def rpy_quaternion(quat):
""" Returns roll, pitch, yaw angle (ZYX-Convention) from a quaternion."""
qw, qx, qy, qz = quat[0], quat[1], quat[2], quat[3]
roll = cs.arctan2(2.0*(qw*qx + qy*qz), 1 - 2*(qx**2+qy**2))
pitch = cs.arcsin(2*(qw*qy-qz*qx))
yaw = cs.arctan2(2*(qw*qz+qx*qy), 1 - 2*(qy**2 + qz**2))
return roll, pitch, yaw
def getEuler(ocp, k):
r11 = ocp.lookup('e11',timestep=k)
r12 = ocp.lookup('e12',timestep=k)
mr13 = -ocp.lookup('e13',timestep=k)
# mr13 -- nan protect
# | mr13' > 1 = 1
# | mr13' < -1 = -1
# | otherwise = mr13'
r23 = ocp.lookup('e23',timestep=k)
r33 = ocp.lookup('e33',timestep=k)
yaw = C.arctan2(r12,r11)
pitch = C.arcsin(mr13)
roll = C.arctan2(r23,r33)
return (yaw,pitch,roll)
def getEuler(ocp, k):
r11 = ocp.lookup('e11', timestep=k)
r12 = ocp.lookup('e12', timestep=k)
mr13 = -ocp.lookup('e13', timestep=k)
# mr13 -- nan protect
# | mr13' > 1 = 1
# | mr13' < -1 = -1
# | otherwise = mr13'
r23 = ocp.lookup('e23', timestep=k)
r33 = ocp.lookup('e33', timestep=k)
yaw = C.arctan2(r12, r11)
pitch = C.arcsin(mr13)
roll = C.arctan2(r23, r33)
return (yaw, pitch, roll)
def getWindAnglesFrom_v_bw_b(airspeed, v_bw_b):
alpha = C.arctan2(v_bw_b[2], v_bw_b[0])
beta = C.arcsin(v_bw_b[1] / airspeed)
return (alpha, beta)
def carouselModel(conf):
'''
pass this a conf, and it'll return you a dae
'''
# empty Dae
dae = Dae()
# add some differential states/algebraic vars/controls/params
dae.addZ("nu")
dae.addX( [ "x"
, "y"
, "z"
, "e11"
, "e12"
, "e13"
, "e21"
, "e22"
, "e23"
, "e31"
, "e32"
, "e33"
, "dx"
, "dy"
, "dz"
, "w_bn_b_x"
, "w_bn_b_y"
, "w_bn_b_z"
, "ddelta"
, "r"
, "dr"
, "aileron"
, "elevator"
, "motor_torque"
, "ddr"
] )
if 'cn_rudder' in conf:
dae.addX('rudder')
dae.addU('drudder')
if 'cL_flaps' in conf:
dae.addX('flaps')
dae.addU('dflaps')
if conf['delta_parameterization'] == 'linear':
dae.addX('delta')
dae['cos_delta'] = C.cos(dae['delta'])
dae['sin_delta'] = C.sin(dae['delta'])
dae_delta_residual = dae.ddt('delta') - dae['ddelta']
elif conf['delta_parameterization'] == 'cos_sin':
dae.addX("cos_delta")
dae.addX("sin_delta")
norm = dae['cos_delta']**2 + dae['sin_delta']**2
if 'stabilize_invariants' in conf and conf['stabilize_invariants'] == True:
pole_delta = 0.5
else:
pole_delta = 0.0
cos_delta_dot_st = -pole_delta/2.* ( dae['cos_delta'] - dae['cos_delta'] / norm )
sin_delta_dot_st = -pole_delta/2.* ( dae['sin_delta'] - dae['sin_delta'] / norm )
dae_delta_residual = C.veccat([dae.ddt('cos_delta') - (-dae['sin_delta']*dae['ddelta'] + cos_delta_dot_st),
dae.ddt('sin_delta') - ( dae['cos_delta']*dae['ddelta'] + sin_delta_dot_st) ])
else:
raise ValueError('unrecognized delta_parameterization "'+conf['delta_parameterization']+'"')
dae.addU( [ "daileron"
