def test_der(self):
T = 1
M = 1
b = 1
t0 = 0
x0 = 0
ocp = Ocp(t0=t0, T=T)
x = ocp.state()
u = ocp.control()
ocp.set_der(x, u)
y = 2 * x
ocp.subject_to(ocp.der(y) <= 2 * b)
ocp.subject_to(-2 * b <= ocp.der(y))
ocp.add_objective(ocp.at_tf(x))
ocp.subject_to(ocp.at_t0(x) == x0)
ocp.solver('ipopt')
ocp.method(MultipleShooting(N=4, M=M, intg='rk'))
sol = ocp.solve()
ts, xs = sol.sample(x, grid='control')
self.assertAlmostEqual(xs[0], x0, places=6)
self.assertAlmostEqual(xs[-1], x0 - b * T, places=6)
self.assertAlmostEqual(ts[0], t0)
self.assertAlmostEqual(ts[-1], t0 + T)
def test_integral(self):
t0 = 1.2
T = 5.7
ocp = Ocp(t0=t0, T=T)
x = ocp.state()
u = ocp.control()
ocp.set_der(x, u)
ocp.subject_to(ocp.at_t0(x) == 0)
ocp.subject_to(u <= 1)
f = ocp.integral(x * ocp.t)
ocp.add_objective(-f) # (t-t0)*t -> t^3/3-t^2/2*t0
ocp.solver('ipopt')
opts = {"abstol": 1e-8, "reltol": 1e-8, "quad_err_con": True}
for method in [
MultipleShooting(intg='rk'),
MultipleShooting(intg='cvodes', intg_options=opts),
#MultipleShooting(intg='idas',intg_options=opts),
DirectCollocation()
]:
ocp.method(method)
sol = ocp.solve()
ts, xs = sol.sample(f, grid='control')
I = lambda t: t**3 / 3 - t**2 / 2 * t0
x_ref = I(t0 + T) - I(t0)
assert_array_almost_equal(xs[-1], x_ref)
def vdp(method,grid='control'):
ocp = Ocp(T=10)
# Define 2 states
x1 = ocp.state()
x2 = ocp.state()
# Define 1 control
u = ocp.control(order=0)
# Specify ODE
ocp.set_der(x1, (1 - x2**2) * x1 - x2 + u)
ocp.set_der(x2, x1)
# Lagrange objective
ocp.add_objective(ocp.integral(x1**2 + x2**2 + u**2))
# Path constraints
ocp.subject_to(-1 <= (u <= 1))
ocp.subject_to(x1 >= -0.25, grid=grid)
# Initial constraints
ocp.subject_to(ocp.at_t0(x1) == 0)
ocp.subject_to(ocp.at_t0(x2) == 1)
# Pick an NLP solver backend
ocp.solver('ipopt')
# Pick a solution method
ocp.method(method)
return (ocp, x1, x2, u)
def test_param(self):
ocp = Ocp(T=1)
x = ocp.state()
u = ocp.control()
p = ocp.parameter()
ocp.set_der(x, u)
ocp.subject_to(u <= 1)
ocp.subject_to(-1 <= u)
ocp.add_objective(ocp.at_tf(x))
ocp.subject_to(ocp.at_t0(x) == p)
ocp.solver('ipopt')
ocp.method(MultipleShooting())
ocp.set_value(p, 0)
sol = ocp.solve()
ts, xs = sol.sample(x, grid='control')
self.assertAlmostEqual(xs[0], 0)
ocp.set_value(p, 1)
sol = ocp.solve()
ts, xs = sol.sample(x, grid='control')
self.assertAlmostEqual(xs[0], 1)
def integrator_control_problem(T=1, u_max=1, x0=0, stage_method=None, t0=0):
if stage_method is None:
stage_method = MultipleShooting()
ocp = Ocp(t0=t0, T=T)
x = ocp.state()
u = ocp.control()
ocp.set_der(x, u)
ocp.subject_to(u <= u_max)
ocp.subject_to(-u_max <= u)
ocp.add_objective(ocp.at_tf(x))
if x0 is not None:
ocp.subject_to(ocp.at_t0(x) == x0)
ocp.solver('ipopt')
ocp.method(stage_method)
return (ocp, x, u)
def test_basic_t0_free(self):
xf = 2
t0 = 0
for T in [2]:
for x0 in [0, 1]:
for b in [1, 2]:
for method in [
MultipleShooting(N=4, intg='rk'),
MultipleShooting(N=4, intg='cvodes'),
MultipleShooting(N=4, intg='idas'),
DirectCollocation(N=4)
]:
ocp = Ocp(t0=FreeTime(2), T=T)
x = ocp.state()
u = ocp.control()
ocp.set_der(x, u)
ocp.subject_to(u <= b)
ocp.subject_to(-b <= u)
ocp.add_objective(ocp.tf)
ocp.subject_to(ocp.at_t0(x) == x0)
ocp.subject_to(ocp.at_tf(x) == xf)
ocp.subject_to(ocp.t0 >= 0)
ocp.solver('ipopt')
ocp.method(method)
sol = ocp.solve()
ts, xs = sol.sample(x, grid='control')
self.assertAlmostEqual(xs[0], x0, places=6)
self.assertAlmostEqual(xs[-1], xf, places=6)
self.assertAlmostEqual(ts[0], t0)
self.assertAlmostEqual(ts[-1], t0 + T)
def bang_bang_problem(stage_method):
ocp = Ocp(T=FreeTime(1))
p = ocp.state()
v = ocp.state()
u = ocp.control()
ocp.set_der(p, v)
ocp.set_der(v, u)
ocp.subject_to(u <= 1)
ocp.subject_to(-1 <= u)
ocp.add_objective(ocp.T)
ocp.subject_to(ocp.at_t0(p) == 0)
ocp.subject_to(ocp.at_t0(v) == 0)
ocp.subject_to(ocp.at_tf(p) == 1)
ocp.subject_to(ocp.at_tf(v) == 0)
ocp.solver('ipopt')
ocp.method(stage_method)
return (ocp, ocp.solve(), p, v, u)
def test_dae_casadi(self):
# cross check with dae_colloation
xref = 0.1 # chariot reference
l = 1. #- -> crane, + -> pendulum
m = 1.
