I am using the ACADO toolkit to minimize the time for a small aircraft to go from takeoff to cruise. I have 4 differential states: velocity, range, height, and flight path angle, and 1 control: u. When I run the code, I get an error:
[ACADO] Error: The integration routine stopped as the required accuracy can not be obtained
Code: (RET_UNSUCCESSFUL_RETURN_FROM_INTEGRATOR_RK45)
Consequently, I also get several other errors stating that the NLP Solver Fails, and that the initialization of the optimization algorithm failed. I'm not exactly sure what I am doing wrong that the algorithm is not working. This is my first time using ACADO, and I am struggling to find good resources. Code below:
BEGIN_ACADO; % Always start with "BEGIN_ACADO".
acadoSet('problemname', 'stackOverflow');
DifferentialState v; % Velocity [m/s]
DifferentialState r; % Range [m]
DifferentialState h; % Height [m]
DifferentialState gamma; % Flight Path Angle [deg]
Parameter T; % Minimize Time
Control u; % Control input = Pitch angle
alpha = minus(u,gamma); % Angle of attack [deg]
thrust = mtimes(plus(.0088,mtimes(.000842,mtimes(alpha,pi/180))),v^2); % Thrust [N]
m = double(4.2); % mass [kg]
g = double(9.81); % gravity [m/s^2]
%% Diferential Equation
f = acado.DifferentialEquation(0, T); % Set the differential equation object
% Write down the ODE
f.add(dot(v) == (1/m)*(thrust*cos(alpha)-thrust-(m*g*sin(gamma))));
f.add(dot(r) == v*cos(gamma));
f.add(dot(h) == v*sin(gamma));
f.add(dot(gamma) == 1/(m*v)*(thrust*sin(alpha)-thrust-m*g*sin(gamma)));
%% Optimal Control Problem
ocp = acado.OCP(0.0, T); % Set up the Optimal Control Problem (OCP)
ocp.minimizeMayerTerm(T); % Minimize the consumed energy
ocp.subjectTo( f ); % Optimize w.r.t your differential equation
ocp.subjectTo( 'AT_START', r == 0.0 ); % r(0) = 0
ocp.subjectTo( 'AT_START', v == 0.0 ); % v(0) = 0
ocp.subjectTo( 'AT_START', h == 10.0 ); % h(0) = 1
ocp.subjectTo( 'AT_START', gamma == 0.0 ); % gamma(0) = 1
ocp.subjectTo( 'AT_END' , h == 61.0 ); % h(T) = Cruise Altitude
ocp.subjectTo( 'AT_END' , v == 24.0 ); % v(T) = Cruise Velocity
ocp.subjectTo( 'AT_END' , gamma == 0.0 ); % gamma(T) = Cruise Flight Angle
ocp.subjectTo( 14.013 <= v <= 27.0 ); % path constraint on speed
ocp.subjectTo( 0 <= v*sin(gamma) <= 3.33 ); % Restrict the max. rate of climb
ocp.subjectTo( 3 <= alpha <= 3.3 ); % Possible cruise windows for stability
%% Optimization Algorithm
algo =acado.OptimizationAlgorithm(ocp); % Set up the optimization algorithm, link it to your OCP
algo.set( 'KKT_TOLERANCE', 1e-8 ); % Set a custom KKT tolerance
END_ACADO;
% Run the test
out = stackOverflow_RUN();
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
To add to this post, the cost function I am trying to solve is below. I suspect that I am using the incorrect method to solve this, as there is nowhere to define the weighted matrices, but I still do not understand why my program is failing. The insert image functionality does not seem to work in these forums, so the imgur link below is a way to see the cost function. https://imgur.com/a/wAJAm89
Last edit: Derek Biega 2018-11-21
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
I've also tried implementing this function using LSQ, and am receiving the exact same error. I have no idea what could be wrong. here is that altered code:
clear; clc; close all;
BEGIN_ACADO; % Always start with "BEGIN_ACADO".
acadoSet('problemname', 'stackOverflow');
DifferentialState v; % Velocity [m/s]
DifferentialState r; % Range [m]
DifferentialState h; % Height [m]
DifferentialState gamma; % Flight Path Angle [deg]
Parameter T; % We would like to minize the T, so T is a parameter
Control u; % Control input = Pitch angle [deg]
alpha = minus(u,gamma); % Angle of attack [deg] ( will be constrained)
thrust = mtimes(plus(.0088,mtimes(.000842,mtimes(alpha,pi/180))),v^2); % Thrust [N]
m = 4.2; % mass [kg]
g = 9.81; % gravity [m/s^2]
%% Diferential Equation
f = acado.DifferentialEquation(0, T); % Set the differential equation object. We would like to minize the time.
