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util.py
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util.py
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import numpy as np
import itertools
from casadi import *
import casadi as cs
import random
import matplotlib.pyplot as plt
from scipy.spatial.transform import Rotation
π = np.pi
def plot_solve(X, J, x_goal, x_dims=None, color_agents=False, n_d=2, ax=None):
"""Plot the resultant trajectory on plt.gcf()"""
if n_d not in (2, 3):
raise ValueError()
if not x_dims:
x_dims = [X.shape[1]]
if not ax:
if n_d == 2:
ax = plt.gca()
else:
ax = plt.gcf().add_subplot(projection="3d")
ax.set_box_aspect([1.5, 1.5, 1])
N = X.shape[0]
n = np.arange(N)
cm = plt.cm.Set2
# cm = plt.cm.viridis
X_split = split_agents(X, x_dims)
x_goal_split = split_agents(x_goal.reshape(1, -1), x_dims)
for i, (Xi, xg) in enumerate(zip(X_split, x_goal_split)):
c = n
if n_d == 2:
if color_agents:
c = cm.colors[i]
ax.plot(Xi[:, 0], Xi[:, 1], c=c, lw=5)
else:
ax.scatter(Xi[:, 0], Xi[:, 1], c=c)
ax.scatter(Xi[0, 0], Xi[0, 1], 80, "g", "d", label="$x_0$")
ax.scatter(xg[0, 0], xg[0, 1], 80, "r", "x", label="$x_f$")
else:
if color_agents:
# c = [cm.colors[i]] * Xi.shape[0]
c = cm.colors[i]
ax.plot(Xi[:, 0], Xi[:, 1], Xi[:, 2], c=c, lw=2)
# ax.scatter(Xi[:, 0], Xi[:, 1], Xi[:, 2], c=c, lw=2)
ax.scatter(
Xi[0, 0], Xi[0, 1], Xi[0, 2],
s=50, c="w", marker="d", edgecolors="k", label="$x_0$")
ax.scatter(
xg[0, 0], xg[0, 1], xg[0, 2],
s=50, c="k", marker="x", label="$x_f$")
ax.scatter(
Xi[-1, 0], Xi[-1, 1], Xi[-1,2],
s=50, color=c, marker="o", edgecolors="k")
plt.margins(0.1)
plt.title(f"Final Cost: {J:.3g}")
plt.draw()
def randomize_locs(n_pts, random=False, rel_dist=3.0, var=3.0, n_d=2):
"""Uniformly randomize locations of points in N-D while enforcing
a minimum separation between them.
"""
# Distance to move away from center if we're too close.
Δ = 0.1 * n_pts
x = var * np.random.uniform(-1, 1, (n_pts, n_d))
if random:
return x
# Determine the pair-wise indicies for an arbitrary number of agents.
pair_inds = np.array(list(itertools.combinations(range(n_pts), 2)))
move_inds = np.arange(n_pts)
# Keep moving points away from center until we satisfy radius
while move_inds.size:
center = np.mean(x, axis=0)
distances = compute_pairwise_distance(x.flatten(), [n_d] * n_pts).T
move_inds = pair_inds[distances.flatten() <= rel_dist]
x[move_inds] += Δ * (x[move_inds] - center)
return x
def face_goal(x0, xf):
"""Make the agents face the direction of their goal with a little noise"""
VAR = 0.01
dX = xf[:, :2] - x0[:, :2]
headings = np.arctan2(*np.rot90(dX, 1))
x0[:, -1] = headings + VAR * np.random.randn(x0.shape[0])
xf[:, -1] = headings + VAR * np.random.randn(x0.shape[0])
return x0, xf
def random_setup(
n_agents, n_states, is_rotation=False, n_d=2, energy=None, do_face=False, **kwargs
):
"""Create a randomized set up of initial and final positions"""
# We don't have to normlize for energy here
x_i = randomize_locs(n_agents, n_d=n_d, **kwargs)
# Rotate the initial points by some amount about the center.
if is_rotation:
θ = π + random.uniform(-π / 4, π / 4)
R = Rotation.from_euler("z", θ).as_matrix()[:2, :2]
x_f = x_i @ R - x_i.mean(axis=0)
else:
x_f = randomize_locs(n_agents, n_d=n_d, **kwargs)
x0 = np.c_[x_i, np.zeros((n_agents, n_states - n_d))]
xf = np.c_[x_f, np.zeros((n_agents, n_states - n_d))]
if do_face:
x0, xf = face_goal(x0, xf)
x0 = x0.reshape(-1, 1)
xf = xf.reshape(-1, 1)
