Deadlocks and Collisions

Deadlocks and Collisions#

In this notebook, we will look at two negative events that may happen while navigating: collisions and deadlocks. We will first learn own to visualize them during a simulation, then how to perform many simulations to assess the impact of two parameters: the safety radius and barrier angle.

We are going to color colliding agents in red and deadlocked agents in blue

[1]:

from navground.sim.ui.video import display_video, display_video_from_run

def decorate(agent):
    if agent.has_been_in_collision_since(world.time - 1.0):
        return {'fill': 'red'}
    if agent.has_been_stuck_since(world.time - 1.0):
        return {'fill': 'blue'}
    return {}

We start by specifying an experiment with safety_margin=0, which is an unsafe setup that will lead to collisions.

[2]:

from navground import sim

yaml = """
type: Cross
agent_margin: 0.1
side: 4
target_margin: 0.1
tolerance: 0.5
groups:
  -
    type: thymio
    number: 20
    radius: 0.08
    control_period: 0.1
    speed_tolerance: 0.02
    kinematics:
      type: 2WDiff
      wheel_axis: 0.094
      max_speed: 0.166
    behavior:
      type: HL
      optimal_speed: 0.12
      horizon: 5.0
      tau: 0.5
      eta: 0.25
      safety_margin: 0.0
    state_estimation:
      type: Bounded
      range: 5.0
"""

[3]:

scenario = sim.load_scenario(yaml)
world = sim.World()
scenario.init_world(world, 0)

We run the simulation for some time with some agents colliding shoulder-to-shoulder.

[4]:

display_video(world, time_step=0.1, duration=120, factor=10, decorate=decorate, display_width=300)

[4]:

Try now to increase the safety margin to 0.5, which is so large that it will rapidly lead to deadlocked agents, which are colored in blue.

[5]:

yaml = """
type: Cross
agent_margin: 0.1
side: 4
target_margin: 0.1
tolerance: 0.5
groups:
  -
    type: thymio
    number: 20
    radius: 0.08
    control_period: 0.1
    speed_tolerance: 0.02
    kinematics:
      type: 2WDiff
      wheel_axis: 0.094
      max_speed: 0.166
    behavior:
      type: HL
      optimal_speed: 0.12
      horizon: 5.0
      tau: 0.5
      eta: 0.25
      safety_margin: 0.5
    state_estimation:
      type: Bounded
      range: 5.0
"""

[6]:

scenario = sim.load_scenario(yaml)
world = sim.World()
scenario.init_world(world, 0)

display_video(world, time_step=0.1, duration=120, factor=10, decorate=decorate, display_width=300)

[6]:

In between these two extrema, there should be good trade-off with no collisions and no deadlocks. We invistigate it with an experiment where we vary the safety margin.

[7]:

from navground import sim

yaml = """
steps: 3000
time_step: 0.1
record_collisions: true
record_deadlocks: true
record_safety_violation: true
record_efficacy: true
terminated_when_idle_or_stuck: true
runs: 250
run_index: 0
scenario:
  type: Cross
  agent_margin: 0.1
  side: 4
  target_margin: 0.1
  tolerance: 0.5
  groups:
    -
      type: thymio
      number: 20
      radius: 0.08
      control_period: 0.1
      speed_tolerance: 0.02
      kinematics:
        type: 2WDiff
        wheel_axis: 0.094
        max_speed: 0.166
      behavior:
        type: HL
        optimal_speed: 0.12
        horizon: 5.0
        tau: 0.5
        eta: 0.5
        safety_margin:
          sampler: uniform
          from: 0.0
          to: 0.25
          once: true
      state_estimation:
        type: Bounded
        range: 5.0
"""

[8]:

from tqdm.notebook import tqdm

experiment = sim.load_experiment(yaml)
experiment.save_directory = ""

with tqdm() as bar:
    experiment.setup_tqdm(bar)
    experiment.run(keep=True, number_of_threads=8)

We import all relevant data into a pandas frame where we also define

  • “safe”: no collisions

  • “fluid”: no deadlocks

  • “ok”: when safe and fluid

[9]:

import numpy as np
import pandas as pd


def count_deadlocks(deadlock_time, final_time):
    is_deadlocked = np.logical_and(deadlock_time > 0, deadlock_time < (final_time - 5.0))
    return sum(is_deadlocked)

def extract_data(experiment):
    collisions = []
    deadlocks = []
    efficacy = []
    sms = []
    bas = []
    seeds = []
    for i, run in experiment.runs.items():
        world = run.world
        sm = np.unique([agent.behavior.safety_margin for agent in world.agents])
        ba = np.unique([agent.behavior.barrier_angle for agent in world.agents])
        sms += list(sm)
        bas += list(ba)
        seeds.append(run.seed)
        final_time = run.world.time
        deadlocks.append(count_deadlocks(run.deadlocks, final_time))
        collisions.append(len(run.collisions))
        efficacy.append(run.efficacy.mean())

    df = pd.DataFrame({
        'seeds': seeds,
        'safety_margin': sms,
        'deadlocks': deadlocks,
        'collisions': collisions,
        'barrier_angle': bas,
        'efficacy': efficacy})
    df['safe'] = (df.collisions == 0).astype(int)
    df['fluid'] = (df.deadlocks == 0).astype(int)
    df['ok'] = ((df.deadlocks == 0) & (df.collisions == 0)).astype(int)
    return df

[10]:

data = extract_data(experiment)
data.describe()