f.linkMatlabODE('ode'); % Link to a Matlab ODE
%% Optimal Control Problem
ocp = acado.OCP(0.0, T, 50); % Set up the Optimal Control Problem (OCP)
% Start at 0, go to T, 50 intervals
Q = [.01 0 0 0; 0 1 0 0; 0 0 0 0; 0 0 0 0];
obj = {v, r, h, gamma}; % the LSQ-Function
R = zeros(1,4); % The reference
ocp.minimizeLSQ( Q, obj, R ); % Minimize this Least Squares Term
ocp.subjectTo( f ); % Optimize with respect to your differential equation
ocp.subjectTo( 'AT_START', r == 0.0 ); % r(0) = 0
ocp.subjectTo( 'AT_START', v == 0.0 ); % v(0) = 0
ocp.subjectTo( 'AT_START', h == 10.0 ); % h(0) = 1
ocp.subjectTo( 'AT_START', gamma == 0.0 ); % gamma(0) = 1
ocp.subjectTo( 'AT_END' , h == 61.0 ); % h(T) = Cruise Altitude
ocp.subjectTo( 'AT_END' , v == 24.0 ); % v(T) = Cruise Velocity
ocp.subjectTo( 'AT_END' , gamma == 0.0 ); % gamma(T) = Cruise Flight (Should be 0 at cruise)
ocp.subjectTo( 14.013 <= v <= 27.0 ); % path constraint on speed
ocp.subjectTo( 0 <= v*sin(gamma) <= 3.33 ); % Restrict the max. rate of climb
ocp.subjectTo( 3 <= alpha <= 3.3 ); % Possible cruise windows for stability
%% Optimization Algorithm
algo = acado.OptimizationAlgorithm(ocp); % Set up the optimization algorithm, link it to your OCP
algo.set( 'INTEGRATOR_TOLERANCE', 1e-8 ); % Set a custom KKT tolerance
algo.set( 'KKT_TOLERANCE', 1e-4 ); % Set a custom KKT tolerance
END_ACADO;
% Run the test
out = stackOverflowTest_RUN();
Full error output: [ACADO] Error: The integration routine stopped as the required accuracy can not be obtained
Code: (RET_UNSUCCESSFUL_RETURN_FROM_INTEGRATOR_RK45)
File: C:\Users\djbie\ACADOtoolkit\acado\integrator\integrator_runge_kutta.cpp
Line: 1394
So I've found out that this error is being triggered due to the values I select for my constraints. However, I do not understand why my selected values are flagging the system as such.
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
I am using the ACADO toolkit to minimize the time for a small aircraft to go from takeoff to cruise. I have 4 differential states: velocity, range, height, and flight path angle, and 1 control: u. When I run the code, I get an error:
Consequently, I also get several other errors stating that the NLP Solver Fails, and that the initialization of the optimization algorithm failed. I'm not exactly sure what I am doing wrong that the algorithm is not working. This is my first time using ACADO, and I am struggling to find good resources. Code below:
BEGIN_ACADO; % Always start with "BEGIN_ACADO". acadoSet('problemname', 'stackOverflow'); DifferentialState v; % Velocity [m/s] DifferentialState r; % Range [m] DifferentialState h; % Height [m] DifferentialState gamma; % Flight Path Angle [deg] Parameter T; % Minimize Time Control u; % Control input = Pitch angle alpha = minus(u,gamma); % Angle of attack [deg] thrust = mtimes(plus(.0088,mtimes(.000842,mtimes(alpha,pi/180))),v^2); % Thrust [N] m = double(4.2); % mass [kg] g = double(9.81); % gravity [m/s^2] %% Diferential Equation f = acado.DifferentialEquation(0, T); % Set the differential equation object % Write down the ODE f.add(dot(v) == (1/m)*(thrust*cos(alpha)-thrust-(m*g*sin(gamma)))); f.add(dot(r) == v*cos(gamma)); f.add(dot(h) == v*sin(gamma)); f.add(dot(gamma) == 1/(m*v)*(thrust*sin(alpha)-thrust-m*g*sin(gamma))); %% Optimal Control Problem ocp = acado.OCP(0.0, T); % Set up the Optimal Control Problem (OCP) ocp.minimizeMayerTerm(T); % Minimize the consumed energy ocp.subjectTo( f ); % Optimize w.r.t your differential equation ocp.subjectTo( 'AT_START', r == 0.0 ); % r(0) = 0 ocp.subjectTo( 'AT_START', v == 0.0 ); % v(0) = 0 ocp.subjectTo( 'AT_START', h == 10.0 ); % h(0) = 1 ocp.subjectTo( 'AT_START', gamma == 0.0 ); % gamma(0) = 1 ocp.subjectTo( 'AT_END' , h == 61.0 ); % h(T) = Cruise Altitude ocp.subjectTo( 'AT_END' , v == 24.0 ); % v(T) = Cruise Velocity ocp.subjectTo( 'AT_END' , gamma == 0.0 ); % gamma(T) = Cruise Flight Angle ocp.subjectTo( 14.013 <= v <= 27.0 ); % path constraint on speed ocp.subjectTo( 0 <= v*sin(gamma) <= 3.33 ); % Restrict the max. rate of climb ocp.subjectTo( 3 <= alpha <= 3.3 ); % Possible cruise windows for stability %% Optimization Algorithm algo =acado.OptimizationAlgorithm(ocp); % Set up the optimization algorithm, link it to your OCP algo.set( 'KKT_TOLERANCE', 1e-8 ); % Set a custom KKT tolerance END_ACADO; % Run the test out = stackOverflow_RUN();To add to this post, the cost function I am trying to solve is below. I suspect that I am using the incorrect method to solve this, as there is nowhere to define the weighted matrices, but I still do not understand why my program is failing. The insert image functionality does not seem to work in these forums, so the imgur link below is a way to see the cost function.
