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control_test.py
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control_test.py
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# Copyright 2019 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from functools import partial
from absl.testing import absltest
import numpy as onp
from jax import lax
from jax import test_util as jtu
import jax.numpy as np
from examples import control
from jax.config import config
config.parse_flags_with_absl()
FLAGS = config.FLAGS
def one_step_lqr(dim, T):
Q = np.stack(T * (np.eye(dim),))
q = np.zeros((T, dim))
R = np.zeros((T, dim, dim))
r = np.zeros((T, dim))
M = np.zeros((T, dim, dim))
A = np.stack(T * (np.eye(dim),))
B = np.stack(T * (np.eye(dim),))
return control.LqrSpec(Q, q, R, r, M, A, B)
def control_from_lqr(lqr):
T, dim, _ = lqr.Q.shape
dot = np.dot
def cost(t, x, u):
return (
dot(dot(lqr.Q[t], x), x) + dot(lqr.q[t], x) +
dot(dot(lqr.R[t], u), u) + dot(lqr.r[t], u) +
dot(dot(lqr.M[t], u), x))
def dynamics(t, x, u):
return dot(lqr.A[t], x) + dot(lqr.B[t], u)
return control.ControlSpec(cost, dynamics, T, dim, dim)
def one_step_control(dim, T):
def cost(t, x, u):
return np.dot(x, x)
def dynamics(t, x, u):
return x + u
return control.ControlSpec(cost, dynamics, T, dim, dim)
class ControlExampleTest(jtu.JaxTestCase):
def testTrajectoryCyclicIntegerCounter(self):
num_states = 3
def dynamics(t, x, u):
return (x + u) % num_states
T = 10
U = np.ones((T, 1))
X = control.trajectory(dynamics, U, np.zeros(1))
expected = np.arange(T + 1) % num_states
expected = np.reshape(expected, (T + 1, 1))
self.assertAllClose(X, expected, check_dtypes=False)
U = 2 * np.ones((T, 1))
X = control.trajectory(dynamics, U, np.zeros(1))
expected = np.cumsum(2 * np.ones(T)) % num_states
expected = np.concatenate((np.zeros(1), expected))
expected = np.reshape(expected, (T + 1, 1))
self.assertAllClose(X, expected, check_dtypes=False)
def testTrajectoryTimeVarying(self):
T = 6
def clip(x, lo, hi):
return np.minimum(hi, np.maximum(lo, x))
def dynamics(t, x, u):
# computes `(x + u) if t > T else 0`
return (x + u) * clip(t - T, 0, 1)
U = np.ones((2 * T, 1))
X = control.trajectory(dynamics, U, np.zeros(1))
expected = np.concatenate((np.zeros(T + 1), np.arange(T)))
expected = np.reshape(expected, (2 * T + 1, 1))
self.assertAllClose(X, expected, check_dtypes=True)
def testTrajectoryCyclicIndicator(self):
num_states = 3
def position(x):
'''finds the index of a standard basis vector, e.g. [0, 1, 0] -> 1'''
x = np.cumsum(x)
x = 1 - x
return np.sum(x, dtype=np.int32)
def dynamics(t, x, u):
'''moves the next standard basis vector'''
idx = (position(x) + u[0]) % num_states
return lax.dynamic_slice_in_dim(np.eye(num_states), idx, 1)[0]
T = 8
U = np.ones((T, 1), dtype=np.int32)
X = control.trajectory(dynamics, U, np.eye(num_states, dtype=np.int32)[0])
expected = np.vstack((np.eye(num_states),) * 3)
self.assertAllClose(X, expected, check_dtypes=True)
def testLqrSolve(self):
dim, T = 2, 10
p = one_step_lqr(dim, T)
K, k = control.lqr_solve(p)
K_ = -np.stack(T * (np.eye(dim),))
self.assertAllClose(K, K_, check_dtypes=True, atol=1e-6, rtol=1e-6)
self.assertAllClose(k, np.zeros((T, dim)), check_dtypes=True)
def testLqrPredict(self):
randn = onp.random.RandomState(0).randn
dim, T = 2, 10
p = one_step_lqr(dim, T)
x0 = randn(dim)
X, U = control.lqr_predict(p, x0)
