def main():
nSteps = 15
print "creating model"
dae = models.pendulum(nSteps=nSteps)
print "setting up OCP"
ocp = MultipleShootingStage(dae, nSteps)
# make the integrator
print "setting up dynamics constraints"
integratorOptions = [ ("reltol",1e-7)
, ("abstol",1e-9)
, ("t0",0)
, ("tf",1)
, ('name','integrator')
, ("linear_solver_creator",C.CSparse)
# , ("linear_solver_creator",C.LapackLUDense)
, ("linear_solver","user_defined")
]
ocp.setIdasIntegrator(integratorOptions)
# constrain invariants
def invariantErrs():
f = C.SXFunction( [dae.xVec(),dae.uVec(),dae.pVec()]
, [dae.output('invariants')]
)
f.setOption('name','invariant errors')
f.init()
return f
[c0] = invariantErrs().call([ocp.states[:,0],ocp.actions[:,0],ocp.params])
ocp.addConstraint(c0,'==',0)
# bounds
r = 0.3
ocp.setBound('x',(-0.5,0.5))
ocp.setBound('z',(-0.5,0.5))
ocp.setBound('dx',(-5,5))
ocp.setBound('dz',(-5,5))
ocp.setBound('torque',(-50,50))
ocp.setBound('m',(0.3,0.5))
ocp.setBound('endTime',(0.01,5.0))
# boundary conditions
ocp.setBound('x',(r,r),timestep=0)
ocp.setBound('z',(0,0),timestep=0)
ocp.setBound('x',(0,0),timestep=nSteps-1)
ocp.setBound('z',(-r*1.5,-r/2),timestep=nSteps-1)
ocp.setBound('dx',(0,0),timestep=0)
ocp.setBound('dz',(0,0),timestep=0)
ocp.setBound('dx',(0,0),timestep=nSteps-1)
ocp.setBound('dz',(0,0),timestep=nSteps-1)
# make the solver
ocp.setObjective(ocp.lookup('endTime'))
context = zmq.Context(1)
publisher = context.socket(zmq.PUB)
publisher.bind("tcp://*:5563")
# callback function
class MyCallback:
def __init__(self):
self.iter = 0
def __call__(self,f,*args):
xOpt = f.input(C.NLP_X_OPT)
self.iter = self.iter + 1
xup = ocp.devectorize(xOpt)
po = rawe.kite_pb2.PendulumOpt()
po.x.extend(list(xup['x']))
po.z.extend(list(xup['z']))
po.endTime = xup['endTime']
po.iters = self.iter
publisher.send_multipart(["pendulum-opt", po.SerializeToString()])
def makeCallback():
nd = ocp.getDesignVars().size()
nc = ocp._constraints.getG().size()
c = C.PyFunction( MyCallback(), C.nlpsolverOut(x_opt=C.sp_dense(nd,1), cost=C.sp_dense(1,1), lambda_x=C.sp_dense(nd,1), lambda_g = C.sp_dense(nc,1), g = C.sp_dense(nc,1) ), [C.sp_dense(1,1)] )
c.init()
return c
# solver
solverOptions = [ ("iteration_callback",makeCallback())
# , ("derivative_test","first-order")
, ("linear_solver","ma57")
]
constraintFunOptions = [('numeric_jacobian',False)]
ocp.setSolver( C.IpoptSolver, solverOptions=solverOptions, constraintFunOptions=constraintFunOptions )
# initial conditions
ocp.setXGuess([r,0,0,0])
ocp.setGuess('torque',0)
ocp.setGuess('m',0.4)
ocp.setGuess('endTime',0.5)
#ocp.setBounds()
# solve!
opt = ocp.devectorize(ocp.solve())
# Plot the results
plt.figure(1)
plt.clf()
time = numpy.linspace(0,opt['endTime'],opt['x'].size())
plt.plot(time, opt['x'], '--')
plt.plot(time, opt['z'], '-')
plt.plot(time, opt['dx'], '-.')
