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758 lines (640 loc) · 31.1 KB
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"""flatsys_test.py - test flat system module
RMM, 29 Jun 2019
This test suite checks to make sure that the basic functions supporting
differential flat systetms are functioning. It doesn't do exhaustive
testing of operations on flat systems. Separate unit tests should be
created for that purpose.
"""
import numpy as np
import pytest
import scipy as sp
import re
import warnings
import os
import platform
import control as ct
import control.flatsys as fs
import control.optimal as opt
# Set tolerances for lower/upper bound tests
atol = 1e-4
rtol = 1e-4
class TestFlatSys:
"""Test differential flat systems"""
@pytest.mark.parametrize(
" xf, uf, Tf, basis",
[([1, 0], [0], 2, fs.PolyFamily(6)),
([0, 1], [0], 3, fs.PolyFamily(6)),
([0, 1], [0], 3, fs.BezierFamily(6)),
([0, 1], [0], 3, fs.BSplineFamily([0, 1.5, 3], 4)),
([1, 1], [1], 4, fs.PolyFamily(6)),
([1, 1], [1], 4, fs.BezierFamily(6)),
([1, 1], [1], 4, fs.BSplineFamily([0, 1.5, 3], 4))])
def test_double_integrator(self, xf, uf, Tf, basis):
# Define a second order integrator
sys = ct.StateSpace([[-1, 1], [0, -2]], [[0], [1]], [[1, 0]], 0)
flatsys = fs.LinearFlatSystem(sys)
x1, u1, = [0, 0], [0]
traj = fs.point_to_point(flatsys, Tf, x1, u1, xf, uf, basis=basis)
# Verify that the trajectory computation is correct
x, u = traj.eval([0, Tf])
np.testing.assert_array_almost_equal(x1, x[:, 0])
np.testing.assert_array_almost_equal(u1, u[:, 0])
np.testing.assert_array_almost_equal(xf, x[:, 1])
np.testing.assert_array_almost_equal(uf, u[:, 1])
# Simulate the system and make sure we stay close to desired traj
T = np.linspace(0, Tf, 100)
xd, ud = traj.eval(T)
t, y, x = ct.forced_response(sys, T, ud, x1, return_x=True)
np.testing.assert_array_almost_equal(x, xd, decimal=3)
@pytest.fixture
def vehicle_flat(self):
"""Differential flatness for a kinematic car"""
def vehicle_flat_forward(x, u, params={}):
b = params.get('wheelbase', 3.) # get parameter values
zflag = [np.zeros(3), np.zeros(3)] # list for flag arrays
zflag[0][0] = x[0] # flat outputs
zflag[1][0] = x[1]
zflag[0][1] = u[0] * np.cos(x[2]) # first derivatives
zflag[1][1] = u[0] * np.sin(x[2])
thdot = (u[0]/b) * np.tan(u[1]) # dtheta/dt
zflag[0][2] = -u[0] * thdot * np.sin(x[2]) # second derivatives
zflag[1][2] = u[0] * thdot * np.cos(x[2])
return zflag
def vehicle_flat_reverse(zflag, params={}):
b = params.get('wheelbase', 3.) # get parameter values
x = np.zeros(3); u = np.zeros(2) # vectors to store x, u
x[0] = zflag[0][0] # x position
x[1] = zflag[1][0] # y position
x[2] = np.arctan2(zflag[1][1], zflag[0][1]) # angle
u[0] = zflag[0][1] * np.cos(x[2]) + zflag[1][1] * np.sin(x[2])
thdot_v = zflag[1][2] * np.cos(x[2]) - zflag[0][2] * np.sin(x[2])
u[1] = np.arctan2(thdot_v, u[0]**2 / b)
return x, u
def vehicle_update(t, x, u, params):
b = params.get('wheelbase', 3.) # get parameter values
dx = np.array([
np.cos(x[2]) * u[0],
np.sin(x[2]) * u[0],
(u[0]/b) * np.tan(u[1])
])
return dx
def vehicle_output(t, x, u, params): return x
# Create differentially flat input/output system
return fs.FlatSystem(
vehicle_flat_forward, vehicle_flat_reverse, vehicle_update,
vehicle_output, inputs=('v', 'delta'), outputs=('x', 'y', 'theta'),
states=('x', 'y', 'theta'))
@pytest.mark.parametrize("basis", [
fs.PolyFamily(6), fs.PolyFamily(8), fs.BezierFamily(6),
fs.BSplineFamily([0, 10], 8),
fs.BSplineFamily([0, 5, 10], 4)
])
def test_kinematic_car(self, vehicle_flat, basis):
# Define the endpoints of the trajectory
x0 = [0., -2., 0.]; u0 = [10., 0.]
xf = [100., 2., 0.]; uf = [10., 0.]