self.assertAllClose(X[0], x0, check_dtypes=True)
self.assertAllClose(U[0], -x0, check_dtypes=True,
atol=1e-6, rtol=1e-6)
self.assertAllClose(X[1:], np.zeros((T, 2)), check_dtypes=True,
atol=1e-6, rtol=1e-6)
self.assertAllClose(U[1:], np.zeros((T - 1, 2)), check_dtypes=True,
atol=1e-6, rtol=1e-6)
def testIlqrWithLqrProblem(self):
randn = onp.random.RandomState(0).randn
dim, T, num_iters = 2, 10, 3
lqr = one_step_lqr(dim, T)
p = control_from_lqr(lqr)
x0 = randn(dim)
X, U = control.ilqr(num_iters, p, x0, np.zeros((T, dim)))
self.assertAllClose(X[0], x0, check_dtypes=True)
self.assertAllClose(U[0], -x0, check_dtypes=True)
self.assertAllClose(X[1:], np.zeros((T, 2)), check_dtypes=True)
self.assertAllClose(U[1:], np.zeros((T - 1, 2)), check_dtypes=True)
def testIlqrWithLqrProblemSpecifiedGenerally(self):
randn = onp.random.RandomState(0).randn
dim, T, num_iters = 2, 10, 3
p = one_step_control(dim, T)
x0 = randn(dim)
X, U = control.ilqr(num_iters, p, x0, np.zeros((T, dim)))
self.assertAllClose(X[0], x0, check_dtypes=True)
self.assertAllClose(U[0], -x0, check_dtypes=True)
self.assertAllClose(X[1:], np.zeros((T, 2)), check_dtypes=True)
self.assertAllClose(U[1:], np.zeros((T - 1, 2)), check_dtypes=True)
def testIlqrWithNonlinearProblem(self):
def cost(t, x, u):
return (x[0] ** 2. + 1e-3 * u[0] ** 2.) / (t + 1.)
def dynamics(t, x, u):
return (x ** 2. - u ** 2.) / (t + 1.)
T, num_iters, d = 10, 7, 1
p = control.ControlSpec(cost, dynamics, T, d, d)
x0 = np.array([0.2])
X, U = control.ilqr(num_iters, p, x0, 1e-5 * np.ones((T, d)))
assert_close = partial(self.assertAllClose, atol=1e-2, check_dtypes=True)
assert_close(X[0], x0)
assert_close(U[0] ** 2., x0 ** 2.)
assert_close(X[1:], np.zeros((T, d)))
assert_close(U[1:], np.zeros((T - 1, d)))
def testMpcWithLqrProblem(self):
randn = onp.random.RandomState(0).randn
dim, T, num_iters = 2, 10, 3
lqr = one_step_lqr(dim, T)
p = control_from_lqr(lqr)
x0 = randn(dim)
solver = partial(control.ilqr, num_iters)
X, U = control.mpc_predict(solver, p, x0, np.zeros((T, dim)))
self.assertAllClose(X[0], x0, check_dtypes=True)
self.assertAllClose(U[0], -x0, check_dtypes=True)
self.assertAllClose(X[1:], np.zeros((T, 2)), check_dtypes=True)
self.assertAllClose(U[1:], np.zeros((T - 1, 2)), check_dtypes=True)
def testMpcWithLqrProblemSpecifiedGenerally(self):
randn = onp.random.RandomState(0).randn
dim, T, num_iters = 2, 10, 3
p = one_step_control(dim, T)
x0 = randn(dim)
solver = partial(control.ilqr, num_iters)
X, U = control.mpc_predict(solver, p, x0, np.zeros((T, dim)))
self.assertAllClose(X[0], x0, check_dtypes=True)
self.assertAllClose(U[0], -x0, check_dtypes=True)
self.assertAllClose(X[1:], np.zeros((T, 2)), check_dtypes=True)
self.assertAllClose(U[1:], np.zeros((T - 1, 2)), check_dtypes=True)
def testMpcWithNonlinearProblem(self):
def cost(t, x, u):
return (x[0] ** 2. + 1e-3 * u[0] ** 2.) / (t + 1.)
def dynamics(t, x, u):
return (x ** 2. - u ** 2.) / (t + 1.)
T, num_iters, d = 10, 7, 1
p = control.ControlSpec(cost, dynamics, T, d, d)
x0 = np.array([0.2])
solver = partial(control.ilqr, num_iters)
X, U = control.mpc_predict(solver, p, x0, 1e-5 * np.ones((T, d)))
assert_close = partial(self.assertAllClose, atol=1e-2, check_dtypes=True)
assert_close(X[0], x0)
assert_close(U[0] ** 2., x0 ** 2.)
assert_close(X[1:], np.zeros((T, d)))
assert_close(U[1:], np.zeros((T - 1, d)))
if __name__ == '__main__':
absltest.main()