plt.plot(time, opt['dz'], '--')
time = numpy.linspace(0,opt['endTime'],opt['torque'].size())
plt.plot(time,opt['torque']/20,'--')
plt.title("pendulum swingup optimization")
plt.xlabel('time')
plt.legend(['x','z','vx','vz','torque'])
plt.grid()
plt.show()
def main():
nSteps = 15
print "creating model"
dae = models.pendulum(nSteps=nSteps)
print "setting up OCP"
ocp = MultipleShootingStage(dae, nSteps)
# make the integrator
print "setting up dynamics constraints"
integratorOptions = [
("reltol", 1e-7),
("abstol", 1e-9),
("t0", 0),
("tf", 1),
("name", "integrator"),
("linear_solver_creator", C.CSparse)
# , ("linear_solver_creator",C.LapackLUDense)
,
("linear_solver", "user_defined"),
]
ocp.setIdasIntegrator(integratorOptions)
# constrain invariants
def invariantErrs():
f = C.SXFunction([dae.xVec(), dae.uVec(), dae.pVec()], [dae.output("invariants")])
f.setOption("name", "invariant errors")
f.init()
return f
[c0] = invariantErrs().call([ocp.states[:, 0], ocp.actions[:, 0], ocp.params])
ocp.addConstraint(c0, "==", 0)
# bounds
r = 0.3
ocp.setBound("x", (-0.5, 0.5))
ocp.setBound("z", (-0.5, 0.5))
ocp.setBound("dx", (-5, 5))
ocp.setBound("dz", (-5, 5))
ocp.setBound("torque", (-50, 50))
ocp.setBound("m", (0.3, 0.5))
ocp.setBound("endTime", (0.01, 5.0))
# boundary conditions
ocp.setBound("x", (r, r), timestep=0)
ocp.setBound("z", (0, 0), timestep=0)
ocp.setBound("x", (0, 0), timestep=nSteps - 1)
ocp.setBound("z", (-r * 1.5, -r / 2), timestep=nSteps - 1)
ocp.setBound("dx", (0, 0), timestep=0)
ocp.setBound("dz", (0, 0), timestep=0)
ocp.setBound("dx", (0, 0), timestep=nSteps - 1)
ocp.setBound("dz", (0, 0), timestep=nSteps - 1)
# make the solver
ocp.setObjective(ocp.lookup("endTime"))
context = zmq.Context(1)
publisher = context.socket(zmq.PUB)
publisher.bind("tcp://*:5563")
# callback function
class MyCallback:
def __init__(self):
self.iter = 0
def __call__(self, f, *args):
xOpt = f.input(C.NLP_X_OPT)
self.iter = self.iter + 1
xup = ocp.devectorize(xOpt)
po = rawe.kite_pb2.PendulumOpt()
po.x.extend(list(xup["x"]))
po.z.extend(list(xup["z"]))
po.endTime = xup["endTime"]
po.iters = self.iter
publisher.send_multipart(["pendulum-opt", po.SerializeToString()])
def makeCallback():
nd = ocp.getDesignVars().size()
nc = ocp._constraints.getG().size()
c = C.PyFunction(
MyCallback(),
C.nlpsolverOut(
x_opt=C.sp_dense(nd, 1),
cost=C.sp_dense(1, 1),
lambda_x=C.sp_dense(nd, 1),
lambda_g=C.sp_dense(nc, 1),
g=C.sp_dense(nc, 1),
),
[C.sp_dense(1, 1)],
)
c.init()
return c
# solver
solverOptions = [
("iteration_callback", makeCallback())
# , ("derivative_test","first-order")
,
("linear_solver", "ma57"),
]
constraintFunOptions = [("numeric_jacobian", False)]
ocp.setSolver(C.IpoptSolver, solverOptions=solverOptions, constraintFunOptions=constraintFunOptions)
# initial conditions
ocp.setXGuess([r, 0, 0, 0])
ocp.setGuess("torque", 0)
ocp.setGuess("m", 0.4)
ocp.setGuess("endTime", 0.5)
# ocp.setBounds()
# solve!
opt = ocp.devectorize(ocp.solve())
# Plot the results
plt.figure(1)
plt.clf()
time = numpy.linspace(0, opt["endTime"], opt["x"].size())
plt.plot(time, opt["x"], "--")
plt.plot(time, opt["z"], "-")
plt.plot(time, opt["dx"], "-.")
plt.plot(time, opt["dz"], "--")
time = numpy.linspace(0, opt["endTime"], opt["torque"].size())
plt.plot(time, opt["torque"] / 20, "--")
plt.title("pendulum swingup optimization")
plt.xlabel("time")
plt.legend(["x", "z", "vx", "vz", "torque"])
plt.grid()
plt.show()
