From 36722074ca4b11f7f7cd4d613ad2bacb2ac8fb52 Mon Sep 17 00:00:00 2001
From: Adam Sitabkhan <adam.sitabkhan@gmail.com>
Date: Sun, 19 Jan 2025 16:01:20 -0600
Subject: [PATCH] Subgoals added to place_grid without center matching
---
guided_mrmp/controllers/place_grid.py | 299 +++++++++++++++++---------
1 file changed, 192 insertions(+), 107 deletions(-)
diff --git a/guided_mrmp/controllers/place_grid.py b/guided_mrmp/controllers/place_grid.py
index b940dca..b1766aa 100644
--- a/guided_mrmp/controllers/place_grid.py
+++ b/guided_mrmp/controllers/place_grid.py
@@ -1,31 +1,38 @@
import cvxpy as cp
import numpy as np
+import time
-def place_grid(robot_locations, cell_size=1, grid_shape=(5, 5), return_loss=False):
+def place_grid(robot_locations, cell_size, grid_size=5, subgoals=[], obstacles=[]):
"""
Place a grid to cover robot locations with alignment to centers.
inputs:
- robot_locations (list): locations of robots involved in conflict [[x,y], [x,y], ...]
- cell_size (float): the width of each grid cell in continuous space
- - grid_shape (tuple): (# of rows, # of columns) of the grid
+ - grid_size (tuple): width of the grid in cells
+ - obstacles (list): locations of circular obstacles [[x,y,r], [x,y,r], ...]
outputs:
- origin (tuple): bottom-left corner of the grid in continuous space
- cell_centers (list): centers of grid cells for each robot (same order as robot_locations)
- - loss: when return_loss=True, sum of squared differences loss
"""
+ start_time = time.time()
+
robot_locations = np.array(robot_locations)
+ subgoals = np.array(subgoals)
+ obstacles = np.array(obstacles)
N = len(robot_locations)
# Decision variable: Bottom-left corner of the grid in continuous space
- origin = cp.Variable(2, name='origin')
+ bottom_left = cp.Variable(2, name='origin')
+ # Defin top right for convenience
+ top_right = bottom_left + grid_size * cell_size
# Decision variable: Integer grid indices for each robot
grid_indices = cp.Variable((N, 2), integer=True, name='grid_indices')
# Calculate cell centers for each robot based on grid indices
# Reshape origin to (1, 2) for broadcasting
- cell_centers = cp.reshape(origin, (1, 2), order='C') + grid_indices * cell_size + cell_size / 2
+ cell_centers = cp.reshape(bottom_left, (1, 2), order='C') + grid_indices * cell_size + cell_size / 2
# Objective: Minimize the sum of squared distances
cost = cp.sum_squares(robot_locations - cell_centers)
@@ -37,102 +44,126 @@ def place_grid(robot_locations, cell_size=1, grid_shape=(5, 5), return_loss=Fals
constraints.append(grid_indices >= 0)
# Grid indices must fit within grid bounds
- if grid_shape[0] == grid_shape[1]: # Square grid
- constraints.append(grid_indices <= grid_shape[0] - 1)
- else: # Rectangular grid
- constraints.append(grid_indices[:,0] <= grid_shape[1] - 1)
- constraints.append(grid_indices[:,1] <= grid_shape[0] - 1)
+ constraints.append(grid_indices <= grid_size - 1)
# No two robots can share a cell
# Use Big M method to ensure unique grid indices
- M = max(grid_shape) * 10
+ M_ind = 10 * grid_size # Big M relative to grid indices
+ M_cts = 10 * max(max(robot_locations[:,0]) - min(robot_locations[:,0]), max(robot_locations[:,1]) - min(robot_locations[:,1])) # Big M relative to robot locations