Tf = 10
# Find trajectory between initial and final conditions
traj = fs.point_to_point(vehicle_flat, Tf, x0, u0, xf, uf, basis=basis)
# Verify that the trajectory computation is correct
x, u = traj.eval([0, Tf])
np.testing.assert_array_almost_equal(x0, x[:, 0])
np.testing.assert_array_almost_equal(u0, u[:, 0])
np.testing.assert_array_almost_equal(xf, x[:, 1])
np.testing.assert_array_almost_equal(uf, u[:, 1])
# Simulate the system and make sure we stay close to desired traj
# Note: this can sometimes fail since system is open loop unstable
T = np.linspace(0, Tf, 100)
xd, ud = traj.eval(T)
resp = ct.input_output_response(vehicle_flat, T, ud, x0)
if not np.allclose(resp.states, xd, atol=1e-2, rtol=1e-2):
pytest.xfail("system is open loop unstable => errors can build")
# integrate equations and compare to desired
t, y, x = ct.input_output_response(
vehicle_flat, T, ud, x0, return_x=True)
np.testing.assert_allclose(x, xd, atol=0.01, rtol=0.01)
@pytest.mark.parametrize(
"basis, guess, constraints, method", [
(fs.PolyFamily(8, T=10), 'prev', None, None),
(fs.BezierFamily(8, T=10), 'linear', None, None),
(fs.BSplineFamily([0, 10], 8), None, None, None),
(fs.BSplineFamily([0, 10], 8), 'prev', None, 'trust-constr'),
(fs.BSplineFamily([0, 10], [6, 8], vars=2), 'prev', None, None),
(fs.BSplineFamily([0, 5, 10], 5), 'linear', None, 'slsqp'),
(fs.BSplineFamily([0, 10], 8), None, ([8, -0.1], [12, 0.1]), None),
(fs.BSplineFamily([0, 5, 10], 5, 3), None, None, None),
])
def test_kinematic_car_ocp(
self, vehicle_flat, basis, guess, constraints, method):
# Define the endpoints of the trajectory
x0 = [0., -2., 0.]; u0 = [10., 0.]
xf = [40., 2., 0.]; uf = [10., 0.]
Tf = 4
timepts = np.linspace(0, Tf, 10)
# Find trajectory between initial and final conditions
traj_p2p = fs.point_to_point(
vehicle_flat, Tf, x0, u0, xf, uf, basis=basis)
# Verify that the trajectory computation is correct
x, u = traj_p2p.eval(timepts)
np.testing.assert_array_almost_equal(x0, x[:, 0])
np.testing.assert_array_almost_equal(u0, u[:, 0])
np.testing.assert_array_almost_equal(xf, x[:, -1])
np.testing.assert_array_almost_equal(uf, u[:, -1])
#
# Re-solve as optimal control problem
#
# Define the cost function (mainly penalize steering angle)
traj_cost = opt.quadratic_cost(
vehicle_flat, None, np.diag([0.1, 10]), x0=xf, u0=uf)
# Set terminal cost to bring us close to xf
terminal_cost = opt.quadratic_cost(
vehicle_flat, 1e3 * np.eye(3), None, x0=xf)
# Implement terminal constraints if specified
if constraints:
input_constraints = opt.input_range_constraint(
vehicle_flat, *constraints)
else:
input_constraints = None
# Use a straight line as an initial guess for the trajectory
if guess == 'prev':
initial_guess = traj_p2p.eval(timepts)[0][0:2]
elif guess == 'linear':
initial_guess = np.array(
[x0[i] + (xf[i] - x0[i]) * timepts/Tf for i in (0, 1)])
else:
initial_guess = None
# Solve the optimal trajectory
traj_ocp = fs.solve_flat_ocp(
vehicle_flat, timepts, x0, u0,
cost=traj_cost, constraints=input_constraints,
terminal_cost=terminal_cost, basis=basis,
initial_guess=initial_guess,
minimize_kwargs={'method': method},
)