, "delevator"
, "dmotor_torque"
, 'dddr'
] )
# add wind parameter if wind shear is in configuration
if 'wind_model' in conf:
if conf['wind_model']['name'] == 'hardcoded':
dae['w0'] = conf['wind_model']['hardcoded_value']
elif conf['wind_model']['name'] != 'random_walk':
dae.addP( ['w0'] )
# set some state derivatives as outputs
dae['ddx'] = dae.ddt('dx')
dae['ddy'] = dae.ddt('dy')
dae['ddz'] = dae.ddt('dz')
dae['ddt_w_bn_b_x'] = dae.ddt('w_bn_b_x')
dae['ddt_w_bn_b_y'] = dae.ddt('w_bn_b_y')
dae['ddt_w_bn_b_z'] = dae.ddt('w_bn_b_z')
dae['w_bn_b'] = C.veccat([dae['w_bn_b_x'], dae['w_bn_b_y'], dae['w_bn_b_z']])
# some outputs in for plotting
dae['carousel_RPM'] = dae['ddelta']*60/(2*C.pi)
dae['aileron_deg'] = dae['aileron']*180/C.pi
dae['elevator_deg'] = dae['elevator']*180/C.pi
dae['daileron_deg_s'] = dae['daileron']*180/C.pi
dae['delevator_deg_s'] = dae['delevator']*180/C.pi
# tether tension == radius*nu where nu is alg. var associated with x^2+y^2+z^2-r^2==0
dae['tether_tension'] = dae['r']*dae['nu']
# theoretical mechanical power
dae['mechanical_winch_power'] = -dae['tether_tension']*dae['dr']
# carousel2 motor model from thesis data
dae['rpm'] = -dae['dr']/0.1*60/(2*C.pi)
dae['torque'] = dae['tether_tension']*0.1
dae['electrical_winch_power'] = 293.5816373499238 + \
0.0003931623408*dae['rpm']*dae['rpm'] + \
0.0665919381751*dae['torque']*dae['torque'] + \
0.1078628659825*dae['rpm']*dae['torque']
dae['R_c2b'] = C.blockcat([[dae['e11'],dae['e12'],dae['e13']],
[dae['e21'],dae['e22'],dae['e23']],
[dae['e31'],dae['e32'],dae['e33']]])
dae["yaw"] = C.arctan2(dae["e12"], dae["e11"]) * 180.0 / C.pi
dae["pitch"] = C.arcsin( -dae["e13"] ) * 180.0 / C.pi
dae["roll"] = C.arctan2(dae["e23"], dae["e33"]) * 180.0 / C.pi
# line angle
dae['cos_line_angle'] = \
-(dae['e31']*dae['x'] + dae['e32']*dae['y'] + dae['e33']*dae['z']) / C.sqrt(dae['x']**2 + dae['y']**2 + dae['z']**2)
dae['line_angle_deg'] = C.arccos(dae['cos_line_angle'])*180.0/C.pi
(massMatrix, rhs, dRexp) = setupModel(dae, conf)
if 'stabilize_invariants' in conf and conf['stabilize_invariants'] == True:
RotPole = 0.5
else:
RotPole = 0.0
Rst = RotPole*C.mul( dae['R_c2b'], (C.inv(C.mul(dae['R_c2b'].T,dae['R_c2b'])) - numpy.eye(3)) )
ode = C.veccat([
C.veccat([dae.ddt(name) for name in ['x','y','z']]) - C.veccat([dae['dx'],dae['dy'],dae['dz']]),
C.veccat([dae.ddt(name) for name in ["e11","e12","e13",
"e21","e22","e23",
"e31","e32","e33"]]) - ( dRexp.T.reshape([9,1]) + Rst.reshape([9,1]) ),
dae_delta_residual,
# C.veccat([dae.ddt(name) for name in ['dx','dy','dz']]) - C.veccat([dae['ddx'],dae['ddy'],dae['ddz']]),
# C.veccat([dae.ddt(name) for name in ['w1','w2','w3']]) - C.veccat([dae['dw1'],dae['dw2'],dae['dw3']]),
# dae.ddt('ddelta') - dae['dddelta'],
dae.ddt('r') - dae['dr'],