for i in range(N):
for j in range(i+1, N):
# At least one of the two constraints below must be true
- y1 = cp.Variable(boolean=True)
- y2 = cp.Variable(boolean=True)
- constraints.append(y1 + y2 >= 1)
+ xsep = cp.Variable(boolean=True)
+ ysep = cp.Variable(boolean=True)
+ constraints.append(xsep + ysep >= 1)
# Enforces separation by at least 1 in the x direction
- if robot_locations[i, 0] >= robot_locations[j, 0]:
- constraints.append(grid_indices[i, 0] - grid_indices[j, 0] + M * (1 - y1) >= 1)
- else:
- constraints.append(grid_indices[j, 0] - grid_indices[i, 0] + M * (1 - y1) >= 1)
+ b0 = cp.Variable(boolean=True) # b0 = 0 if robot i's x >= robot j's x, 1 otherwise
+ # b0 = 0
+ constraints.append(robot_locations[j, 0] - robot_locations[i, 0] <= M_cts * b0)
+ constraints.append(grid_indices[i, 0] - grid_indices[j, 0] + M_ind * b0 + M_ind * (1 - xsep) >= 1)
+ # b0 = 1
+ constraints.append(robot_locations[i, 0] - robot_locations[j, 0] <= M_cts * (1 - b0))
+ constraints.append(grid_indices[j, 0] - grid_indices[i, 0] + M_ind * (1 - b0) + M_ind * (1 - xsep) >= 1)
# Enforces separation by at least 1 in the y direction
- if robot_locations[i, 1] >= robot_locations[j, 1]:
- constraints.append(grid_indices[i, 1] - grid_indices[j, 1] + M * (1 - y2) >= 1)
- else:
- constraints.append(grid_indices[j, 1] - grid_indices[i, 1] + M * (1 - y2) >= 1)
+ b1 = cp.Variable(boolean=True) # b1 = 0 if robot i's y >= robot j's y, 1 otherwise
+ # b1 = 0
+ constraints.append(robot_locations[j, 1] - robot_locations[i, 1] <= M_cts * b1)
+ constraints.append(grid_indices[i, 1] - grid_indices[j, 1] + M_ind * b1 + M_ind * (1 - ysep) >= 1)
+ # b1 = 1
+ constraints.append(robot_locations[i, 1] - robot_locations[j, 1] <= M_cts * (1 - b1))
+ constraints.append(grid_indices[j, 1] - grid_indices[i, 1] + M_ind * (1 - b1) + M_ind * (1 - ysep) >= 1)
+
+ # All robots and subgoals must be within grid bounds
+ for sg in subgoals:
+ constraints.append(bottom_left <= sg)
+ constraints.append(sg <= top_right)
# Solve the optimization problem
+ prob_init_start_time = time.time()
prob = cp.Problem(cp.Minimize(cost), constraints)
+ solve_start_time = time.time()
prob.solve(solver=cp.SCIP)
+ solve_end_time = time.time()
+
+ print("Time to add vars/constraints:", prob_init_start_time - start_time)
+ print("Time to parse:", solve_start_time - prob_init_start_time)
+ print("Time to solve:", solve_end_time - solve_start_time)
- if prob.status not in ["optimal", "optimal_inaccurate"]:
+ if prob.status != "optimal":
print("Problem could not be solved to optimality.")
return None
- if return_loss:
- return origin.value, cell_centers.value, prob.value
- return origin.value, cell_centers.value
+ return bottom_left.value, cell_centers.value
-# This currently does not follow DCP, working on it
-def place_grid_with_rotation(robot_locations, grid_size=5, return_loss=False):
+def two_corner_place_grid(robot_locations, grid_size=5, subgoals=[], obstacles=[]):
"""
- Place a square grid to cover robot locations with alignment to centers. Allows for rotation and scaling of the grid.
+ Place a grid to cover robot locations with alignment to centers.
inputs:
- robot_locations (list): locations of robots involved in conflict [[x,y], [x,y], ...]