# Normalize to satisfy the desired energy of the problem.
if energy:
x0 = normalize_energy(x0, [n_states] * n_agents, energy, n_d)
xf = normalize_energy(xf, [n_states] * n_agents, energy, n_d)
return x0, xf
def setup_n_quads_V2(n_quads,r_safety):
n_states = 12
x0,v0 = set_random(n_quads,r_safety,False)
x_0 = np.zeros((n_states*n_quads,))
for agent,(pos,vel) in enumerate(zip(x0,v0)):
x_0[agent*n_states:(agent+1)*n_states][:3] = pos
x_0[agent*n_states:(agent+1)*n_states][6:9] = vel
x_0 = x_0.reshape(-1,1)
xf,vf = set_random(n_quads,r_safety,True)
x_f = np.zeros((n_states*n_quads,))
for agent,(pos_f,vel_f) in enumerate(zip(xf,vf)):
x_f[agent*n_states:(agent+1)*n_states][:3] = pos_f
x_f[agent*n_states:(agent+1)*n_states][6:9] = vel_f
x_f = x_f.reshape(-1,1)
return x_0, x_f
def set_random(n_quads, r_safety, target):
for times in range(100):
ini_x=[]
for i in range(n_quads):
for j in range(1000):
if n_quads <= 10:
ini=np.random.rand(3)*np.array([3.5,3.5,2.5])
elif n_quads > 10 and n_quads <20:
ini=np.random.rand(3)*np.array([7, 7, 3.0])
elif n_quads >= 20 and n_quads <50:
ini=np.random.rand(3)*np.array([15,15,3.5])
RIGHT=True
for k in range(len(ini_x)):
if target:
if(np.linalg.norm(ini-ini_x[k])<r_safety+0.1):
RIGHT=False
else:
if(np.linalg.norm(ini-ini_x[k])<r_safety+0.05):
RIGHT=False
if RIGHT:
ini_x+=[ini]
break
if len(ini_x)==n_quads:
print("positions retrieved")
break
if (times+1)%10==0:
print('Try %s times, cannot find. Keep trying.'%(times+1))
if times == 99:
print('please decrease the number of robots')
ini_v=[]
for i in range(n_quads):
ini_v+=[np.zeros(3)]
return ini_x, ini_v
def compute_energy(x, x_dims, n_d=2):
"""Determine the sum of distances from the origin"""
return np.linalg.norm(x[pos_mask(x_dims, n_d)].reshape(-1, n_d), axis=1).sum()
def normalize_energy(x, x_dims, energy=10.0, n_d=2):
"""Zero-center the coordinates and then ensure the sum of
squared distances == energy
"""
# Don't mutate x's data for this function, keep it pure.
x = x.copy()
n_agents = len(x_dims)
center = x[pos_mask(x_dims, n_d)].reshape(-1, n_d).mean(0)
x[pos_mask(x_dims, n_d)] -= np.tile(center, n_agents).reshape(-1, 1)
x[pos_mask(x_dims, n_d)] *= energy / compute_energy(x, x_dims, n_d)
assert x.size == sum(x_dims)
return x
def perturb_state(x, x_dims, n_d=2, var=0.5):
"""Add a little noise to the start to knock off perfect symmetries"""
x = x.copy()
x[pos_mask(x_dims, n_d)] += var * np.random.randn(*x[pos_mask(x_dims, n_d)].shape)
return x
def pos_mask(x_dims, n_d=2):
"""Return a mask that's true wherever there's a spatial position"""
return np.array([i % x_dims[0] < n_d for i in range(sum(x_dims))])
def paper_setup_3_quads(random = False):
x0 = np.array([[0.2, 1.5, 1.2, 0, 0, 0,
2.5, 1.5, 1.3, 0, 0, 0,
-0.8, 1.3, 0.8, 0, 0, 0]],
dtype=float).T
xf = np.array([[2.5, 1.5, 1.5, 0, 0, 0,
0.2, 1.5, 1.9, 0, 0, 0,
1.7, 1.3, 1.2, 0, 0, 0]]).T
if random == True:
x0[pos_mask([6]*3, 3)] += 0.05*np.random.randn(9, 1)
xf[pos_mask([6]*3, 3)] += 0.05*np.random.randn(9, 1)
return x0, xf
def paper_setup_5_quads(random = False):