xd, ud = traj_ocp.eval(timepts)
if not traj_ocp.success:
# Known failure cases
if re.match(".*precision loss.*", traj_ocp.message):
pytest.xfail("precision loss in some configurations")
elif re.match("Iteration limit.*", traj_ocp.message) and \
re.match(
"conda ubuntu-3.* Generic", os.getenv('JOBNAME', '')) and \
np.__version__ == '1.24.0':
pytest.xfail("gh820: iteration limit exceeded")
else:
# Dump out information to allow creation of an exception
print("Platform: ", platform.platform())
print("Python: ", platform.python_version())
np.show_config()
print("JOBNAME: ", os.getenv('JOBNAME'))
pytest.fail(
"unknown failure; view output to identify configuration")
# Make sure the constraints are satisfied
if input_constraints:
_, _, lb, ub = input_constraints
for i in range(ud.shape[0]):
assert all(lb[i] - ud[i] < rtol * abs(lb[i]) + atol)
assert all(ud[i] - ub[i] < rtol * abs(ub[i]) + atol)
def test_flat_default_output(self, vehicle_flat):
# Construct a flat system with the default outputs
flatsys = fs.FlatSystem(
vehicle_flat.forward, vehicle_flat.reverse, vehicle_flat.updfcn,
inputs=vehicle_flat.ninputs, outputs=vehicle_flat.ninputs,
states=vehicle_flat.nstates)
# Define the endpoints of the trajectory
x0 = [0., -2., 0.]; u0 = [10., 0.]
xf = [100., 2., 0.]; uf = [10., 0.]
Tf = 10
# Find trajectory between initial and final conditions
basis = fs.PolyFamily(6)
traj1 = fs.point_to_point(vehicle_flat, Tf, x0, u0, xf, uf, basis=basis)
traj2 = fs.point_to_point(flatsys, Tf, x0, u0, xf, uf, basis=basis)
# Verify that the trajectory computation is correct
T = np.linspace(0, Tf, 10)
x1, u1 = traj1.eval(T)
x2, u2 = traj2.eval(T)
np.testing.assert_array_almost_equal(x1, x2)
np.testing.assert_array_almost_equal(u1, u2)
# Run a simulation and verify that the outputs are correct
resp1 = ct.input_output_response(vehicle_flat, T, u1, x0)
resp2 = ct.input_output_response(flatsys, T, u1, x0)
np.testing.assert_array_almost_equal(resp1.outputs[0:2], resp2.outputs)
@pytest.mark.parametrize("basis", [
fs.PolyFamily(8),
fs.BSplineFamily([0, 5, 10], 6),
fs.BSplineFamily([0, 3, 7, 10], 4, 2)
])
def test_flat_cost_constr(self, basis):
# Double integrator system
sys = ct.ss([[0, 1], [0, 0]], [[0], [1]], [[1, 0]], 0)
flat_sys = fs.LinearFlatSystem(sys)
# Define the endpoints of the trajectory
x0 = [1, 0]; u0 = [0]
xf = [0, 0]; uf = [0]
Tf = 10
T = np.linspace(0, Tf, 100)
# Find trajectory between initial and final conditions
traj = fs.point_to_point(
flat_sys, Tf, x0, u0, xf, uf, basis=basis)
x, u = traj.eval(T)
np.testing.assert_array_almost_equal(x0, x[:, 0])
np.testing.assert_array_almost_equal(u0, u[:, 0])
np.testing.assert_array_almost_equal(xf, x[:, -1])
np.testing.assert_array_almost_equal(uf, u[:, -1])
# Solve with a cost function
timepts = np.linspace(0, Tf, 10)
cost_fcn = opt.quadratic_cost(
flat_sys, np.diag([0, 0]), 1, x0=xf, u0=uf)
traj_cost = fs.point_to_point(
flat_sys, timepts, x0, u0, xf, uf, cost=cost_fcn,
basis=basis,
# initial_guess='lstsq',
# minimize_kwargs={'method': 'trust-constr'}
)
# Verify that the trajectory computation is correct
x_cost, u_cost = traj_cost.eval(T)
np.testing.assert_array_almost_equal(x0, x_cost[:, 0])