- - grid_size (float): the number of cells in each row/column of the grid
+ - cell_size (float): the width of each grid cell in continuous space
+ - grid_size (tuple): width of the grid in cells
+ - obstacles (list): locations of circular obstacles [[x,y,r], [x,y,r], ...]
outputs:
- - bottom_left (tuple): bottom-left corner of the grid in continuous space
- - top_right (tuple): top-right corner of the grid in continuous space
+ - origin (tuple): bottom-left corner of the grid in continuous space
- cell_centers (list): centers of grid cells for each robot (same order as robot_locations)
- - loss: when return_loss=True, sum of squared differences loss
"""
+ start_time = time.time()
+
robot_locations = np.array(robot_locations)
+ subgoals = np.array(subgoals)
+ obstacles = np.array(obstacles)
N = len(robot_locations)
- # Decision variables: Bottom-left and top-right corners of the grid in continuous space
+ # Decision variable: Bottom-left corner of the grid in continuous space
bottom_left = cp.Variable(2, name='bottom_left')
top_right = cp.Variable(2, name='top_right')
+ # Bottom-right and top-left corners of the grid for convenience
+ # bottom_right = 0.5 * cp.hstack([bottom_left[0] + top_right[0] - bottom_left[1] + top_right[1],
+ # bottom_left[0] - top_right[0] + bottom_left[1] + top_right[1]])
+ # top_left = 0.5 * cp.hstack([bottom_left[0] + top_right[0] + bottom_left[1] - top_right[1],
+ # -bottom_left[0] + top_right[0] + bottom_left[1] + top_right[1]])
+ bottom_right = cp.Variable(2, name='bottom_right')
+ top_left = cp.Variable(2, name='top_left')
+
+ grid_x_hat = cp.Variable(2, name='grid_x_hat')
+ grid_y_hat = cp.Variable(2, name='grid_y_hat')
+
# Decision variable: Integer grid indices for each robot
grid_indices = cp.Variable((N, 2), integer=True, name='grid_indices')
-
- # Define bottom-right and top-left corners of the grid
- bottom_right = (1 / 2) * cp.hstack([
- bottom_left[0] + top_right[0] - bottom_left[1] + top_right[1],
- bottom_left[0] - top_right[0] + bottom_left[1] + top_right[1]
- ])
- top_left = (1 / 2) * cp.hstack([
- bottom_left[0] + top_right[0] + bottom_left[1] - top_right[1],
- -bottom_left[0] + top_right[0] + bottom_left[1] + top_right[1]
- ])
-
- # Define basis vectors for the grid
- # Vector pointing from **left -> right** on the grid, with length equal to the width of one cell (1 grid index)
- x_prime_hat = (bottom_right - bottom_left) * (1 / grid_size)
- # Vector pointing from **bottom -> top** on the grid, with length equal to the width of one cell (1 grid index)
- y_prime_hat = (top_left - bottom_left) * (1 / grid_size)
# Calculate cell centers for each robot based on grid indices
- cell_centers = cp.vstack([bottom_left for _ in range(N)]) # Grid origin point
- cell_centers += cp.vstack([x_prime_hat * (grid_indices[i,0] + 0.5) for i in range(N)]) # Component of cell centers in the x_prime direction
- cell_centers += cp.vstack([y_prime_hat * (grid_indices[i,1] + 0.5) for i in range(N)]) # Component of cell centers in the y_prime direction
- print(cell_centers)
+ # Reshape origin to (1, 2) for broadcasting
+ grid_x_offsets = cp.Variable((N, 2), name='grid_x_offsets')
