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MPCExample.cpp
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MPCExample.cpp
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/**
* @file MPCExample.cpp
* @author Giulio Romualdi
* @copyright Released under the terms of the LGPLv2.1 or later, see LGPL.TXT
* @date 2018
*/
// osqp-eigen
#include "OsqpEigen/OsqpEigen.h"
// eigen
#include <Eigen/Dense>
#include <iostream>
void setDynamicsMatrices(Eigen::Matrix<double, 12, 12> &a, Eigen::Matrix<double, 12, 4> &b)
{
a << 1., 0., 0., 0., 0., 0., 0.1, 0., 0., 0., 0., 0. ,
0., 1., 0., 0., 0., 0., 0., 0.1, 0., 0., 0., 0. ,
0., 0., 1., 0., 0., 0., 0., 0., 0.1, 0., 0., 0. ,
0.0488, 0., 0., 1., 0., 0., 0.0016, 0., 0., 0.0992, 0., 0. ,
0., -0.0488, 0., 0., 1., 0., 0., -0.0016, 0., 0., 0.0992, 0. ,
0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.0992,
0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0. ,
0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0. ,
0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0. ,
0.9734, 0., 0., 0., 0., 0., 0.0488, 0., 0., 0.9846, 0., 0. ,
0., -0.9734, 0., 0., 0., 0., 0., -0.0488, 0., 0., 0.9846, 0. ,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.9846;
b << 0., -0.0726, 0., 0.0726,
-0.0726, 0., 0.0726, 0. ,
-0.0152, 0.0152, -0.0152, 0.0152,
-0., -0.0006, -0., 0.0006,
0.0006, 0., -0.0006, 0.0000,
0.0106, 0.0106, 0.0106, 0.0106,
0, -1.4512, 0., 1.4512,
-1.4512, 0., 1.4512, 0. ,
-0.3049, 0.3049, -0.3049, 0.3049,
-0., -0.0236, 0., 0.0236,
0.0236, 0., -0.0236, 0. ,
0.2107, 0.2107, 0.2107, 0.2107;
}
void setInequalityConstraints(Eigen::Matrix<double, 12, 1> &xMax, Eigen::Matrix<double, 12, 1> &xMin,
Eigen::Matrix<double, 4, 1> &uMax, Eigen::Matrix<double, 4, 1> &uMin)
{
double u0 = 10.5916;
// input inequality constraints
uMin << 9.6 - u0,
9.6 - u0,
9.6 - u0,
9.6 - u0;
uMax << 13 - u0,
13 - u0,
13 - u0,
13 - u0;
// state inequality constraints
xMin << -M_PI/6,-M_PI/6,-OsqpEigen::INFTY,-OsqpEigen::INFTY,-OsqpEigen::INFTY,-1.,
-OsqpEigen::INFTY, -OsqpEigen::INFTY,-OsqpEigen::INFTY,-OsqpEigen::INFTY,
-OsqpEigen::INFTY,-OsqpEigen::INFTY;
xMax << M_PI/6,M_PI/6, OsqpEigen::INFTY,OsqpEigen::INFTY,OsqpEigen::INFTY,
OsqpEigen::INFTY, OsqpEigen::INFTY,OsqpEigen::INFTY,OsqpEigen::INFTY,
OsqpEigen::INFTY,OsqpEigen::INFTY,OsqpEigen::INFTY;
}
void setWeightMatrices(Eigen::DiagonalMatrix<double, 12> &Q, Eigen::DiagonalMatrix<double, 4> &R)
{
Q.diagonal() << 0, 0, 10., 10., 10., 10., 0, 0, 0, 5., 5., 5.;
R.diagonal() << 0.1, 0.1, 0.1, 0.1;
}
void castMPCToQPHessian(const Eigen::DiagonalMatrix<double, 12> &Q, const Eigen::DiagonalMatrix<double, 4> &R, int mpcWindow,
Eigen::SparseMatrix<double> &hessianMatrix)
{
hessianMatrix.resize(12*(mpcWindow+1) + 4 * mpcWindow, 12*(mpcWindow+1) + 4 * mpcWindow);
//populate hessian matrix
for(int i = 0; i<12*(mpcWindow+1) + 4 * mpcWindow; i++){
if(i < 12*(mpcWindow+1)){
int posQ=i%12;
float value = Q.diagonal()[posQ];
if(value != 0)
hessianMatrix.insert(i,i) = value;