x0 = np.array([[0.5, 1.5, 1.5, 0, 0, 0,
2.5, 1.5, 1.2, 0, 0, 0,
1.0, -1.3, 0.8, 0, 0, 0,
-2.0, 2.0, 1.9, 0, 0, 0,
3.0, -1.5, 1.4, 0, 0, 0]],
dtype=float).T
xf = np.array([[2.5, 1.5, 1.5, 0, 0, 0,
0.5, 1.5, 1.7, 0, 0, 0,
1.5, 2.2, 1.0, 0, 0, 0,
3.0, -1.5, 1.4, 0, 0, 0,
1.0, -1.3, 0.8, 0, 0, 0,
]]).T
if random == True:
x0[pos_mask([6]*5, 3)] += 0.05*np.random.randn(15, 1)
xf[pos_mask([6]*5, 3)] += 0.05*np.random.randn(15, 1)
return x0, xf
def setup_n_quads(n, r_safety):
right = False
while not right:
x0, xf = random_setup(n, 6, n_d=3, energy=n*2, var=n*1.5)
# Print for debugging
# print("x0:", x0)
# print("xf:", xf)
# print("min distance at x0:", compute_pairwise_distance(x0, [6] * n, 3).min())
# print("min distance at xf:", compute_pairwise_distance(xf, [6] * n, 3).min())
for i in range(2, len(x0), 6):
if x0[i] <= 0.0:
x0[i] = 2.0 + np.random.rand(1,) * 1.5
if xf[i] <= 0.0:
xf[i] = 1.0 + np.random.rand(1,) * 0.5
if compute_pairwise_distance(x0, [6] * n, 3).min() > r_safety and compute_pairwise_distance(xf, [6] * n, 3).min() > r_safety:
right = True
else:
print("Conditions not satisfied. Retrying...")
return x0, xf
def distance_to_goal(x,xf,n_agents,n_states):
n_d = 3
return np.linalg.norm((x - xf).reshape(n_agents, n_states)[:, :n_d], axis=1)
def split_agents(Z, z_dims):
"""Partition a cartesian product state or control for individual agents"""
return np.split(np.atleast_2d(Z), np.cumsum(z_dims[:-1]), axis=1)
def split_agents_gen(z, z_dims):
"""Generator version of ``split_agents``"""
dim = z_dims[0]
for i in range(len(z_dims)):
yield z[i * dim : (i + 1) * dim]
def split_graph(Z, z_dims, graph):
"""Split up the state or control by grouping their ID's according to the graph"""
assert len(set(z_dims)) == 1
# Create a mapping from the graph to indicies.
mapping = {id_: i for i, id_ in enumerate(list(graph))}
n_z = z_dims[0]
z_split = []
for ids in graph.values():
inds = [mapping[id_] for id_ in ids]
z_split.append(
np.concatenate([Z[:, i * n_z : (i + 1) * n_z] for i in inds], axis=1)
)
return z_split
def define_inter_graph_threshold(X, radius, x_dims, ids, n_dims=None):
"""Compute the interaction graph based on a simple thresholded distance
for each pair of agents sampled over the trajectory
"""
planning_radii = 3.0 * radius
if n_dims:
rel_dists = np.array([compute_pairwise_distance_nd_Sym(X, x_dims, n_dims)])
else:
rel_dists = compute_pairwise_distance(X, x_dims)
graph = {id_: [id_] for id_ in ids}
# print(graph)
pair_inds = np.array(list(itertools.combinations(ids, 2)))
distances_dict = {} # Store distances for all pairs
# Populate initial connections based on distance
for i, pair in enumerate(pair_inds):
# Convert pair to a tuple to use as a dictionary key
pair_tuple = tuple(pair)
if np.any(rel_dists[:, i] < planning_radii):
graph[pair_tuple[0]].append(pair_tuple[1])
graph[pair_tuple[1]].append(pair_tuple[0])
distances_dict[pair_tuple] = rel_dists[:, i]
# Ensure the graph is always connected
for id_ in ids:
if len(graph[id_]) == 1: # If an agent has no neighbors
# Find the nearest neighbor by checking all distances
nearest_distance = float('inf')
