def generate_root_polytope(self):
gurobi_model = grb.Model()
gurobi_model.setParam('OutputFlag', self.output_flag)
input = generate_input_region(gurobi_model, self.input_template, self.input_boundaries, self.env_input_size)
x_results = optimise(self.analysis_template, gurobi_model, input)
if x_results is None:
print("Model unsatisfiable")
return None
root = tuple(x_results)
return root
def generate_nn_polyhedral_guard(self, nn, chosen_action, output_flag):
gurobi_model = grb.Model()
gurobi_model.setParam('OutputFlag', output_flag)
gurobi_model.setParam('Threads', 2)
observation = gurobi_model.addMVar(shape=(2, ),
lb=float("-inf"),
ub=float("inf"),
name="observation")
Experiment.generate_nn_guard(gurobi_model,
observation,
nn,
action_ego=chosen_action)
observable_template = Experiment.octagon(2)
# self.env_input_size = 2
observable_result = optimise(observable_template, gurobi_model,
observation)
# self.env_input_size = 6
return observable_template, observable_result
def check_intersection(self, poly1, poly2, eps=1e-5):
'''checks if a polytope is inside another (even partially)'''
gurobi_model = grb.Model()
gurobi_model.setParam('OutputFlag', self.output_flag)
input1 = generate_input_region(gurobi_model, self.analysis_template,
poly1, self.env_input_size)
generate_region_constraints(
gurobi_model,
self.analysis_template,
input1,
poly2,
self.env_input_size,
eps=eps) # use epsilon to prevent single points
x_results = optimise(self.analysis_template, gurobi_model, input1)
if x_results is None:
# not contained
return False
else:
return True
def post_milp(self, x, nn, output_flag, t, template):
"""milp method"""
post = []
for chosen_action in range(2):
gurobi_model = grb.Model()
gurobi_model.setParam('OutputFlag', output_flag)
gurobi_model.setParam('Threads', 2)
input = generate_input_region(gurobi_model, template, x,
self.env_input_size)
max_theta, min_theta, max_theta_dot, min_theta_dot = self.get_theta_bounds(
gurobi_model, input)
sin_cos_table = self.get_sin_cos_table(max_theta,
min_theta,
max_theta_dot,
min_theta_dot,
action=chosen_action)
feasible_action = CartpoleExperiment.generate_nn_guard(
gurobi_model, input, nn, action_ego=chosen_action)
if feasible_action:
x_prime_results = optimise(template, gurobi_model,
input) # h representation
x_prime = generate_input_region(gurobi_model, template,
x_prime_results,
self.env_input_size)
thetaacc, xacc = CartpoleExperiment.generate_angle_milp(
gurobi_model, x_prime, sin_cos_table)
# apply dynamic
x_second = self.apply_dynamic(
x_prime,
gurobi_model,
thetaacc=thetaacc,
xacc=xacc,
env_input_size=self.env_input_size)
gurobi_model.update()
gurobi_model.optimize()
found_successor, x_prime_results = self.h_repr_to_plot(
gurobi_model, template, x_second)
if found_successor:
post.append(tuple(x_prime_results))
return post
def additional_seen(self):
# adds an element that captures all the states where battery is <=0
gurobi_model = grb.Model()
gurobi_model.setParam('OutputFlag', self.output_flag)
additional = [
self.safe_angle, self.safe_angle,
float("inf"),
float("inf"),
float("inf"),
float("inf"),
float("inf"),
float("inf")
]
input = generate_input_region(gurobi_model,
Experiment.octagon(self.env_input_size),
additional, self.env_input_size)
x_results = optimise(self.analysis_template, gurobi_model, input)
if x_results is None:
print("Model unsatisfiable")
return None
root = tuple(x_results)
return [(root, 0)]
def show_sampleplot2d(self):
'''Generates a plot from the probability of encountering an unsafe state from a sample of points'''
root = self.generate_root_polytope()
# convert to intervals
gurobi_model = grb.Model()