np.testing.assert_array_almost_equal(u0, u_cost[:, 0])
np.testing.assert_array_almost_equal(xf, x_cost[:, -1])
np.testing.assert_array_almost_equal(uf, u_cost[:, -1])
# Make sure that we got a different answer than before
assert np.any(np.abs(x - x_cost) > 0.1)
# Re-solve with constraint on the y deviation
lb, ub = [-2, -0.1], [2, 0]
lb, ub = [-2, np.min(x_cost[1])*0.95], [2, 1]
constraints = [opt.state_range_constraint(flat_sys, lb, ub)]
# Make sure that the previous solution violated at least one constraint
assert np.any(x_cost[0, :] < lb[0]) or np.any(x_cost[0, :] > ub[0]) \
or np.any(x_cost[1, :] < lb[1]) or np.any(x_cost[1, :] > ub[1])
traj_const = fs.point_to_point(
flat_sys, timepts, x0, u0, xf, uf, cost=cost_fcn,
constraints=constraints, basis=basis,
# minimize_kwargs={'method': 'trust-constr'}
)
assert traj_const.success
# Verify that the trajectory computation is correct
x_cost, u_cost = traj_cost.eval(timepts) # re-eval on timepts
x_const, u_const = traj_const.eval(timepts)
np.testing.assert_array_almost_equal(x0, x_const[:, 0])
np.testing.assert_array_almost_equal(u0, u_const[:, 0])
np.testing.assert_array_almost_equal(xf, x_const[:, -1])
np.testing.assert_array_almost_equal(uf, u_const[:, -1])
# Make sure that the solution respects the bounds (with some slop)
for i in range(x_const.shape[0]):
assert all(lb[i] - x_const[i] < rtol * abs(lb[i]) + atol)
assert all(x_const[i] - ub[i] < rtol * abs(ub[i]) + atol)
# Solve the same problem with a nonlinear constraint type
nl_constraints = [
(sp.optimize.NonlinearConstraint, lambda x, u: x, lb, ub)]
traj_nlconst = fs.point_to_point(
flat_sys, timepts, x0, u0, xf, uf, cost=cost_fcn,
constraints=nl_constraints, basis=basis,
)
x_nlconst, u_nlconst = traj_nlconst.eval(timepts)
np.testing.assert_almost_equal(x_const, x_nlconst, decimal=2)
np.testing.assert_almost_equal(u_const, u_nlconst, decimal=2)
@pytest.mark.parametrize("basis", [
# fs.PolyFamily(8),
fs.BSplineFamily([0, 3, 7, 10], 5, 2)])
def test_flat_solve_ocp(self, basis):
# Double integrator system
sys = ct.ss([[0, 1], [0, 0]], [[0], [1]], [[1, 0]], 0)
flat_sys = fs.LinearFlatSystem(sys)
# Define the endpoints of the trajectory
x0 = [1, 0]; u0 = [0]
xf = [-1, 0]; uf = [0]
Tf = 10
T = np.linspace(0, Tf, 100)
# Find trajectory between initial and final conditions
traj = fs.point_to_point(
flat_sys, Tf, x0, u0, xf, uf, basis=basis)
x, u = traj.eval(T)
np.testing.assert_array_almost_equal(x0, x[:, 0])
np.testing.assert_array_almost_equal(u0, u[:, 0])
np.testing.assert_array_almost_equal(xf, x[:, -1])
np.testing.assert_array_almost_equal(uf, u[:, -1])
# Solve with a terminal cost function
timepts = np.linspace(0, Tf, 10)
terminal_cost = opt.quadratic_cost(
flat_sys, 1e3, 1e3, x0=xf, u0=uf)
traj_cost = fs.solve_flat_ocp(
flat_sys, timepts, x0, u0,
terminal_cost=terminal_cost, basis=basis)
# Verify that the trajectory computation is correct
x_cost, u_cost = traj_cost.eval(T)
np.testing.assert_array_almost_equal(x0, x_cost[:, 0])
np.testing.assert_array_almost_equal(u0, u_cost[:, 0])
np.testing.assert_array_almost_equal(xf, x_cost[:, -1])