+ grid_y_offsets = cp.Variable((N, 2), name='grid_y_offsets')
+ cell_centers = cp.reshape(bottom_left, (1, 2), order='C') + grid_x_offsets + grid_y_offsets
# Objective: Minimize the sum of squared distances
cost = cp.sum_squares(robot_locations - cell_centers)
- # Initialize constraints
+ # Constraints
constraints = []
- # The top right corner of the grid can't be below or to the left of the bottom left corner
+ # Ensure top-right and bottom-left corners are in the right orientation
constraints.append(top_right >= bottom_left)
+ # Fixing bottom-right and top-left corners
+ constraints.append(2 * bottom_right[0] == bottom_left[0] + top_right[0] - bottom_left[1] + top_right[1])
+ constraints.append(2 * bottom_right[1] == bottom_left[0] - top_right[0] + bottom_left[1] + top_right[1])
+ constraints.append(2 * top_left[0] == bottom_left[0] + top_right[0] + bottom_left[1] - top_right[1])
+ constraints.append(2 * top_left[1] == -bottom_left[0] + top_right[0] + bottom_left[1] + top_right[1])
+
+ # Defining grid_x_hat and grid_y_hat based on corners
+ constraints.append(grid_x_hat == (bottom_right - bottom_left) * (1 / grid_size))
+ constraints.append(grid_y_hat == (top_left - bottom_left) * (1 / grid_size))
+
+ # Defining offsets in cell centers calculation
+ constraints.append(grid_x_offsets == grid_x_hat * grid_indices)
+
# Grid indices must be non-negative
constraints.append(grid_indices >= 0)
@@ -140,52 +171,64 @@ def place_grid_with_rotation(robot_locations, grid_size=5, return_loss=False):
constraints.append(grid_indices <= grid_size - 1)
# No two robots can share a cell
- M = 1e6 # Sufficiently large constant for Big-M
+ # Use Big M method to ensure unique grid indices
+ M_ind = 10 * grid_size # Big M relative to grid indices
+ M_cts = 10 * max(max(robot_locations[:,0]) - min(robot_locations[:,0]), max(robot_locations[:,1]) - min(robot_locations[:,1])) # Big M relative to robot locations
for i in range(N):
for j in range(i+1, N):
- x_separated = cp.Variable(boolean=True)
- y_separated = cp.Variable(boolean=True)
-
- # Robot i's coordinate in the x_prime direction
- robot_i_x_prime = robot_locations[i] @ x_prime_hat
- # Robot j's coordinate in the x_prime direction
- robot_j_x_prime = robot_locations[j] @ x_prime_hat
-
- b0 = cp.Variable(boolean=True)
- # When b1 = 1, robot i's x_prime coordinate is greater than robot j's
- constraints.append(robot_i_x_prime - robot_j_x_prime <= M * b0)
- # When b1 = 0, robot j's x_prime coordinate is greater than robot i's
- constraints.append(robot_j_x_prime - robot_i_x_prime <= M * (1 - b0))
- # Enforces separation by at least 1 between the robots' x indices on the grid
- constraints.append((2 * b0 - 1) * (grid_indices[i, 0] - grid_indices[j, 0]) + M * (1 - x_separated) >= 1)
+ # At least one of the two constraints below must be true
+ xsep = cp.Variable(boolean=True)
+ ysep = cp.Variable(boolean=True)
+ constraints.append(xsep + ysep >= 1)
- # Robot i's coordinate in the y_prime direction
- robot_i_y_prime = robot_locations[i] @ y_prime_hat
- # Robot j's coordinate in the y_prime direction
- robot_j_y_prime = robot_locations[j] @ y_prime_hat
+ # Enforces separation by at least 1 in the x direction