dae.ddt('dr') - dae['ddr'],
dae.ddt('aileron') - dae['daileron'],
dae.ddt('elevator') - dae['delevator'],
dae.ddt('motor_torque') - dae['dmotor_torque'],
dae.ddt('ddr') - dae['dddr']
])
if 'rudder' in dae:
ode = C.veccat([ode, dae.ddt('rudder') - dae['drudder']])
if 'flaps' in dae:
ode = C.veccat([ode, dae.ddt('flaps') - dae['dflaps']])
if 'useVirtualTorques' in conf:
_v = conf[ 'useVirtualTorques' ]
if isinstance(_v, str):
_type = _v
_which = True, True, True
else:
assert isinstance(_v, dict)
_type = _v["type"]
_which = _v["which"]
if _type == 'random_walk':
if _which[ 0 ]:
ode = C.veccat([ode,
dae.ddt('t1_disturbance') - dae['dt1_disturbance']])
if _which[ 1 ]:
ode = C.veccat([ode,
dae.ddt('t2_disturbance') - dae['dt2_disturbance']])
if _which[ 2 ]:
ode = C.veccat([ode,
dae.ddt('t3_disturbance') - dae['dt3_disturbance']])
elif _type == 'parameter':
if _which[ 0 ]:
ode = C.veccat([ode, dae.ddt('t1_disturbance')])
if _which[ 1 ]:
ode = C.veccat([ode, dae.ddt('t2_disturbance')])
if _which[ 2 ]:
ode = C.veccat([ode, dae.ddt('t3_disturbance')])
if 'useVirtualForces' in conf:
_v = conf[ 'useVirtualForces' ]
if isinstance(_v, str):
_type = _v
_which = True, True, True
else:
assert isinstance(_v, dict)
_type = _v["type"]
_which = _v["which"]
if _type is 'random_walk':
if _which[ 0 ]:
ode = C.veccat([ode,
dae.ddt('f1_disturbance') - dae['df1_disturbance']])
if _which[ 1 ]:
ode = C.veccat([ode,
dae.ddt('f2_disturbance') - dae['df2_disturbance']])
if _which[ 2 ]:
ode = C.veccat([ode,
dae.ddt('f3_disturbance') - dae['df3_disturbance']])
elif _type == 'parameter':
if _which[ 0 ]:
ode = C.veccat([ode, dae.ddt('f1_disturbance')])
if _which[ 1 ]:
ode = C.veccat([ode, dae.ddt('f2_disturbance')])
if _which[ 2 ]:
ode = C.veccat([ode, dae.ddt('f3_disturbance')])
if 'wind_model' in conf and conf['wind_model']['name'] == 'random_walk':
tau_wind = conf['wind_model']['tau_wind']
ode = C.veccat([ode,
dae.ddt('wind_x') - (-dae['wind_x'] / tau_wind + dae['delta_wind_x'])
, dae.ddt('wind_y') - (-dae['wind_y'] / tau_wind + dae['delta_wind_y'])
, dae.ddt('wind_z') - (-dae['wind_z'] / tau_wind + dae['delta_wind_z'])
])
if 'stabilize_invariants' in conf and conf['stabilize_invariants'] == True:
cPole = 0.5
else:
cPole = 0.0
rhs[-1] -= 2*cPole*dae['cdot'] + cPole*cPole*dae['c']
psuedoZVec = C.veccat([dae.ddt(name) for name in ['ddelta','dx','dy','dz','w_bn_b_x','w_bn_b_y','w_bn_b_z']]+[dae['nu']])
alg = C.mul(massMatrix, psuedoZVec) - rhs
dae.setResidual([ode,alg])
return dae
def getWindAnglesFrom_v_bw_b(airspeed, v_bw_b):
alpha = C.arctan2(v_bw_b[2], v_bw_b[0])
beta = C.arcsin(v_bw_b[1] / airspeed)
return (alpha, beta)
def carouselModel(conf):
'''