gurobi_model.setParam('OutputFlag', self.output_flag)
input = generate_input_region(gurobi_model, self.input_template, self.input_boundaries, self.env_input_size)
x_results = optimise(self.input_template, gurobi_model, input)
if x_results is None:
print("Model unsatisfiable")
return None
root2d = tuple(x_results)
# samples = polytope.sample(1000, self.analysis_template, np.array(root))
even_samples = self.generate_spaced_samples((-root2d[3], root2d[2]), (-root2d[1], root2d[0]))
samples = list(even_samples)
nn = self.get_nn_fn()
t_max = 200
n_trajectories = 500
probabilities = []
proc_ids = []
with StandardProgressBar(prefix="Preparing AbstractStepWorkers ", max_value=len(samples)) as bar:
while len(samples) != 0 or len(proc_ids) != 0:
while len(proc_ids) < self.n_workers and len(samples) != 0:
sample = samples.pop(0) - np.array([28, 0])
proc_ids.append(sample_trajectory.remote(sample, nn, t_max, n_trajectories))
bar.update(bar.value + 1)
ready_ids, proc_ids = ray.wait(proc_ids, num_returns=len(proc_ids), timeout=0.5)
if len(ready_ids) != 0:
results_list = ray.get(ready_ids)
for result in results_list:
n_failures = result
probabilities.append(n_failures / n_trajectories)
# bar.update(len(probabilities))
print(probabilities)
def post_milp(self, x, nn, output_flag, t, template):
post = []
observable_template_action1 = self.observable_templates[1]
observable_result_action1 = self.observable_results[1]
observable_template_action0 = self.observable_templates[0]
observable_result_action0 = self.observable_results[0]
def standard_op():
gurobi_model = grb.Model()
gurobi_model.setParam('OutputFlag', output_flag)
input = generate_input_region(gurobi_model, template, x,
self.env_input_size)
z = self.apply_dynamic(input, gurobi_model, self.env_input_size)
return gurobi_model, z, input
# case 0
gurobi_model, z, input = standard_op()
feasible0 = self.generate_guard(gurobi_model, z, case=0) # bounce
if feasible0: # action is irrelevant in this case
# apply dynamic
x_prime_results = optimise(template, gurobi_model, z)
gurobi_model = grb.Model()
gurobi_model.setParam('OutputFlag', output_flag)
input2 = generate_input_region(gurobi_model, template,
x_prime_results,
self.env_input_size)
x_second = self.apply_dynamic2(input2,
gurobi_model,
case=0,
env_input_size=self.env_input_size)
found_successor, x_second_results = self.h_repr_to_plot(
gurobi_model, template, x_second)
if found_successor:
post.append(tuple(x_second_results))
# case 1 : ball going down and hit
gurobi_model, z, input = standard_op()
feasible11 = self.generate_guard(gurobi_model, z, case=1)
if feasible11:
generate_region_constraints(gurobi_model,
observable_template_action1, input,
observable_result_action1, 2)
gurobi_model.optimize()
feasible12 = gurobi_model.status
# feasible12 = self.generate_nn_guard(gurobi_model, input, nn, action_ego=1) # check for action =1 over input (not z!)
if feasible12:
# apply dynamic
x_prime_results = optimise(template, gurobi_model, z)
gurobi_model = grb.Model()
gurobi_model.setParam('OutputFlag', output_flag)
input2 = generate_input_region(gurobi_model, template,
x_prime_results,
self.env_input_size)
x_second = self.apply_dynamic2(
input2,
gurobi_model,
case=1,
env_input_size=self.env_input_size)
found_successor, x_second_results = self.h_repr_to_plot(
gurobi_model, template, x_second)
if found_successor:
post.append(tuple(x_second_results))
# case 2 : ball going up and hit
gurobi_model, z, input = standard_op()
feasible21 = self.generate_guard(gurobi_model, z, case=2)
if feasible21:
generate_region_constraints(gurobi_model,
observable_template_action1, input,
observable_result_action1, 2)
gurobi_model.optimize()