+ b0 = cp.Variable(boolean=True) # b0 = 0 if robot i's x >= robot j's x, 1 otherwise
+ # b0 = 0
+ constraints.append(robot_locations[j, 0] - robot_locations[i, 0] <= M_cts * b0)
+ constraints.append(grid_indices[i, 0] - grid_indices[j, 0] + M_ind * b0 + M_ind * (1 - xsep) >= 1)
+ # b0 = 1
+ constraints.append(robot_locations[i, 0] - robot_locations[j, 0] <= M_cts * (1 - b0))
+ constraints.append(grid_indices[j, 0] - grid_indices[i, 0] + M_ind * (1 - b0) + M_ind * (1 - xsep) >= 1)
- b1 = cp.Variable(boolean=True)
- # When b1 = 1, robot i's y_prime coordinate is greater than robot j's
- constraints.append(robot_i_y_prime - robot_j_y_prime <= M * b1)
- # When b1 = 0, robot j's y_prime coordinate is greater than robot i's
- constraints.append(robot_j_y_prime - robot_i_y_prime <= M * (1 - b1))
- # Enforces separation by at least 1 between the robots' y indices on the grid
- constraints.append((2 * b1 - 1) * (grid_indices[i, 1] - grid_indices[j, 1]) + M * (1 - y_separated) >= 1)
-
- # Robots must be separated in at least one of the x, y directions
- constraints.append(x_separated + y_separated >= 1)
+ # Enforces separation by at least 1 in the y direction
+ b1 = cp.Variable(boolean=True) # b1 = 0 if robot i's y >= robot j's y, 1 otherwise
+ # b1 = 0
+ constraints.append(robot_locations[j, 1] - robot_locations[i, 1] <= M_cts * b1)
+ constraints.append(grid_indices[i, 1] - grid_indices[j, 1] + M_ind * b1 + M_ind * (1 - ysep) >= 1)
+ # b1 = 1
+ constraints.append(robot_locations[i, 1] - robot_locations[j, 1] <= M_cts * (1 - b1))
+ constraints.append(grid_indices[j, 1] - grid_indices[i, 1] + M_ind * (1 - b1) + M_ind * (1 - ysep) >= 1)
# Solve the optimization problem
+ prob_init_start_time = time.time()
prob = cp.Problem(cp.Minimize(cost), constraints)
+ solve_start_time = time.time()
prob.solve(solver=cp.SCIP)
+ solve_end_time = time.time()
+
+ print("Time to add vars/constraints:", prob_init_start_time - start_time)
+ print("Time to parse:", solve_start_time - prob_init_start_time)
+ print("Time to solve:", solve_end_time - solve_start_time)
- if prob.status not in ["optimal", "optimal_inaccurate"]:
+ if prob.status != "optimal":
print("Problem could not be solved to optimality.")
return None
- if return_loss:
- return bottom_left.value, top_right.value, cell_centers.value, prob.value
- return bottom_left.value, top_right.value, cell_centers.value
+ print("Grid Indices:", grid_indices.value)
+
+ return bottom_left.value, cell_centers.value
+
+
+def mccormick_envelope(w, x, xl, xu, y, yl, yu):
+ """
+ Generates McCormick envelope constraints
+ """
+ mec = []
+ mec.append(w >= xl*y + x*yl - xl*yl)
+ mec.append(w >= xu*y + x*yu - xu*yu)
+ mec.append(w <= xu*y + x*yl - xu*yl)
+ mec.append(w >= x*yu + xl*y - xl*yu)
+ return mec
def plot_grid(bottom_left, top_right, grid_size):
@@ -211,13 +254,52 @@ def plot_grid(bottom_left, top_right, grid_size):
[(bottom_left + i * y_prime_hat)[1], (bottom_right + i * y_prime_hat)[1]], 'k-')
-def main(seed, num_robots, plot):
+def get_roomba_locs(low, high, num_robots, radius=0.5):
+ """
+ Generates a list of roomba locations within the box bounded by points (low, low), (high, low), (high, high), (low, high).