pass this a conf, and it'll return you a dae
'''
# empty Dae
dae = Dae()
# add some differential states/algebraic vars/controls/params
dae.addZ("nu")
dae.addX( [ "x"
, "y"
, "z"
, "e11"
, "e12"
, "e13"
, "e21"
, "e22"
, "e23"
, "e31"
, "e32"
, "e33"
, "dx"
, "dy"
, "dz"
, "w_bn_b_x"
, "w_bn_b_y"
, "w_bn_b_z"
, "ddelta"
, "r"
, "dr"
, "aileron"
, "elevator"
, "motor_torque"
, "ddr"
] )
if 'cn_rudder' in conf:
dae.addX('rudder')
dae.addU('drudder')
if 'cL_flaps' in conf:
dae.addX('flaps')
dae.addU('dflaps')
if conf['delta_parameterization'] == 'linear':
dae.addX('delta')
dae['cos_delta'] = C.cos(dae['delta'])
dae['sin_delta'] = C.sin(dae['delta'])
dae_delta_residual = dae.ddt('delta') - dae['ddelta']
elif conf['delta_parameterization'] == 'cos_sin':
dae.addX("cos_delta")
dae.addX("sin_delta")
norm = dae['cos_delta']**2 + dae['sin_delta']**2
if 'stabilize_invariants' in conf and conf['stabilize_invariants'] == True:
pole_delta = 0.5
else:
pole_delta = 0.0
cos_delta_dot_st = -pole_delta/2.* ( dae['cos_delta'] - dae['cos_delta'] / norm )
sin_delta_dot_st = -pole_delta/2.* ( dae['sin_delta'] - dae['sin_delta'] / norm )
dae_delta_residual = C.veccat([dae.ddt('cos_delta') - (-dae['sin_delta']*dae['ddelta'] + cos_delta_dot_st),
dae.ddt('sin_delta') - ( dae['cos_delta']*dae['ddelta'] + sin_delta_dot_st) ])
else:
raise ValueError('unrecognized delta_parameterization "'+conf['delta_parameterization']+'"')
if "parametrizeInputsAsOnlineData" in conf and conf[ "parametrizeInputsAsOnlineData" ] is True:
dae.addP( [ "daileron",
"delevator",
"dmotor_torque",
'dddr' ] )
else:
dae.addU( [ "daileron",
"delevator",
"dmotor_torque",
'dddr' ] )
# add wind parameter if wind shear is in configuration
if 'wind_model' in conf:
if conf['wind_model']['name'] == 'hardcoded':
dae['w0'] = conf['wind_model']['hardcoded_value']
elif conf['wind_model']['name'] != 'random_walk':
dae.addP( ['w0'] )
# set some state derivatives as outputs
dae['ddx'] = dae.ddt('dx')
dae['ddy'] = dae.ddt('dy')
dae['ddz'] = dae.ddt('dz')
dae['ddt_w_bn_b_x'] = dae.ddt('w_bn_b_x')
dae['ddt_w_bn_b_y'] = dae.ddt('w_bn_b_y')
dae['ddt_w_bn_b_z'] = dae.ddt('w_bn_b_z')
dae['w_bn_b'] = C.veccat([dae['w_bn_b_x'], dae['w_bn_b_y'], dae['w_bn_b_z']])
# some outputs in for plotting
dae['carousel_RPM'] = dae['ddelta']*60/(2*C.pi)
dae['aileron_deg'] = dae['aileron']*180/C.pi
dae['elevator_deg'] = dae['elevator']*180/C.pi
dae['daileron_deg_s'] = dae['daileron']*180/C.pi
dae['delevator_deg_s'] = dae['delevator']*180/C.pi
# tether tension == radius*nu where nu is alg. var associated with x^2+y^2+z^2-r^2==0
dae['tether_tension'] = dae['r']*dae['nu']
# theoretical mechanical power
dae['mechanical_winch_power'] = -dae['tether_tension']*dae['dr']