np.testing.assert_array_almost_equal(uf, u_cost[:, -1])
# Solve with trajectory and terminal cost functions
trajectory_cost = opt.quadratic_cost(flat_sys, 0, 1, x0=xf, u0=uf)
traj_cost = fs.solve_flat_ocp(
flat_sys, timepts, x0, u0, terminal_cost=terminal_cost,
trajectory_cost=trajectory_cost, basis=basis)
# Verify that the trajectory computation is correct
x_cost, u_cost = traj_cost.eval(T)
np.testing.assert_array_almost_equal(x0, x_cost[:, 0])
np.testing.assert_array_almost_equal(u0, u_cost[:, 0])
# Make sure we got close on the terminal condition
assert all(np.abs(x_cost[:, -1] - xf) < 0.1)
# Make sure that we got a different answer than before
assert np.any(np.abs(x - x_cost) > 0.1)
# Re-solve with constraint on the y deviation
lb, ub = [-2, np.min(x_cost[1])*0.95], [2, 1]
constraints = [opt.state_range_constraint(flat_sys, lb, ub)]
# Make sure that the previous solution violated at least one constraint
assert np.any(x_cost[0, :] < lb[0]) or np.any(x_cost[0, :] > ub[0]) \
or np.any(x_cost[1, :] < lb[1]) or np.any(x_cost[1, :] > ub[1])
traj_const = fs.solve_flat_ocp(
flat_sys, timepts, x0, u0,
terminal_cost=terminal_cost, trajectory_cost=trajectory_cost,
trajectory_constraints=constraints, basis=basis,
)
# Verify that the trajectory computation is correct
x_const, u_const = traj_const.eval(timepts)
np.testing.assert_array_almost_equal(x0, x_const[:, 0])
np.testing.assert_array_almost_equal(u0, u_const[:, 0])
# Make sure we got close on the terminal condition
assert all(np.abs(x_cost[:, -1] - xf) < 0.1)
# Make sure that the solution respects the bounds (with some slop)
for i in range(x_const.shape[0]):
assert all(lb[i] - x_const[i] < rtol * abs(lb[i]) + atol)
assert all(x_const[i] - ub[i] < rtol * abs(ub[i]) + atol)
# Solve the same problem with a nonlinear constraint type
# Use alternative keywords as well
nl_constraints = [
(sp.optimize.NonlinearConstraint, lambda x, u: x, lb, ub)]
traj_nlconst = fs.solve_flat_ocp(
flat_sys, timepts, x0, u0,
cost=trajectory_cost, terminal_cost=terminal_cost,
constraints=nl_constraints, basis=basis,
)
x_nlconst, u_nlconst = traj_nlconst.eval(timepts)
np.testing.assert_almost_equal(x_const, x_nlconst)
np.testing.assert_almost_equal(u_const, u_nlconst)
def test_bezier_basis(self):
bezier = fs.BezierFamily(4)
time = np.linspace(0, 1, 100)
# Sum of the Bezier curves should be one
np.testing.assert_almost_equal(
1, sum([bezier(i, time) for i in range(4)]))
# Sum of derivatives should be zero
for k in range(1, 5):
np.testing.assert_almost_equal(
0, sum([bezier.eval_deriv(i, k, time) for i in range(4)]))
# Compare derivatives to formulas
np.testing.assert_almost_equal(
bezier.eval_deriv(1, 0, time), 3 * time - 6 * time**2 + 3 * time**3)
np.testing.assert_almost_equal(
bezier.eval_deriv(1, 1, time), 3 - 12 * time + 9 * time**2)
np.testing.assert_almost_equal(
bezier.eval_deriv(1, 2, time), -12 + 18 * time)
# Make sure that the second derivative integrates to the first
time = np.linspace(0, 1, 1000)
dt = np.diff(time)
for N in range(5):
bezier = fs.BezierFamily(N)
for i in range(N):
for j in range(1, N+1):
np.testing.assert_allclose(
np.diff(bezier.eval_deriv(i, j-1, time)) / dt,