+ The roombas must be separated by at least 2 * radius
+ """
+ locs = []
+ while len(locs) < num_robots:
+ locs.append(np.random.uniform(low, high, 2))
+ for other_loc in locs[:-1]:
+ if np.linalg.norm(np.array(locs[-1]) - np.array(other_loc)) <= 2 * radius:
+ locs = locs[:-1]
+ break
+ return np.array(locs)
+
+
+def main(seed, num_robots, plot, two_corner):
if seed is not None:
np.random.seed(seed)
- robot_locations = np.random.uniform(low=0, high=7.5, size=(num_robots, 2))
- cell_size = 1.5
- grid_shape = (5, 5)
+ if not two_corner:
+ roomba_radius = 0.5
+ robot_locations = get_roomba_locs(low=0, high=6, num_robots=num_robots, radius=roomba_radius)
+ # robot_locations = np.random.uniform(low=0, high=5, size=(num_robots, 2))
+ cell_size = 2.5 * roomba_radius
+ grid_size = 5
+ # subgoals = np.random.uniform(low=0, high=6, size=(num_robots, 2))
+ subgoals = np.array([[0, 0], [0, 6], [6, 6], [6, 0]])
+
+ bottom_left, cell_centers = place_grid(robot_locations=robot_locations,
+ cell_size=cell_size,
+ grid_size=grid_size,
+ subgoals=subgoals)
+
+ print("Grid Origin (Bottom-Left Corner):", bottom_left)
+ print("Cell Centers:", cell_centers)
+
+ top_right = np.array(bottom_left) + grid_size * cell_size
+ else:
+ grid_size = 5
+ robot_locations = np.random.uniform(low=0, high=5, size=(num_robots, 2))
+ print("Robot Locations:", robot_locations)
+
+ bottom_left, top_right, grid_indices = two_corner_place_grid(robot_locations, grid_size)
+ print("Grid Bottom-Left Corner:", bottom_left)
+ print("Grid Top-Right Corner:", top_right)
+ print("Grid Indices:", grid_indices)
if plot:
import matplotlib.pyplot as plt
@@ -225,12 +307,7 @@ def main(seed, num_robots, plot):
fig, ax = plt.subplots()
- origin, cell_centers = place_grid(robot_locations, cell_size, grid_shape)
- print("Grid Origin (Bottom-Left Corner):", origin)
-
-
- top_right = np.array(origin) + np.array(grid_shape) * cell_size
- plot_grid(origin, top_right, grid_size=5)
+ plot_grid(bottom_left, top_right, grid_size=grid_size)
# Plot cell centers
cell_centers = np.array(cell_centers)
@@ -243,13 +320,18 @@ def main(seed, num_robots, plot):
robot_locations = np.array(robot_locations)
plt.scatter(robot_locations[:, 0], robot_locations[:, 1], c='r', label='Robot Locations')
for (x, y) in robot_locations:
- circle = patches.Circle((x, y), radius=0.5, edgecolor='r', fill=False, linewidth=2)
+ circle = patches.Circle((x, y), radius=roomba_radius, edgecolor='r', fill=False, linewidth=2)
ax.add_patch(circle)
+
+ if not two_corner:
+ subgoals = np.array(subgoals)
+ plt.scatter(subgoals[:, 0], subgoals[:, 1], c='orange', marker='^', label='Subgoals')
+ for (x, y) in subgoals:
+ circle = patches.Circle((x, y), radius=roomba_radius, edgecolor='orange', fill=False, linewidth=2)
+ ax.add_patch(circle)
plt.legend(loc='upper left')
- # ax.set_xlim(0, 5)
- # ax.set_ylim(0, 5)
ax.set_aspect('equal')
plt.show()
@@ -266,13 +348,16 @@ if __name__ == "__main__":
parser.add_argument(
"--num_robots",
type=int,
- default=2
+ default=3
)
parser.add_argument(
"--plot",
- type=bool,
- default=False
+ action='store_true'
+ )
+ parser.add_argument(
+ "--two_corner",
+ action='store_true'
)
args = parser.parse_args()
- main(args.seed, args.num_robots, args.plot)
\ No newline at end of file
+ main(args.seed, args.num_robots, args.plot, args.two_corner)
\ No newline at end of file
--
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