# carousel2 motor model from thesis data
dae['rpm'] = -dae['dr']/0.1*60/(2*C.pi)
dae['torque'] = dae['tether_tension']*0.1
dae['electrical_winch_power'] = 293.5816373499238 + \
0.0003931623408*dae['rpm']*dae['rpm'] + \
0.0665919381751*dae['torque']*dae['torque'] + \
0.1078628659825*dae['rpm']*dae['torque']
dae['R_c2b'] = C.blockcat([[dae['e11'],dae['e12'],dae['e13']],
[dae['e21'],dae['e22'],dae['e23']],
[dae['e31'],dae['e32'],dae['e33']]])
dae["yaw"] = C.arctan2(dae["e12"], dae["e11"]) * 180.0 / C.pi
dae["pitch"] = C.arcsin( -dae["e13"] ) * 180.0 / C.pi
dae["roll"] = C.arctan2(dae["e23"], dae["e33"]) * 180.0 / C.pi
# line angle
dae['cos_line_angle'] = \
-(dae['e31']*dae['x'] + dae['e32']*dae['y'] + dae['e33']*dae['z']) / C.sqrt(dae['x']**2 + dae['y']**2 + dae['z']**2)
dae['line_angle_deg'] = C.arccos(dae['cos_line_angle'])*180.0/C.pi
(massMatrix, rhs, dRexp) = setupModel(dae, conf)
if 'stabilize_invariants' in conf and conf['stabilize_invariants'] == True:
RotPole = 0.5
else:
RotPole = 0.0
Rst = RotPole*C.mul( dae['R_c2b'], (C.inv(C.mul(dae['R_c2b'].T,dae['R_c2b'])) - numpy.eye(3)) )
ode = C.veccat([
C.veccat([dae.ddt(name) for name in ['x','y','z']]) - C.veccat([dae['dx'],dae['dy'],dae['dz']]),
C.veccat([dae.ddt(name) for name in ["e11","e12","e13",
"e21","e22","e23",
"e31","e32","e33"]]) - ( dRexp.T.reshape([9,1]) + Rst.reshape([9,1]) ),
dae_delta_residual,
# C.veccat([dae.ddt(name) for name in ['dx','dy','dz']]) - C.veccat([dae['ddx'],dae['ddy'],dae['ddz']]),
# C.veccat([dae.ddt(name) for name in ['w1','w2','w3']]) - C.veccat([dae['dw1'],dae['dw2'],dae['dw3']]),
# dae.ddt('ddelta') - dae['dddelta'],
dae.ddt('r') - dae['dr'],
dae.ddt('dr') - dae['ddr'],
dae.ddt('aileron') - dae['daileron'],
dae.ddt('elevator') - dae['delevator'],
dae.ddt('motor_torque') - dae['dmotor_torque'],
dae.ddt('ddr') - dae['dddr']
])
if 'rudder' in dae:
ode = C.veccat([ode, dae.ddt('rudder') - dae['drudder']])
if 'flaps' in dae:
ode = C.veccat([ode, dae.ddt('flaps') - dae['dflaps']])
if 'useVirtualTorques' in conf:
_v = conf[ 'useVirtualTorques' ]
if isinstance(_v, str):
_type = _v
_which = True, True, True
else:
assert isinstance(_v, dict)
_type = _v["type"]
_which = _v["which"]
if _type == 'random_walk':
if _which[ 0 ]:
ode = C.veccat([ode,
dae.ddt('t1_disturbance') - dae['dt1_disturbance']])
if _which[ 1 ]:
ode = C.veccat([ode,
dae.ddt('t2_disturbance') - dae['dt2_disturbance']])
if _which[ 2 ]:
ode = C.veccat([ode,
dae.ddt('t3_disturbance') - dae['dt3_disturbance']])
elif _type == 'parameter':
if _which[ 0 ]:
ode = C.veccat([ode, dae.ddt('t1_disturbance')])
if _which[ 1 ]:
ode = C.veccat([ode, dae.ddt('t2_disturbance')])
if _which[ 2 ]:
ode = C.veccat([ode, dae.ddt('t3_disturbance')])
