def main():
nk = 15
print "creating model"
dae = pendulum_model.pendulum_model()
dae.addP('endTime')
print "setting up OCP"
ocp = Coll(dae, nk=nk,nicp=1,deg=4)
# 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.xVec(0),ocp.uVec(0),ocp.pVec()])
ocp.constrain(c0,'==',0)
# bounds
r = 0.3
ocp.bound('x',(-0.5,0.5))
ocp.bound('z',(-0.5,0.5))
ocp.bound('dx',(-5,5))
ocp.bound('dz',(-5,5))
ocp.bound('torque',(-50,50))
ocp.bound('m',(0.3,0.5))
ocp.bound('endTime',(0.01,1.5))
# boundary conditions
ocp.bound('x',(r,r),timestep=0)
ocp.bound('z',(0,0),timestep=0)
ocp.bound('x',(0,0),timestep=-1)
ocp.bound('z',(-r*1.5,-r/2),timestep=-1)
ocp.bound('dx',(0,0),timestep=0)
ocp.bound('dz',(0,0),timestep=0)
ocp.bound('dx',(0,0),timestep=-1)
ocp.bound('dz',(0,0),timestep=-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 = numpy.array(f.input(C.NLP_X_OPT))
self.iter = self.iter + 1
xup = ocp.devectorize(xOpt)['vardict']
po = 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()])
# solver
solverOptions = [ ("linear_solver","ma27")
# , ("derivative_test","first-order")
, ("expand_f",True)
, ("expand_g",True)
, ("generate_hessian",True)
# , ("max_iter",1000)
, ("tol",1e-4)
]
constraintFunOptions = [('numeric_jacobian',False)]
# initial conditions
ocp.guessX([r,0,0,0])
ocp.guess('torque',0)
ocp.guess('m',0)
ocp.guess('endTime',0.3)
ocp.setupCollocation( ocp.lookup('endTime') )
ocp.setupSolver( solverOpts=solverOptions,
constraintFunOpts=constraintFunOptions,
callback=MyCallback() )
opt = ocp.solve()
# Plot the results
plt.figure(1)
plt.clf()
legend = []
for name in ocp.dae.xNames():
legend.append(name)
plt.plot(opt['tgrid'],opt['vardict'][name])#,'--')
for name in ocp.dae.uNames():
legend.append(name)
plt.plot(opt['tgrid'],opt['vardict'][name]/20)#,'--')
plt.title("pendulum swingup optimization")
plt.xlabel('time')
plt.legend(legend)
plt.grid()
plt.show()