}
else{
int posR=i%4;
float value = R.diagonal()[posR];
if(value != 0)
hessianMatrix.insert(i,i) = value;
}
}
}
void castMPCToQPGradient(const Eigen::DiagonalMatrix<double, 12> &Q, const Eigen::Matrix<double, 12, 1> &xRef, int mpcWindow,
Eigen::VectorXd &gradient)
{
Eigen::Matrix<double,12,1> Qx_ref;
Qx_ref = Q * (-xRef);
// populate the gradient vector
gradient = Eigen::VectorXd::Zero(12*(mpcWindow+1) + 4*mpcWindow, 1);
for(int i = 0; i<12*(mpcWindow+1); i++){
int posQ=i%12;
float value = Qx_ref(posQ,0);
gradient(i,0) = value;
}
}
void castMPCToQPConstraintMatrix(const Eigen::Matrix<double, 12, 12> &dynamicMatrix, const Eigen::Matrix<double, 12, 4> &controlMatrix,
int mpcWindow, Eigen::SparseMatrix<double> &constraintMatrix)
{
constraintMatrix.resize(12*(mpcWindow+1) + 12*(mpcWindow+1) + 4 * mpcWindow, 12*(mpcWindow+1) + 4 * mpcWindow);
// populate linear constraint matrix
for(int i = 0; i<12*(mpcWindow+1); i++){
constraintMatrix.insert(i,i) = -1;
}
for(int i = 0; i < mpcWindow; i++)
for(int j = 0; j<12; j++)
for(int k = 0; k<12; k++){
float value = dynamicMatrix(j,k);
if(value != 0){
constraintMatrix.insert(12 * (i+1) + j, 12 * i + k) = value;
}
}
for(int i = 0; i < mpcWindow; i++)
for(int j = 0; j < 12; j++)
for(int k = 0; k < 4; k++){
float value = controlMatrix(j,k);
if(value != 0){
constraintMatrix.insert(12*(i+1)+j, 4*i+k+12*(mpcWindow + 1)) = value;
}
}
for(int i = 0; i<12*(mpcWindow+1) + 4*mpcWindow; i++){
constraintMatrix.insert(i+(mpcWindow+1)*12,i) = 1;
}
}
void castMPCToQPConstraintVectors(const Eigen::Matrix<double, 12, 1> &xMax, const Eigen::Matrix<double, 12, 1> &xMin,
const Eigen::Matrix<double, 4, 1> &uMax, const Eigen::Matrix<double, 4, 1> &uMin,
const Eigen::Matrix<double, 12, 1> &x0,
int mpcWindow, Eigen::VectorXd &lowerBound, Eigen::VectorXd &upperBound)
{
// evaluate the lower and the upper inequality vectors
Eigen::VectorXd lowerInequality = Eigen::MatrixXd::Zero(12*(mpcWindow+1) + 4 * mpcWindow, 1);
Eigen::VectorXd upperInequality = Eigen::MatrixXd::Zero(12*(mpcWindow+1) + 4 * mpcWindow, 1);
for(int i=0; i<mpcWindow+1; i++){
lowerInequality.block(12*i,0,12,1) = xMin;
upperInequality.block(12*i,0,12,1) = xMax;
}
for(int i=0; i<mpcWindow; i++){
lowerInequality.block(4 * i + 12 * (mpcWindow + 1), 0, 4, 1) = uMin;
upperInequality.block(4 * i + 12 * (mpcWindow + 1), 0, 4, 1) = uMax;
}
// evaluate the lower and the upper equality vectors
Eigen::VectorXd lowerEquality = Eigen::MatrixXd::Zero(12*(mpcWindow+1),1 );
Eigen::VectorXd upperEquality;
lowerEquality.block(0,0,12,1) = -x0;
upperEquality = lowerEquality;
lowerEquality = lowerEquality;
// merge inequality and equality vectors
lowerBound = Eigen::MatrixXd::Zero(2*12*(mpcWindow+1) + 4*mpcWindow,1 );
lowerBound << lowerEquality,
lowerInequality;
upperBound = Eigen::MatrixXd::Zero(2*12*(mpcWindow+1) + 4*mpcWindow,1 );
upperBound << upperEquality,
upperInequality;
}
void updateConstraintVectors(const Eigen::Matrix<double, 12, 1> &x0,