if 'useVirtualForces' in conf:
_v = conf[ 'useVirtualForces' ]
if isinstance(_v, str):
_type = _v
_which = True, True, True
else:
assert isinstance(_v, dict)
_type = _v["type"]
_which = _v["which"]
if _type is 'random_walk':
if _which[ 0 ]:
ode = C.veccat([ode,
dae.ddt('f1_disturbance') - dae['df1_disturbance']])
if _which[ 1 ]:
ode = C.veccat([ode,
dae.ddt('f2_disturbance') - dae['df2_disturbance']])
if _which[ 2 ]:
ode = C.veccat([ode,
dae.ddt('f3_disturbance') - dae['df3_disturbance']])
elif _type == 'parameter':
if _which[ 0 ]:
ode = C.veccat([ode, dae.ddt('f1_disturbance')])
if _which[ 1 ]:
ode = C.veccat([ode, dae.ddt('f2_disturbance')])
if _which[ 2 ]:
ode = C.veccat([ode, dae.ddt('f3_disturbance')])
if 'wind_model' in conf and conf['wind_model']['name'] == 'random_walk':
tau_wind = conf['wind_model']['tau_wind']
ode = C.veccat([ode,
dae.ddt('wind_x') - (-dae['wind_x'] / tau_wind + dae['delta_wind_x'])
, dae.ddt('wind_y') - (-dae['wind_y'] / tau_wind + dae['delta_wind_y'])
, dae.ddt('wind_z') - (-dae['wind_z'] / tau_wind + dae['delta_wind_z'])
])
if 'stabilize_invariants' in conf and conf['stabilize_invariants'] == True:
cPole = 0.5
else:
cPole = 0.0
rhs[-1] -= 2*cPole*dae['cdot'] + cPole*cPole*dae['c']
psuedoZVec = C.veccat([dae.ddt(name) for name in ['ddelta','dx','dy','dz','w_bn_b_x','w_bn_b_y','w_bn_b_z']]+[dae['nu']])
alg = C.mul(massMatrix, psuedoZVec) - rhs
dae.setResidual([ode,alg])
return dae
eLe1 = - eTe2*we3 + eTe3*we2
eLe2 = - eTe3*we1 + eTe1*we3
eLe3 = - eTe1*we2 + eTe2*we1
# AERODYNAMIC COEEFICIENTS
# #################
vT1 = wE1
vT2 = -lT*w3 + wE2
vT3 = lT*w2 + wE3
# alpha = alpha0-wE3/wE1
# beta = wE2/C.sqrt(wE1*wE1 + wE3*wE3)
alpha = alpha0 + C.arctan2(-wE3,wE1)
beta = C.arcsin(wE2/vKite)
#NOTE: beta & alphaTail are compensated for the tail motion induced by
#omega @>@>
# alphaTail = alpha0-vT3/vT1
# betaTail = vT2/C.sqrt(vT1*vT1 + vT3*vT3)
alphaTail = alpha0 + C.arctan2(-vT3,vT1)
betaTail = C.arcsin(vT2/vKite)
dae.addOutput('alpha(deg)', alpha*180/C.pi)
dae.addOutput('alphaTail(deg)', alphaTail*180/C.pi)
dae.addOutput('beta(deg)', beta*180/C.pi)
dae.addOutput('betaTail(deg)', betaTail*180/C.pi)
# cL = cLA*alpha + cLe*elevator + cL0
# cD = cDA*alpha + cDA2*alpha*alpha + cDB2*beta*beta + cDe*elevator + cDr*aileron + cD0
def traverse(node, casadi_syms, rootnode):
#print node
#print node.args
#print len(node.args)
if len(node.args)==0:
# Handle symbols
if(node.is_Symbol):
return casadi_syms[node.name]
# Handle numbers and constants
if node.is_Zero:
return 0
if node.is_Number:
return float(node)
trig = sympy.functions.elementary.trigonometric
if len(node.args)==1:
# Handle unary operators
child = traverse(node.args[0], casadi_syms, rootnode) # Recursion!