[10]:
seeds safety_margin deadlocks collisions barrier_angle efficacy safe fluid ok
count 250.000000 250.000000 250.000000 250.000000 2.500000e+02 250.000000 250.000000 250.000000 250.000000
mean 124.500000 0.127183 2.568000 4.424000 1.570796e+00 0.745850 0.788000 0.764000 0.556000
std 72.312977 0.073709 5.243219 16.482077 2.224900e-16 0.132497 0.409545 0.425474 0.497851
min 0.000000 0.001417 0.000000 0.000000 1.570796e+00 0.205297 0.000000 0.000000 0.000000
25% 62.250000 0.054341 0.000000 0.000000 1.570796e+00 0.737490 1.000000 1.000000 0.000000
50% 124.500000 0.126612 0.000000 0.000000 1.570796e+00 0.792123 1.000000 1.000000 1.000000
75% 186.750000 0.193269 0.000000 0.000000 1.570796e+00 0.829279 1.000000 1.000000 1.000000
max 249.000000 0.249757 19.000000 157.000000 1.570796e+00 0.859686 1.000000 1.000000 1.000000

We plot the consequences of the safety margin on deadlocks and collisions. We see that

  • for low safety margins, there are collisions

  • for high safety margins, there are deadlocks

[11]:

ax = data.plot.scatter(x='safety_margin', y='collisions', color='r')
data.plot.scatter(ax=ax.twinx(), x='safety_margin', y='deadlocks', color='b');
../_images/tutorials_deadlocks_and_collisions_17_0.png

Efficacy measures how much agents are progressing towards their target (1 = ideal, 0 = stuck). Looking at efficacy gives a more fine-grained picture than deadlocks, which are still visible on the right (points lower than the slowing degrading line).

[12]:

data.plot.scatter(x='safety_margin', y='efficacy', color='k');
../_images/tutorials_deadlocks_and_collisions_19_0.png

Deadlocks can be mitigated by reducing the barrier angle but this may cause collisions. We investigate the effect of safety margin and barrier angle with a larger experiment where we vary both parameters.

[13]:

from navground import sim

yaml = """
steps: 3000
time_step: 0.1
record_collisions: true
record_deadlocks: true
record_safety_violation: false
record_efficacy: true
terminated_when_idle_or_stuck: true
runs: 5000
scenario:
  type: Cross
  agent_margin: 0.1
  side: 4
  target_margin: 0.1
  tolerance: 0.5
  groups:
    -
      type: thymio
      number: 20
      radius: 0.08
      control_period: 0.1
      speed_tolerance: 0.02
      kinematics:
        type: 2WDiff
        wheel_axis: 0.094
        max_speed: 0.166
      behavior:
        type: HL
        optimal_speed: 0.12
        horizon: 5.0
        tau: 0.5
        eta: 0.5
        safety_margin:
          sampler: uniform
          from: 0.0
          to: 0.25
          once: true
        barrier_angle:
          sampler: uniform
          from: 0.7854
          to: 1.5708
          once: true
      state_estimation:
        type: Bounded
        range: 5.0
"""

[14]:

experiment = sim.load_experiment(yaml)

with tqdm() as bar:
    experiment.setup_tqdm(bar)
    experiment.run(keep=True, number_of_threads=8)

[15]:

data = extract_data(experiment)
data.describe()

[15]:
seeds safety_margin deadlocks collisions barrier_angle efficacy safe fluid ok
count 5000.000000 5000.000000 5000.000000 5000.000000 5000.000000 5000.000000 5000.000000 5000.000000 5000.000000
mean 2499.500000 0.123464 0.594600 23.151800 1.179999 0.783691 0.598000 0.945000 0.543000
std 1443.520003 0.072286 2.705201 53.899475 0.227654 0.075513 0.490351 0.228003 0.498197
min 0.000000 0.000033 0.000000 0.000000 0.785570 0.182359 0.000000 0.000000 0.000000
25% 1249.750000 0.061341 0.000000 0.000000 0.982294 0.762972 0.000000 1.000000 0.000000
50% 2499.500000 0.122854 0.000000 0.000000 1.184699 0.801590 1.000000 1.000000 1.000000
75% 3749.250000 0.185237 0.000000 15.000000 1.374994 0.828694 1.000000 1.000000 1.000000
max 4999.000000 0.249975 19.000000 580.000000 1.570611 0.865469 1.000000 1.000000 1.000000

Lower barrier angles reduce safety:

[16]:

data.plot.hexbin(x="safety_margin", y="barrier_angle", C="safe",
                 reduce_C_function=np.mean, gridsize=15,
                 title="Probability of safe run");
../_images/tutorials_deadlocks_and_collisions_25_0.png

Higher barrier angles increase the probability of deadlocks:

[17]:

data.plot.hexbin(x="safety_margin", y="barrier_angle", C="fluid",
                 reduce_C_function=np.mean, gridsize=15,
                 title="Probability of deadlock-free run");
../_images/tutorials_deadlocks_and_collisions_27_0.png

For parameters in the dark green region below, agents are behaving well:

[18]:

data.plot.hexbin(x="safety_margin", y="barrier_angle", C="ok",
                 reduce_C_function=np.mean, gridsize=15,
                 title="Probability of ok run");
../_images/tutorials_deadlocks_and_collisions_29_0.png

Finally, we also plot the efficacy:

[19]:

data.plot.hexbin(x="safety_margin", y="barrier_angle", C="efficacy",
                 reduce_C_function=np.mean, gridsize=15,
                 title="Average efficacy");
../_images/tutorials_deadlocks_and_collisions_31_0.png 
[ ]: