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Set of constraints raises Error #702
Description
I am using the python optimal control library to optimise the trajectory of a 2D rocket. Please find attached a minimum reproducible sample code of the optimisation process of the problem. Whenever I am trying to set constraints for only some of the states, I get the error described after the minimum reproducible example. Is there an appropriate way to define multiple separate constraints passed in the "constraints= [..., ..., ...]" argument of the solve.ocp() function? Also, instead of using range -np.inf to np.inf for state parameters that I do not want to bound, is there a value that makes the code ignore the specific state parameter constraints?
T_max_Single = 7607000/9
g = 9.81
m = 114239.00
k = 18.74
I = 16071705.59
import numpy as np
import math
import control as ct
import control.optimal as opt
import matplotlib.pyplot as plt
import logging
import time
import os
plt.style.use("default")
from IPython.display import display
from colorama import *
import sympy as s
from scipy.integrate import odeint
#Definition of the states
def rocket_update(t, x, u, params):
xpos = x[0]
U = x[1]
z = x[2]
W = x[3]
θ = x[4]
q = x[5]
T = u[0]
a = u[1]
# Return the derivative of the state
dydt = np.array([U,
T*np.cos(θ-a)/m,
W,
T*np.sin(θ-a)/m-g,
q,
T*k*np.sin(a)/I])
return(dydt)
def rocket_output(t, x, u, params):
return x # return (full state)
Tf = 8
# Define the rocket movement dynamics as an input/output system
rocket = ct.NonlinearIOSystem(
rocket_update, rocket_output, states=6, name='rocket',
inputs=("T", "α"), outputs=("x", "U", "z", "W", "θ", "q"))
# Define the time horizon (and spacing) for the optimization
horizon = np.linspace(0, Tf, Tf, endpoint=True) #############IMPORTANT
# Provide an intial guess (will be extended to entire horizon)
bend_left = [T_max_Single, 0.01] # slight left veer #############IMPORTANT
# Optimal Control Problem
Initial_x = 0 #m
Final_x = 5 #m
Initial_z = 0 #m
Final_z = 200 #m
Initial_θ = np.pi/2 #m
Final_θ = np.pi/3 #m
Final_Thrust = T_max_Single
x0 = [Initial_x, 0, Initial_z, 0, Initial_θ, 0]; u0 = [bend_left[0], bend_left[1]]
xf = [Final_x, 0, Final_z, 0, Final_θ, 0]; uf = [Final_Thrust, 0]
#T_max_Single
Min_T = 1 * T_max_Single
Max_T = 9 * T_max_Single
a_min = -20* np.pi/180
a_max = 20* np.pi/180
# Approach 3: terminal constraints
#
# We can also remove the cost function on the state and replace it
# with a terminal *constraint* on the state. If a solution is found,
# it guarantees we get to exactly the final state.
#
print("Initialisation of optimisation")
# print("Checkpoint_1")
# Input cost and terminal constraints
R = np.diag([0, 0]) # minimize applied inputs
cost3 = opt.quadratic_cost(rocket, np.zeros((6,6)), R, u0=uf)
con1 = [ opt.input_range_constraint(rocket, [Min_T, a_min], [Max_T, a_max]) ]
terminal = [ opt.state_range_constraint(rocket, [Final_x, -np.inf, Final_z, -np.inf, -np.inf, -np.inf],
[Final_x, np.inf, Final_z, np.inf, np.inf, np.inf]) ]
# Reset logging to its default values
logging.basicConfig(
level=logging.DEBUG, filename="./steering-terminal_constraint.log",
filemode='w', force=True)
# Compute the optimal control
start_time = time.process_time()
result3 = opt.solve_ocp(
rocket, horizon, x0, cost3, con1,
terminal_constraints=terminal, initial_guess=bend_left, log=False, method="trust-constr",
options={'eps': 0.01})
print("* Total time = %5g seconds\n" % (time.process_time() - start_time))
Error:
/opt/anaconda3/lib/python3.8/site-packages/scipy/optimize/_constraints.py:386: OptimizeWarning: At least one constraint is unbounded above and below. Such constraints are ignored.
warn("At least one constraint is unbounded above and below. Such "
/opt/anaconda3/lib/python3.8/site-packages/scipy/optimize/_constraints.py:432: OptimizeWarning: Equality and inequality constraints are specified in the same element of the constraint list. For efficient use with this method, equality and inequality constraints should be specified in separate elements of the constraint list.
warn("Equality and inequality constraints are specified in the same "
Activity
murrayrm commentedon Feb 19, 2022
A couple of issues that might be relevant:
input_range_constraintsto constrain some of the inputs and not others. Depending on the optimizer, this might now work (this is the first warning you are getting). You may need to useinput_poly_constraintsto just constrain the inputs that you care about.methodkeyword insolve_ocp, but there is no such keyword. You want to useminimize_method(andminimize_options). This one is tricky because there is no warning (I found it because I have put in a warning in a PR that I am working on).ThomasGiavasopoulos commentedon Feb 23, 2022
Thank you very much. The second comment described a keyword issue in my uploaded code, which should be fixed.
Regarding your first comment, is there an example where the constraint structures are used in practice?
murrayrm commentedon Feb 23, 2022
This is not a very good answer, but you can find some examples in the unit test code: control/tests/optimal_test.py.
ThomasGiavasopoulos commentedon Feb 23, 2022
Thank you very much! I will be closing the issue now. In case there is any example of use of these constraints in similar examples, I will be delighted to learn about it.
ThomasGiavasopoulos commentedon Feb 24, 2022
I am reopening this issue since I have now improved my opt.solve_ocp() command and wish to fully comply with the documentation of the control library which is otherwise producing results very reliably. As described above, I get the same error messages about the constraints, but the "SLSQP" solver solves correctly. I am using SLSQP solver since my constraints are linear.
This is the part of the code that has changed:
And this is the error message:
How can I correctly define multiple constraints on inputs only and then on states only, in the form: input_constraint_1, input_constraint_2, ... input_constraint_n , state_constraint_1, state_constraint_2, ..., state_constraint_n, and then pass them into the opt.solve_ocp().
I am attempting to promote this excellent solver in my thesis, that is the reason for my need to fully comply with the "grammar" structure of the library.
Thank you for your time.
murrayrm commentedon Mar 20, 2022
The following should work
The output that I get (using a slightly newer devleopment version of the code, so some details may be different) is:
I think this addresses the issue. Re-open is not.