Eigen::VectorXd &lowerBound, Eigen::VectorXd &upperBound)
{
lowerBound.block(0,0,12,1) = -x0;
upperBound.block(0,0,12,1) = -x0;
}
double getErrorNorm(const Eigen::Matrix<double, 12, 1> &x,
const Eigen::Matrix<double, 12, 1> &xRef)
{
// evaluate the error
Eigen::Matrix<double, 12, 1> error = x - xRef;
// return the norm
return error.norm();
}
int main()
{
// set the preview window
int mpcWindow = 20;
// allocate the dynamics matrices
Eigen::Matrix<double, 12, 12> a;
Eigen::Matrix<double, 12, 4> b;
// allocate the constraints vector
Eigen::Matrix<double, 12, 1> xMax;
Eigen::Matrix<double, 12, 1> xMin;
Eigen::Matrix<double, 4, 1> uMax;
Eigen::Matrix<double, 4, 1> uMin;
// allocate the weight matrices
Eigen::DiagonalMatrix<double, 12> Q;
Eigen::DiagonalMatrix<double, 4> R;
// allocate the initial and the reference state space
Eigen::Matrix<double, 12, 1> x0;
Eigen::Matrix<double, 12, 1> xRef;
// allocate QP problem matrices and vectores
Eigen::SparseMatrix<double> hessian;
Eigen::VectorXd gradient;
Eigen::SparseMatrix<double> linearMatrix;
Eigen::VectorXd lowerBound;
Eigen::VectorXd upperBound;
// set the initial and the desired states
x0 << 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ;
xRef << 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0;
// set MPC problem quantities
setDynamicsMatrices(a, b);
setInequalityConstraints(xMax, xMin, uMax, uMin);
setWeightMatrices(Q, R);
// cast the MPC problem as QP problem
castMPCToQPHessian(Q, R, mpcWindow, hessian);
castMPCToQPGradient(Q, xRef, mpcWindow, gradient);
castMPCToQPConstraintMatrix(a, b, mpcWindow, linearMatrix);
castMPCToQPConstraintVectors(xMax, xMin, uMax, uMin, x0, mpcWindow, lowerBound, upperBound);
// instantiate the solver
OsqpEigen::Solver solver;
// settings
//solver.settings()->setVerbosity(false);
solver.settings()->setWarmStart(true);
// set the initial data of the QP solver
solver.data()->setNumberOfVariables(12 * (mpcWindow + 1) + 4 * mpcWindow);
solver.data()->setNumberOfConstraints(2 * 12 * (mpcWindow + 1) + 4 * mpcWindow);
if(!solver.data()->setHessianMatrix(hessian)) return 1;
if(!solver.data()->setGradient(gradient)) return 1;
if(!solver.data()->setLinearConstraintsMatrix(linearMatrix)) return 1;
if(!solver.data()->setLowerBound(lowerBound)) return 1;
if(!solver.data()->setUpperBound(upperBound)) return 1;
// instantiate the solver
if(!solver.initSolver()) return 1;
// controller input and QPSolution vector
Eigen::Vector4d ctr;
Eigen::VectorXd QPSolution;
// number of iteration steps
int numberOfSteps = 50;
for (int i = 0; i < numberOfSteps; i++){
// solve the QP problem
if(!solver.solve()) return 1;
// get the controller input
QPSolution = solver.getSolution();
ctr = QPSolution.block(12 * (mpcWindow + 1), 0, 4, 1);
// save data into file
auto x0Data = x0.data();
// propagate the model
x0 = a * x0 + b * ctr;
// update the constraint bound
updateConstraintVectors(x0, lowerBound, upperBound);
if(!solver.updateBounds(lowerBound, upperBound)) return 1;
}
return 0;
}