# # """ Bouncing ball example (using for loop) ====================================== In this example, we want to shoot a ball from the ground up so that after 2 bounces, it will reach the height of 0.5 meter. """ from rockit import Ocp, DirectMethod, MultipleShooting, FreeTime import matplotlib.pyplot as plt ocp = Ocp() stage = ocp.stage(t0=FreeTime(0), T=FreeTime(1)) p = stage.state() v = stage.state() stage.set_der(p, v) stage.set_der(v, -9.81) stage.subject_to(stage.at_t0(v) >= 0) stage.subject_to(p >= 0) stage.method(MultipleShooting(N=1, M=20, intg='rk')) stage.subject_to(stage.at_t0(p) == 0) ocp.subject_to(stage.t0 == 0) stage_prev = stage
def test_stage_cloning_t0_T(self):
for t0_stage, t0_sol_stage in [(None, 0), (-1, -1),
(FreeTime(-1), -1)]:
for T_stage, T_sol_stage in [(None, 2), (2, 2), (FreeTime(1), 2)]:
kwargs = {}
if t0_stage is not None:
kwargs["t0"] = t0_stage
if T_stage is not None:
kwargs["T"] = T_stage
stage = Stage(**kwargs)
p = stage.state()
v = stage.state()
u = stage.control()
stage.set_der(p, v)
stage.set_der(v, u)
stage.subject_to(u <= 1)
stage.subject_to(-1 <= u)
stage.add_objective(stage.tf)
stage.subject_to(stage.at_t0(p) == 0)
stage.subject_to(stage.at_t0(v) == 0)
stage.subject_to(stage.at_tf(p) == 1)
stage.subject_to(stage.at_tf(v) == 0)
stage.method(MultipleShooting(N=2))
for t0, t0_sol in ([] if t0_stage is None else [
(None, t0_sol_stage)
]) + [(-1, -1), (FreeTime(-1), -1)]:
for T, T_sol in ([] if T_stage is None else [
(None, T_sol_stage)
]) + [(2, 2), (FreeTime(1), 2)]:
ocp = Ocp()
kwargs = {}
if t0 is not None:
kwargs["t0"] = t0
if T is not None:
kwargs["T"] = T
mystage = ocp.stage(stage, **kwargs)
if mystage.is_free_starttime():
ocp.subject_to(mystage.t0 >= t0_sol)
ocp.solver('ipopt')
sol = ocp.solve()
tolerance = 1e-6
ts, ps = sol(mystage).sample(p,
grid='integrator',
refine=10)
ps_ref = np.hstack(
((0.5 * np.linspace(0, 1, 10 + 1)**2)[:-1],
np.linspace(0.5, 1.5, 10 + 1) -
0.5 * np.linspace(0, 1, 10 + 1)**2))
np.testing.assert_allclose(ps, ps_ref, atol=tolerance)
ts_ref = t0_sol + np.linspace(0, 2, 10 * 2 + 1)
ts, vs = sol(mystage).sample(v,
grid='integrator',
refine=10)
np.testing.assert_allclose(ts, ts_ref, atol=tolerance)
vs_ref = np.hstack((np.linspace(0, 1, 10 + 1)[:-1],
np.linspace(1, 0, 10 + 1)))
np.testing.assert_allclose(vs, vs_ref, atol=tolerance)
u_ref = np.array([1.0] * 10 + [-1.0] * 11)
ts, us = sol(mystage).sample(u,
grid='integrator',
refine=10)
np.testing.assert_allclose(us, u_ref, atol=tolerance)
from rockit import Ocp, DirectMethod, MultipleShooting ocp = Ocp() # Rocket example stage = ocp.stage(t0=0, T=1) # Omitting means variable p = stage.state() # Position v = stage.state() # Velocity m = stage.control() # Mass u = stage.control() # Thrust stage.set_der(p, v) stage.set_der(v, (u - 0.05 * v * v) / m) stage.set_der(m, -0.1 * u * u) # Regularize the control stage.add_objective(stage.integral(u**2)) # Path constraints stage.subject_to(u >= 0) stage.subject_to(u <= 0.5) # Initial constraints stage.subject_to(stage.at_t0(p) == 0) stage.subject_to(stage.at_t0(v) == 0) stage.subject_to(stage.at_t0(m) == 1)