Non-symbolic inputs to a to_function when using Direct Collocation method

[loughlindd]

Dear Joris,
Thanks for the great job with the Rockit software.

I am generating a to_function for Optimal Control Problems, but have been faced with an issue : in the master example car_example_parametric, both states are sampled together, but in my case I wish to avoid this, in order to have separate to_function inputs for every state.
This does not cause any problem when using the Multiple Shooting method, but when using the Direct Collocation the to_function cannot be generated. It looks like the Collocation method assigns only one opti placeholder (per control interval) which is a vertcat of all the states. Therefore, when sampling the states individually they are expressed as : vertsplit(opti_x_1){0}, which is not symbolic and therefore cannot be used as a to_function input.

Is this a deliberate limitation to rockit, or do you believe there is a way to overcome this issue ?
Just in case, here is code generating the issue, by commenting/uncommenting lines 77-78.

Thanks for your help
Loughlin

#
#     This file is part of rockit.
#
#     rockit -- Rapid Optimal Control Kit
#     Copyright (C) 2019 MECO, KU Leuven. All rights reserved.
#
#     Rockit is free software; you can redistribute it and/or
#     modify it under the terms of the GNU Lesser General Public
#     License as published by the Free Software Foundation; either
#     version 3 of the License, or (at your option) any later version.
#
#     Rockit is distributed in the hope that it will be useful,
#     but WITHOUT ANY WARRANTY; without even the implied warranty of
#     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
#     Lesser General Public License for more details.
#
#     You should have received a copy of the GNU Lesser General Public
#     License along with CasADi; if not, write to the Free Software
#     Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
#
#

"""
Car accelerating on a linear track
====================================


"""

from rockit import *
from numpy import sin, pi
from casadi import vertcat
import numpy as np
import matplotlib.pyplot as plt

ocp = Ocp(T=FreeTime(1.0))

# Define constants
m = 500
c = 2
d = 1000

# Define states
p = ocp.state()
v = ocp.state()

# Defince controls
F = ocp.control()

# Specify ODE
ocp.set_der(p, v)
ocp.set_der(v, 1/m * (F - c * v**2))

# Lagrange objective
ocp.add_objective(ocp.T)

# Define parameters
F_max = ocp.parameter(grid='control')
p0 = ocp.parameter()

# Path constraints
ocp.subject_to(-F_max <= (F<= F_max))
ocp.subject_to(v >= 0)

# Initial constraints
ocp.subject_to(ocp.at_t0(p)==p0)
ocp.subject_to(ocp.at_t0(v)==0)

# End constraints
ocp.subject_to(ocp.at_tf(p)==d)
ocp.subject_to(ocp.at_tf(v)==0)

# Pick a solver
ocp.solver('ipopt')

# Choose a solution method
ocp.method(MultipleShooting(N=20,M=1,intg='rk')) #This works
# ocp.method(DirectCollocation(N=20,M=1,intg='rk')) #This does not work


# Set values for parameters
ocp.set_value(p0, 1)
ocp.set_value(F_max, 2500*np.ones(20))

# Translate problem to function
T = ocp.value(ocp.T)
p_state = ocp.sample(p,grid='control')[1]
v_state = ocp.sample(v,grid='control')[1]

controls = ocp.sample(F,grid='control-')[1]
test = ocp.to_function('test', [p0, ocp.sample(F_max,grid='control-')[1], T, p_state, v_state, controls], [ocp.sample(F,grid='control')[1], T, p_state, v_state, controls])

# Initial value
sol_T = 1.0
sol_p_state = 0
sol_v_state = 0

sol_controls = 0

# Solve problem for different values for parameters, initializing with previous solution
signal1, sol_T, sol_p_state1, sol_v_state1, sol_controls = test(0, 2500*np.ones(20), sol_T, sol_p_state, sol_v_state, sol_controls)
signal2, sol_T, sol_p_state2, sol_v_state2, sol_controls = test(0, 2500*np.ones(20), sol_T, sol_p_state1, sol_v_state1, sol_controls)
signal3, sol_T, sol_p_state3, sol_v_state3, sol_controls = test(0, 2000*np.ones(20), sol_T, sol_p_state2, sol_v_state2, sol_controls)