feasible22 = gurobi_model.status
# feasible22 = self.generate_nn_guard(gurobi_model, input, nn, action_ego=1) # check for action =1 over input (not z!)
if feasible22:
# apply dynamic
x_prime_results = optimise(template, gurobi_model, z)
gurobi_model = grb.Model()
gurobi_model.setParam('OutputFlag', output_flag)
input2 = generate_input_region(gurobi_model, template,
x_prime_results,
self.env_input_size)
x_second = self.apply_dynamic2(
input2,
gurobi_model,
case=2,
env_input_size=self.env_input_size)
found_successor, x_second_results = self.h_repr_to_plot(
gurobi_model, template, x_second)
if found_successor:
post.append(tuple(x_second_results))
# case 1 alt : ball going down and NO hit
gurobi_model, z, input = standard_op()
feasible11_alt = self.generate_guard(gurobi_model, z, case=1)
if feasible11_alt:
generate_region_constraints(gurobi_model,
observable_template_action0, input,
observable_result_action0, 2)
gurobi_model.optimize()
feasible12_alt = gurobi_model.status
# feasible12_alt = self.generate_nn_guard(gurobi_model, input, nn, action_ego=0) # check for action = 0 over input (not z!)
if feasible12_alt:
# apply dynamic
x_prime_results = optimise(template, gurobi_model, z)
gurobi_model = grb.Model()
gurobi_model.setParam('OutputFlag', output_flag)
input2 = generate_input_region(gurobi_model, template,
x_prime_results,
self.env_input_size)
x_second = self.apply_dynamic2(
input2,
gurobi_model,
case=3,
env_input_size=self.env_input_size)
found_successor, x_second_results = self.h_repr_to_plot(
gurobi_model, template, x_second)
if found_successor:
post.append(tuple(x_second_results))
# case 2 alt : ball going up and NO hit
gurobi_model, z, input = standard_op()
feasible21_alt = self.generate_guard(gurobi_model, z, case=2)
if feasible21_alt:
generate_region_constraints(gurobi_model,
observable_template_action0, input,
observable_result_action0, 2)
gurobi_model.optimize()
feasible22_alt = gurobi_model.status
# feasible22_alt = self.generate_nn_guard(gurobi_model, input, nn, action_ego=0) # check for action = 0 over input (not z!)
if feasible22_alt:
# apply dynamic
x_prime_results = optimise(template, gurobi_model, z)
gurobi_model = grb.Model()
gurobi_model.setParam('OutputFlag', output_flag)
input2 = generate_input_region(gurobi_model, template,
x_prime_results,
self.env_input_size)
x_second = self.apply_dynamic2(
input2,
gurobi_model,
case=3,
env_input_size=self.env_input_size)
found_successor, x_second_results = self.h_repr_to_plot(
gurobi_model, template, x_second)
if found_successor:
post.append(tuple(x_second_results))
# case 3 : ball out of reach and not bounce
gurobi_model, z, input = standard_op()
feasible3 = self.generate_guard(gurobi_model, z,
case=3) # out of reach
if feasible3: # action is irrelevant in this case
# apply dynamic
x_prime_results = optimise(template, gurobi_model, z)
gurobi_model = grb.Model()
gurobi_model.setParam('OutputFlag', output_flag)
input2 = generate_input_region(gurobi_model, template,
x_prime_results,
self.env_input_size)
x_second = self.apply_dynamic2(input2,
gurobi_model,
case=3,
env_input_size=self.env_input_size)
found_successor, x_second_results = self.h_repr_to_plot(
gurobi_model, template, x_second)
if found_successor:
post.append(tuple(x_second_results))
return post
def h_repr_to_plot(self, gurobi_model, template, x_prime):
x_prime_results = optimise(template, gurobi_model,
x_prime) # h representation
return x_prime_results is not None, x_prime_results