https://imgur.com/a/wAJAm89
Last edit: Derek Biega 2018-11-21
I've also tried implementing this function using LSQ, and am receiving the exact same error. I have no idea what could be wrong. here is that altered code:
clear; clc; close all; BEGIN_ACADO; % Always start with "BEGIN_ACADO". acadoSet('problemname', 'stackOverflow'); DifferentialState v; % Velocity [m/s] DifferentialState r; % Range [m] DifferentialState h; % Height [m] DifferentialState gamma; % Flight Path Angle [deg] Parameter T; % We would like to minize the T, so T is a parameter Control u; % Control input = Pitch angle [deg] alpha = minus(u,gamma); % Angle of attack [deg] ( will be constrained) thrust = mtimes(plus(.0088,mtimes(.000842,mtimes(alpha,pi/180))),v^2); % Thrust [N] m = 4.2; % mass [kg] g = 9.81; % gravity [m/s^2] %% Diferential Equation f = acado.DifferentialEquation(0, T); % Set the differential equation object. We would like to minize the time. f.linkMatlabODE('ode'); % Link to a Matlab ODE %% Optimal Control Problem ocp = acado.OCP(0.0, T, 50); % Set up the Optimal Control Problem (OCP) % Start at 0, go to T, 50 intervals Q = [.01 0 0 0; 0 1 0 0; 0 0 0 0; 0 0 0 0]; obj = {v, r, h, gamma}; % the LSQ-Function R = zeros(1,4); % The reference ocp.minimizeLSQ( Q, obj, R ); % Minimize this Least Squares Term ocp.subjectTo( f ); % Optimize with respect to your differential equation ocp.subjectTo( 'AT_START', r == 0.0 ); % r(0) = 0 ocp.subjectTo( 'AT_START', v == 0.0 ); % v(0) = 0 ocp.subjectTo( 'AT_START', h == 10.0 ); % h(0) = 1 ocp.subjectTo( 'AT_START', gamma == 0.0 ); % gamma(0) = 1 ocp.subjectTo( 'AT_END' , h == 61.0 ); % h(T) = Cruise Altitude ocp.subjectTo( 'AT_END' , v == 24.0 ); % v(T) = Cruise Velocity ocp.subjectTo( 'AT_END' , gamma == 0.0 ); % gamma(T) = Cruise Flight (Should be 0 at cruise) ocp.subjectTo( 14.013 <= v <= 27.0 ); % path constraint on speed ocp.subjectTo( 0 <= v*sin(gamma) <= 3.33 ); % Restrict the max. rate of climb ocp.subjectTo( 3 <= alpha <= 3.3 ); % Possible cruise windows for stability %% Optimization Algorithm algo = acado.OptimizationAlgorithm(ocp); % Set up the optimization algorithm, link it to your OCP algo.set( 'INTEGRATOR_TOLERANCE', 1e-8 ); % Set a custom KKT tolerance algo.set( 'KKT_TOLERANCE', 1e-4 ); % Set a custom KKT tolerance END_ACADO; % Run the test out = stackOverflowTest_RUN();Full error output:
[ACADO] Error: The integration routine stopped as the required accuracy can not be obtained
Code: (RET_UNSUCCESSFUL_RETURN_FROM_INTEGRATOR_RK45)
File: C:\Users\djbie\ACADOtoolkit\acado\integrator\integrator_runge_kutta.cpp
Line: 1394
[ACADO] Error: Initialization of NLP solver failed
Code: (RET_UNABLE_TO_INTEGRATE_SYSTEM)
File: C:\Users\djbie\ACADOtoolkit\acado\dynamic_discretization\shooting_method.cpp
Line: 279
[ACADO] Error: Initialization of NLP solver failed
Code: (RET_NLP_INIT_FAILED)
File: C:\Users\djbie\ACADOtoolkit\acado\nlp_solver\scp_method.cpp
Line: 217
[ACADO] Error: Initialization of optimization algorithm failed
Code: (RET_OPTALG_INIT_FAILED)
File: C:\Users\djbie\ACADOtoolkit\acado\optimization_algorithm\optimization_algorithm_base.cpp
Line: 587
Update:
So I've found out that this error is being triggered due to the values I select for my constraints. However, I do not understand why my selected values are flagging the system as such.
Hi,
I actually receive the same errors as you. I don't know if you figured it out.
Thank you!
Hi,
three years later and now I am gettting this since no one answered its hopeless outhere
Thank you for your response
Le jeu. 21 juil. 2022 à 21:07, Youssef Elshebani youssef93@users.sourceforge.net a écrit :