M = 1.
g = 9.81
ocp = Ocp(T=5)
x = ocp.state()
y = ocp.state()
w = ocp.state()
dx = ocp.state()
dy = ocp.state()
dw = ocp.state()
xa = ocp.algebraic()
u = ocp.control()
ocp.set_der(x, dx)
ocp.set_der(y, dy)
ocp.set_der(w, dw)
ddx = (w - x) * xa / m
ddy = g - y * xa / m
ddw = ((x - w) * xa - u) / M
ocp.set_der(dx, ddx)
ocp.set_der(dy, ddy)
ocp.set_der(dw, ddw)
ocp.add_alg((x - w) * (ddx - ddw) + y * ddy + dy * dy + (dx - dw)**2)
ocp.add_objective(
ocp.at_tf((x - xref) * (x - xref) + (w - xref) * (w - xref) +
dx * dx + dy * dy))
ocp.add_objective(
ocp.integral((x - xref) * (x - xref) + (w - xref) * (w - xref)))
ocp.subject_to(-2 <= (u <= 2))
ocp.subject_to(ocp.at_t0(x) == 0)
ocp.subject_to(ocp.at_t0(y) == l)
ocp.subject_to(ocp.at_t0(w) == 0)
ocp.subject_to(ocp.at_t0(dx) == 0)
ocp.subject_to(ocp.at_t0(dy) == 0)
ocp.subject_to(ocp.at_t0(dw) == 0)
#ocp.subject_to(xa>=0,grid='integrator_roots')
ocp.set_initial(y, l)
ocp.set_initial(xa, 9.81)
# Pick an NLP solver backend
# NOTE: default scaling strategy of MUMPS leads to a singular matrix error
ocp.solver(
'ipopt', {
"ipopt.linear_solver": "mumps",
"ipopt.mumps_scaling": 0,
"ipopt.tol": 1e-12
})
# Pick a solution method
method = DirectCollocation(N=50)
ocp.method(method)
# Solve
sol = ocp.solve()
assert_array_almost_equal(
sol.sample(xa, grid='integrator', refine=1)[1][0],
9.81011622448889)
assert_array_almost_equal(
sol.sample(xa, grid='integrator', refine=1)[1][1],
9.865726317147214)
assert_array_almost_equal(
sol.sample(xa, grid='integrator')[1][0], 9.81011622448889)
assert_array_almost_equal(
sol.sample(xa, grid='integrator')[1][1], 9.865726317147214)
assert_array_almost_equal(
sol.sample(xa, grid='control')[1][0], 9.81011622448889)
assert_array_almost_equal(
sol.sample(xa, grid='control')[1][1], 9.865726317147214)
#Define problem parameter
plant_param = {'m': 1, 'I': 1, 'L': 1, 'c': 1}
model_param = {'m': 1.2, 'I': 1.2, 'L': 0.9, 'c': 0.9}
N = 100
T = 10
tgrid = np.linspace(0, T, N)
y_ref_val = np.sin(tgrid)
x0 = [0, 0]
ocp = Ocp(t0=tgrid[0], T=tgrid[-1])
# Define states
x = ocp.state(2)
# Define controls
u = ocp.control()
# Specify ODE
model_rhs = pendulum_ode(x, u, model_param)
ocp.set_der(x, model_rhs)
# Set initial conditions
ocp.subject_to(ocp.at_t0(x) == x0)
# Define reference
y_ref = ocp.parameter(grid='control')
ocp.set_value(y_ref, y_ref_val)
# Define output correction
beta = ocp.parameter(grid='control')
N = 20 dt = 0.5 #effect unclear = how to connect this to rosrate ? #------------- Initialize OCP ocp = Ocp(T=N * dt) #----------------------------------- waypoints ------------------------ #------------------------- System model x = ocp.state() y = ocp.state() theta = ocp.state() v = ocp.control() w = ocp.control() #--------------------------path parameters s_obs = ocp.state() sdot_obs = ocp.control() #-----------------------------ODEs ocp.set_der(x, v * cos(theta)) ocp.set_der(y, v * sin(theta)) ocp.set_der(theta, w) ocp.set_der(s_obs, sdot_obs) #-------------------------------------------------------------------------------#