bezier.eval_deriv(i, j, time)[0:-1],
atol=0.01, rtol=0.01)
# Exception check
with pytest.raises(ValueError, match="index too high"):
bezier.eval_deriv(4, 0, time)
@pytest.mark.parametrize("basis, degree, T", [
(fs.PolyFamily(4), 4, 1),
(fs.PolyFamily(4, 100), 4, 100),
(fs.BezierFamily(4), 4, 1),
(fs.BezierFamily(4, 100), 4, 100),
(fs.BSplineFamily([0, 0.5, 1], 4), 3, 1),
(fs.BSplineFamily([0, 50, 100], 4), 3, 100),
])
def test_basis_derivs(self, basis, degree, T):
"""Make sure that that basis function derivates are correct"""
timepts = np.linspace(0, T, 10000)
dt = timepts[1] - timepts[0]
for i in range(basis.N):
for j in range(degree-1):
# Compare numerical and analytical derivative
np.testing.assert_allclose(
np.diff(basis.eval_deriv(i, j, timepts)) / dt,
basis.eval_deriv(i, j+1, timepts)[0:-1],
atol=1e-2, rtol=1e-4)
def test_point_to_point_errors(self):
"""Test error and warning conditions in point_to_point()"""
# Double integrator system
sys = ct.ss([[0, 1], [0, 0]], [[0], [1]], [[1, 0]], 0)
flat_sys = fs.LinearFlatSystem(sys)
# Define the endpoints of the trajectory
x0 = [1, 0]; u0 = [0]
xf = [0, 0]; uf = [0]
Tf = 10
T = np.linspace(0, Tf, 500)
# Cost function
timepts = np.linspace(0, Tf, 10)
cost_fcn = opt.quadratic_cost(
flat_sys, np.diag([1, 1]), 1, x0=xf, u0=uf)
# Solving without basis specified should be OK
traj = fs.point_to_point(flat_sys, timepts, x0, u0, xf, uf)
x, u = traj.eval(timepts)
np.testing.assert_array_almost_equal(x0, x[:, 0])
np.testing.assert_array_almost_equal(u0, u[:, 0])
np.testing.assert_array_almost_equal(xf, x[:, -1])
np.testing.assert_array_almost_equal(uf, u[:, -1])
# Adding a cost function generates a warning
with pytest.warns(UserWarning, match="optimization not possible"):
traj = fs.point_to_point(
flat_sys, timepts, x0, u0, xf, uf, cost=cost_fcn)
# Make sure we still solved the problem
x, u = traj.eval(timepts)
np.testing.assert_array_almost_equal(x0, x[:, 0])
np.testing.assert_array_almost_equal(u0, u[:, 0])
np.testing.assert_array_almost_equal(xf, x[:, -1])
np.testing.assert_array_almost_equal(uf, u[:, -1])
# Try to optimize with insufficient degrees of freedom
with pytest.warns(UserWarning, match="optimization not possible"):
traj = fs.point_to_point(
flat_sys, timepts, x0, u0, xf, uf, cost=cost_fcn,
basis=fs.PolyFamily(6))
# Make sure we still solved the problem
x, u = traj.eval(timepts)
np.testing.assert_array_almost_equal(x0, x[:, 0])
np.testing.assert_array_almost_equal(u0, u[:, 0])
np.testing.assert_array_almost_equal(xf, x[:, -1])
np.testing.assert_array_almost_equal(uf, u[:, -1])
# Solve with the errors in the various input arguments
with pytest.raises(ValueError, match="Initial state: Wrong shape"):
traj = fs.point_to_point(flat_sys, timepts, np.zeros(3), u0, xf, uf)
with pytest.raises(ValueError, match="Initial input: Wrong shape"):
traj = fs.point_to_point(flat_sys, timepts, x0, np.zeros(3), xf, uf)
with pytest.raises(ValueError, match="Final state: Wrong shape"):
traj = fs.point_to_point(flat_sys, timepts, x0, u0, np.zeros(3), uf)
with pytest.raises(ValueError, match="Final input: Wrong shape"):