if type(node) == trig.cos:
return casadi.cos(child)
if type(node) == trig.sin:
return casadi.sin(child)
if type(node) == trig.tan:
return casadi.tan(child)
if type(node) == trig.cosh:
return casadi.cosh(child)
if type(node) == trig.sinh:
return casadi.sinh(child)
if type(node) == trig.tanh:
return casadi.tanh(child)
if type(node) == trig.cot:
return 1/casadi.tan(child)
if type(node) == trig.acos:
return casadi.arccos(child)
if type(node) == trig.asin:
return casadi.arcsin(child)
if type(node) == trig.atan:
return casadi.arctan(child)
if len(node.args)==2:
# Handle binary operators
left = traverse(node.args[0], casadi_syms, rootnode) # Recursion!
right = traverse(node.args[1], casadi_syms, rootnode) # Recursion!
if node.is_Pow:
return left**right
if type(node) == trig.atan2:
return casadi.arctan2(left,right)
if len(node.args)>=2:
# Handle n-ary operators
child_generator = ( traverse(arg,casadi_syms,rootnode)
for arg in node.args )
if node.is_Add:
return reduce(lambda x, y: x+y, child_generator)
if node.is_Mul:
return reduce(lambda x, y: x*y, child_generator)
if node!=rootnode:
raise Exception("No mapping to casadi for node of type "
+ str(type(node)))
def traverse(node, casadi_syms, rootnode):
#print node
#print node.args
#print len(node.args)
if len(node.args)==0:
# Handle symbols
if(node.is_Symbol):
return casadi_syms[node.name]
# Handle numbers and constants
if node.is_Zero:
return 0
if node.is_Number:
return float(node)
trig = sympy.functions.elementary.trigonometric
if len(node.args)==1:
# Handle unary operators
child = traverse(node.args[0], casadi_syms, rootnode) # Recursion!
if type(node) == trig.cos:
return casadi.cos(child)
if type(node) == trig.sin:
return casadi.sin(child)
if type(node) == trig.tan:
return casadi.tan(child)
if type(node) == trig.cosh:
return casadi.cosh(child)
if type(node) == trig.sinh:
return casadi.sinh(child)
if type(node) == trig.tanh:
return casadi.tanh(child)
if type(node) == trig.cot:
return 1/casadi.tan(child)
if type(node) == trig.acos:
return casadi.arccos(child)
if type(node) == trig.asin:
return casadi.arcsin(child)
if type(node) == trig.atan:
return casadi.arctan(child)
if len(node.args)==2:
# Handle binary operators
left = traverse(node.args[0], casadi_syms, rootnode) # Recursion!
right = traverse(node.args[1], casadi_syms, rootnode) # Recursion!
if node.is_Pow:
return left**right
if type(node) == trig.atan2:
return casadi.arctan2(left,right)
if len(node.args)>=2:
# Handle n-ary operators
child_generator = ( traverse(arg,casadi_syms,rootnode)
for arg in node.args )
if node.is_Add:
return reduce(lambda x, y: x+y, child_generator)
if node.is_Mul:
return reduce(lambda x, y: x*y, child_generator)
if node!=rootnode:
raise Exception("No mapping to casadi for node of type "
+ str(type(node)))
def flightPathAngle(vel_n):
""" Returns the flight-path angle."""
return cs.arcsin(-vel_n[2]/cs.sqrt(vel_n.T@vel_n))#cs.linalg.norm(vel_n))