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/*
* MIT No Attribution
*
* Copyright (C) 2010-2023 Joel Andersson, Joris Gillis, Moritz Diehl, KU Leuven.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of this
* software and associated documentation files (the "Software"), to deal in the Software
* without restriction, including without limitation the rights to use, copy, modify,
* merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
* INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
* PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
*/
#include <iostream>
#include <fstream>
#include <ctime>
#include <casadi/casadi.hpp>
using namespace casadi;
int main(){
std::cout << "program started" << std::endl;
// Dimensions
int nu = 20; // Number of control segments
int nj = 100; // Number of integration steps per control segment
// optimization variable
SX u = SX::sym("u", nu); // control
SX s_0 = 0; // initial position
SX v_0 = 0; // initial speed
SX m_0 = 1; // initial mass
SX dt = 10.0/(nj*nu); // time step
SX alpha = 0.05; // friction
SX beta = 0.1; // fuel consumption rate
// Trajectory
std::vector<SX> s_k, v_k, m_k;
// Integrate over the interval with Euler forward
SX s = s_0, v = v_0, m = m_0;
for(int k=0; k<nu; ++k){
for(int j=0; j<nj; ++j){
s += dt*v;
v += dt / m * (u(k)- alpha * v*v);
m += -dt * beta*u(k)*u(k);
}
s_k.push_back(s);
v_k.push_back(v);
m_k.push_back(m);
}
SX s_all=vertcat(s_k), v_all=vertcat(v_k), m_all=vertcat(m_k);
// Objective function
SX f = dot(u, u);
// Terminal constraints
SX g = vertcat(s, v, v_all);
// Create the NLP
SXDict nlp = {{"x", u}, {"f", f}, {"g", g}};
// Allocate an NLP solver and buffers
Function solver = nlpsol("solver", "ipopt", nlp);
// Bounds on g
std::vector<double> gmin = {10, 0};
std::vector<double> gmax = {10, 0};
gmin.resize(2+nu, -std::numeric_limits<double>::infinity());
gmax.resize(2+nu, 1.1);
// Solve the problem
DMDict arg = {{"lbx", -10},
{"ubx", 10},
{"x0", 0.4},
{"lbg", gmin},
{"ubg", gmax}};
DMDict res = solver(arg);
// Print the optimal cost
double cost(res.at("f"));
std::cout << "optimal cost: " << cost << std::endl;
// Print the optimal solution
std::vector<double> uopt(res.at("x"));
std::cout << "optimal control: " << uopt << std::endl;
// Get the state trajectory
Function xfcn("xfcn", {u}, {s_all, v_all, m_all});
std::vector<double> sopt, vopt, mopt;
xfcn({uopt}, {&sopt, &vopt, &mopt});
std::cout << "position: " << sopt << std::endl;
std::cout << "velocity: " << vopt << std::endl;
std::cout << "mass: " << mopt << std::endl;
// Create Matlab script to plot the solution
std::ofstream file;
std::string filename = "rocket_ipopt_results.m";
file.open(filename.c_str());
file << "% Results file from " __FILE__ << std::endl;
file << "% Generated " __DATE__ " at " __TIME__ << std::endl;
file << std::endl;
file << "cost = " << cost << ";" << std::endl;
file << "u = " << uopt << ";" << std::endl;
// Save results to file
file << "t = linspace(0,10.0," << nu << ");"<< std::endl;
file << "s = " << sopt << ";" << std::endl;
file << "v = " << vopt << ";" << std::endl;
file << "m = " << mopt << ";" << std::endl;
// Finalize the results file
file << std::endl;
file << "% Plot the results" << std::endl;
file << "figure(1);" << std::endl;
file << "clf;" << std::endl << std::endl;
file << "subplot(2,2,1);" << std::endl;
file << "plot(t,s);" << std::endl;
file << "grid on;" << std::endl;
file << "xlabel('time [s]');" << std::endl;
file << "ylabel('position [m]');" << std::endl << std::endl;
file << "subplot(2,2,2);" << std::endl;
file << "plot(t,v);" << std::endl;
file << "grid on;" << std::endl;
file << "xlabel('time [s]');" << std::endl;
file << "ylabel('velocity [m/s]');" << std::endl << std::endl;
file << "subplot(2,2,3);" << std::endl;
file << "plot(t,m);" << std::endl;
file << "grid on;" << std::endl;
file << "xlabel('time [s]');" << std::endl;
file << "ylabel('mass [kg]');" << std::endl << std::endl;
file << "subplot(2,2,4);" << std::endl;
file << "plot(t,u);" << std::endl;
file << "grid on;" << std::endl;
file << "xlabel('time [s]');" << std::endl;
file << "ylabel('Thrust [kg m/s^2]');" << std::endl << std::endl;
file.close();
std::cout << "Results saved to \"" << filename << "\"" << std::endl;
return 0;
}
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