nearest_neighbor_id = None
for (agent1, agent2), distance in distances_dict.items():
if agent1 == id_ or agent2 == id_:
if distance < nearest_distance:
nearest_distance = distance
nearest_neighbor_id = agent2 if agent1 == id_ else agent1
if nearest_neighbor_id is not None:
graph[id_].append(nearest_neighbor_id)
graph[nearest_neighbor_id].append(id_)
# graph = {agent_id: sorted(prob_ids) for agent_id, prob_ids in graph.items()}
graph = {agent_id: sorted(set(prob_ids)) for agent_id, prob_ids in graph.items()} # Remove potential duplicates and sort
return graph
def compute_pairwise_distance_nd_Sym(X, x_dims, n_dims):
"""Analog to the above whenever some agents only use distance in the x-y plane"""
CYLINDER_RADIUS = 0.2
n_states = x_dims[0]
n_agents = len(x_dims)
distances = []
eps = 1e-3
for i, n_dim_i in zip(range(n_agents), n_dims):
for j, n_dim_j in zip(range(i + 1, n_agents), n_dims[i + 1 :]):
n_dim = min(n_dim_i, n_dim_j)
Xi = X[i * n_states : i * n_states + n_dim, :]
Xj = X[j * n_states : j * n_states + n_dim, :]
dX = Xi-Xj
if n_dim == 3:
distances.append(sqrt(dX[0,:]**2 + dX[1,:]**2 + dX[2,:]**2+eps))
else:
distances.append(sqrt(dX[0,:]**2 + dX[1,:]**2 + eps)+CYLINDER_RADIUS)
return distances
def compute_pairwise_distance(X, x_dims, n_d=3):
"""Compute the distance between each pair of agents"""
assert len(set(x_dims)) == 1
n_agents = len(x_dims)
n_states = x_dims[0]
if n_agents == 1:
raise ValueError("Can't compute pairwise distance for one agent.")
pair_inds = np.array(list(itertools.combinations(range(n_agents), 2)))
X_agent = X.reshape(-1, n_agents, n_states).swapaxes(0, 2)
dX = X_agent[:n_d, pair_inds[:, 0]] - X_agent[:n_d, pair_inds[:, 1]]
return np.linalg.norm(dX, axis=0).T
def evaluate_cost(X_curr,
U_curr,
n_states,
n_inputs,
n_agents,
r_min,
x_dims,
n_dims,
xr,
u_ref,
Q,
R,
Qf):
running_cost = 0
coll_cost = 0
terminal_cost = 0
u_ref = u_ref.reshape(-1,1)
X_curr = X_curr.reshape(-1,1)
U_curr = U_curr.reshape(-1,1)
# print(X_curr.shape, U_curr.shape, xr.shape, u_ref.shape)
running_cost += (X_curr-xr).T@ Q @(X_curr-xr)
print(X_curr.shape)
dists = compute_pairwise_distance_nd_Sym(X_curr,x_dims,n_dims)
for dist in dists:
coll_cost += fmin(0,(dist - 2 * r_min))**2 * 200
running_cost += (U_curr-u_ref).T@ R @(U_curr-u_ref)
return float(coll_cost + running_cost + terminal_cost)
def evaluate_cost_trajectory(X_full,
U_full,
r_min,
x_dims,
n_dims,
xr,
u_ref,
Q,
R,
Qf):
running_cost = 0
coll_cost = 0
terminal_cost = 0
# print(X_full.shape, U_full.shape)
for t in range(X_full.shape[0]-1):
running_cost += (X_full[t].reshape(-1,1)-xr).T@Q@(X_full[t].reshape(-1,1)-xr)
distances = compute_pairwise_distance_nd_Sym(X_full[t].reshape(-1,1), x_dims, n_dims)
for dist in distances:
coll_cost += fmin(0,(dist - 2*r_min))**2 * 200
for t in range(U_full.shape[0]):
running_cost += U_full[t].T@R@U_full[t]
terminal_cost = (X_full[-1].reshape(-1,1)-xr).T@Qf@(X_full[-1].reshape(-1,1)-xr)
cost_tot = terminal_cost + coll_cost + running_cost
# print(cost_tot)
return float(cost_tot)