlib.pyplot as plt
import matplotlib.patches as patches
import matplotlib.animation as animation
import math
from scipy.spatial.distance import pdist
# ---------------------------------------------
# build the rmp tree
N = 10
theta = np.arange(0, 2 * np.pi, 2 * np.pi / N)
x_g = np.stack((np.cos(theta), np.sin(theta))).T * 10
r = RMPRoot('root')
def create_mappings_robot(i):
phi = lambda y, i=i: np.array([[y[2 * i, 0]], [y[2 * i + 1, 0]]])
J = lambda y, i=i: np.concatenate((
np.zeros((2, 2 * i)),
np.eye(2),
np.zeros((2, 2 * (N - i - 1)))), axis=1)
J_dot = lambda y, y_dot: np.zeros((2, 2 * N))
return phi, J, J_dot
def create_mappings_pair(i, j):
assert i < j
phi = lambda y, i=i, j=j: np.array([[y[2 * i, 0]], [y[2 * i + 1, 0]], [y[2 * j, 0]], [y[2 * j + 1, 0]]])
J = lambda y, i=i, j=j: np.concatenate(
(np.concatenate((
np.zeros((2, 2 * i)),
np.eye(2),
np.zeros((2, 2 * (N - i - 1)))), axis=1),
np.concatenate((
np.zeros((2, 2 * j)),
np.eye(2),
np.zeros((2, 2 * (N - j - 1)))), axis=1)),
axis=0)
J_dot = lambda y, y_dot: np.zeros((4, 2 * N))
return phi, J, J_dot
robots = []
for i in range(N):
phi, J, J_dot = create_mappings_robot(i)
robot = RMPNode('robot_' + str(i), r, phi, J, J_dot)
robots.append(robot)
count = 0
pairs = []
for i in range(N):
for j in range(N):
if i >= j:
continue
phi, J, J_dot = create_mappings_pair(i, j)
pair = RMPNode('pair_' + str(i) + '_' + str(j), r, phi, J, J_dot)
pairs.append(pair)
count += 1
gas = []
for i in range(N):
ga = GoalAttractorUni(
'ga_robot_' + str(i),
robots[i],
x_g[i],
alpha = 1,
gain = 1,
eta = 2)
gas.append(ga)
iacas = []
for i in range(count):
iaca = CollisionAvoidanceCentralized(
'ca_' + pairs[i].name,
pairs[i],
R = 1)
iacas.append(iaca)
# ----------------------------------------------
# -----------------------------------------
# possible initial configurations
x_0 = - x_g + np.random.randn(*x_g.shape) * 0.2
x = x_0.reshape(-1)
x_dot = np.zeros_like(x)
state_0 = np.concatenate((x, x_dot), axis=None)
r.set_root_state(x, x_dot)
r.pushforward()
r.pullback()
# --------------------------------------------
# --------------------------------------------
# dynamics
def dynamics(t, state):
state = state.reshape(2, -1)
x = state[0]
x_dot = state[1]
r.set_root_state(x, x_dot)
r.pushforward()
r.pullback()
x_ddot = r.resolve()
state_dot = np.concatenate((x_dot, x_ddot), axis=None)
return state_dot
# --------------------------------------------
# ---------------------------------------------
# solve the diff eq
sol = solve_ivp(dynamics, [0, 60], state_0)
# ---------------------------------------------
# --------------------------------------------
# plot trajectories
for i in range(N):
plt.plot(sol.y[2 * i], sol.y[2 * i + 1], 'y--')
plt.plot(x_g[i, 0], x_g[i, 1], 'go')
plt.plot(x_0[i, 0], x_0[i, 1], 'ro')
plt.axis(np.array([-12, 12, -12, 12]))
plt.gca().set_aspect('equal', 'box')
fig = plt.gcf()
ax = plt.gca()
agents, = plt.plot(sol.y[0: 2 * N: 2, 0], sol.y[1: 2 * N + 1: 2, 0], 'ko')
def init(): # only required for blitting to give a clean slate.
return agents,
def animate(i):
nsteps = sol.y.shape[-1]
agents.set_xdata(sol.y[0: 2 * N: 2, i % nsteps])
agents.set_ydata(sol.y[1: 2 * N + 1: 2, i % nsteps])
return agents,
ani = animation.FuncAnimation(
fig, animate, init_func=init, interval=20, blit=True)
plt.show()
# --------------------------------------------