traj = fs.point_to_point(flat_sys, timepts, x0, u0, xf, np.zeros(3))
# Different ways of describing constraints
constraint = opt.input_range_constraint(flat_sys, -100, 100)
with pytest.warns(UserWarning, match="optimization not possible"):
traj = fs.point_to_point(
flat_sys, timepts, x0, u0, xf, uf, constraints=constraint,
basis=fs.PolyFamily(6))
x, u = traj.eval(timepts)
np.testing.assert_array_almost_equal(x0, x[:, 0])
np.testing.assert_array_almost_equal(u0, u[:, 0])
np.testing.assert_array_almost_equal(xf, x[:, -1])
np.testing.assert_array_almost_equal(uf, u[:, -1])
# Constraint that isn't a constraint
with pytest.raises(TypeError, match="must be a list"):
traj = fs.point_to_point(
flat_sys, timepts, x0, u0, xf, uf, constraints=np.eye(2),
basis=fs.PolyFamily(8))
# Unknown constraint type
with pytest.raises(TypeError, match="unknown constraint type"):
traj = fs.point_to_point(
flat_sys, timepts, x0, u0, xf, uf,
constraints=[(None, 0, 0, 0)], basis=fs.PolyFamily(8))
# Unsolvable optimization
constraint = [opt.input_range_constraint(flat_sys, -0.01, 0.01)]
with pytest.warns(UserWarning, match="unable to solve"):
traj = fs.point_to_point(
flat_sys, timepts, x0, u0, xf, uf, constraints=constraint,
basis=fs.PolyFamily(8))
assert not traj.success
# Method arguments, parameters
traj_method = fs.point_to_point(
flat_sys, timepts, x0, u0, xf, uf, cost=cost_fcn,
basis=fs.PolyFamily(8), minimize_method='slsqp')
traj_kwarg = fs.point_to_point(
flat_sys, timepts, x0, u0, xf, uf, cost=cost_fcn,
basis=fs.PolyFamily(8), minimize_kwargs={'method': 'slsqp'})
np.testing.assert_allclose(
traj_method.eval(timepts)[0], traj_kwarg.eval(timepts)[0],
atol=1e-5)
# Unrecognized keywords
with pytest.raises(TypeError, match="unrecognized keyword"):
traj_method = fs.point_to_point(
flat_sys, timepts, x0, u0, xf, uf, solve_ivp_method=None)
def test_solve_flat_ocp_errors(self):
"""Test error and warning conditions in point_to_point()"""
# Double integrator system
sys = ct.ss([[0, 1], [0, 0]], [[0], [1]], [[1, 0]], 0)
flat_sys = fs.LinearFlatSystem(sys)
# Define the endpoints of the trajectory
x0 = [1, 0]; u0 = [0]
xf = [0, 0]; uf = [0]
Tf = 10
T = np.linspace(0, Tf, 500)
# Cost function
timepts = np.linspace(0, Tf, 10)
cost_fcn = opt.quadratic_cost(
flat_sys, np.diag([1, 1]), 1, x0=xf, u0=uf)
# Solving without basis specified should be OK (may generate warning)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
traj = fs.solve_flat_ocp(flat_sys, timepts, x0, u0, cost_fcn)
x, u = traj.eval(timepts)
np.testing.assert_array_almost_equal(x0, x[:, 0])
if not traj.success:
# If unsuccessful, make sure the error is just about precision
assert re.match(".* precision loss.*", traj.message) is not None
x, u = traj.eval(timepts)
np.testing.assert_array_almost_equal(x0, x[:, 0])
np.testing.assert_array_almost_equal(u0, u[:, 0])
# Solving without a cost function generates an error
with pytest.raises(TypeError, match="cost required"):
traj = fs.solve_flat_ocp(flat_sys, timepts, x0, u0)
# Try to optimize with insufficient degrees of freedom
with pytest.raises(ValueError, match="basis set is too small"):
traj = fs.solve_flat_ocp(
flat_sys, timepts, x0, u0, cost=cost_fcn,
basis=fs.PolyFamily(2))
# Solve with the errors in the various input arguments
with pytest.raises(ValueError, match="Initial state: Wrong shape"):
traj = fs.solve_flat_ocp(
flat_sys, timepts, np.zeros(3), u0, cost_fcn)
with pytest.raises(ValueError, match="Initial input: Wrong shape"):
traj = fs.solve_flat_ocp(
flat_sys, timepts, x0, np.zeros(3), cost_fcn)
# Constraint that isn't a constraint
with pytest.raises(TypeError, match="must be a list"):
traj = fs.solve_flat_ocp(
flat_sys, timepts, x0, u0, cost_fcn,
constraints=np.eye(2), basis=fs.PolyFamily(8))
# Unknown constraint type
with pytest.raises(TypeError, match="unknown constraint type"):
traj = fs.solve_flat_ocp(
flat_sys, timepts, x0, u0, cost_fcn,
constraints=[(None, 0, 0, 0)], basis=fs.PolyFamily(8))
# Method arguments, parameters
traj_method = fs.solve_flat_ocp(
flat_sys, timepts, x0, u0, cost=cost_fcn,
basis=fs.PolyFamily(6), minimize_method='slsqp')
traj_kwarg = fs.solve_flat_ocp(
flat_sys, timepts, x0, u0, cost=cost_fcn,
basis=fs.PolyFamily(6), minimize_kwargs={'method': 'slsqp'})
np.testing.assert_allclose(
traj_method.eval(timepts)[0], traj_kwarg.eval(timepts)[0],
atol=1e-5)
# Unrecognized keywords
with pytest.raises(TypeError, match="unrecognized keyword"):
traj_method = fs.solve_flat_ocp(
flat_sys, timepts, x0, u0, cost_fcn, solve_ivp_method=None)
@pytest.mark.parametrize(
"xf, uf, Tf",
[([1, 0], [0], 2),
([0, 1], [0], 3),
([1, 1], [1], 4)])
def test_response(self, xf, uf, Tf):
# Define a second order integrator
sys = ct.StateSpace([[-1, 1], [0, -2]], [[0], [1]], [[1, 0]], 0)
flatsys = fs.LinearFlatSystem(sys)
# Define the basis set
basis = fs.PolyFamily(6)
x1, u1, = [0, 0], [0]
traj = fs.point_to_point(flatsys, Tf, x1, u1, xf, uf, basis=basis)
# Compute the response the regular way
T = np.linspace(0, Tf, 10)
x, u = traj.eval(T)
# Recompute using response()
response = traj.response(T, squeeze=False)
np.testing.assert_array_almost_equal(T, response.time)
np.testing.assert_array_almost_equal(u, response.inputs)
np.testing.assert_array_almost_equal(x, response.states)
@pytest.mark.parametrize(
"basis",
[fs.PolyFamily(4),
fs.BezierFamily(4),
fs.BSplineFamily([0, 1], 4),
fs.BSplineFamily([0, 1], 4, vars=2),
fs.BSplineFamily([0, 1], [4, 3], [2, 1], vars=2),
])
def test_basis_class(self, basis):
timepts = np.linspace(0, 1, 10)
if basis.nvars is None:
# Evaluate function on basis vectors
for j in range(basis.N):
coefs = np.zeros(basis.N)
coefs[j] = 1
np.testing.assert_array_almost_equal(
basis.eval(coefs, timepts),
basis.eval_deriv(j, 0, timepts))
else:
# Evaluate each variable on basis vectors
for i in range(basis.nvars):
for j in range(basis.var_ncoefs(i)):
coefs = np.zeros(basis.var_ncoefs(i))
coefs[j] = 1
np.testing.assert_array_almost_equal(
basis.eval(coefs, timepts, var=i),
basis.eval_deriv(j, 0, timepts, var=i))
# Evaluate multi-variable output
offset = 0
for i in range(basis.nvars):
for j in range(basis.var_ncoefs(i)):
coefs = np.zeros(basis.N)
coefs[offset] = 1
np.testing.assert_array_almost_equal(
basis.eval(coefs, timepts)[i],
basis.eval_deriv(j, 0, timepts, var=i))
offset += 1