Added tests for the MPC tool

dlib/control/mpc.h

@@ -67,7 +67,6 @@ namespace dlib
             matrix<double,S,S> temp = diagm(Q);
             for (unsigned long c = 0; c < horizon; ++c)
             {
-                long i = horizon-c-1;
                 lambda += trans(B)*temp*B;
                 temp = trans(A)*temp*A + diagm(Q);
             }

dlib/test/CMakeLists.txt

@@ -84,6 +84,7 @@ set (tests
    md5.cpp
    member_function_pointer.cpp
    metaprogramming.cpp
+   mpc.cpp
    multithreaded_object.cpp
    numerical_integration.cpp
    object_detector.cpp

dlib/test/makefile

@@ -99,6 +99,7 @@ SRC += max_sum_submatrix.cpp
 SRC += md5.cpp
 SRC += member_function_pointer.cpp
 SRC += metaprogramming.cpp
+SRC += mpc.cpp
 SRC += multithreaded_object.cpp
 SRC += numerical_integration.cpp
 SRC += object_detector.cpp

dlib/test/mpc.cpp

+// Copyright (C) 2015  Davis E. King (davis@dlib.net)
+// License: Boost Software License   See LICENSE.txt for the full license.
+
+
+#include <string>
+#include <sstream>
+
+#include <dlib/control.h>
+#include "tester.h"
+
+namespace  
+{
+    using namespace test;
+    using namespace std;
+    using namespace dlib;
+  
+    logger dlog("test.mpc");
+
+    template <
+        typename EXP1,
+        typename EXP2,
+        typename T, long NR, long NC, typename MM, typename L
+        >
+    unsigned long solve_qp_box_using_smo ( 
+        const matrix_exp<EXP1>& _Q,
+        const matrix_exp<EXP2>& _b,
+        matrix<T,NR,NC,MM,L>& alpha,
+        matrix<T,NR,NC,MM,L>& lower,
+        matrix<T,NR,NC,MM,L>& upper,
+        T eps,
+        unsigned long max_iter
+    )
+    /*!
+        ensures
+            - solves: 0.5*trans(x)*Q*x + trans(b)*x where x is box constrained.
+    !*/
+    {
+        const_temp_matrix<EXP1> Q(_Q);
+        const_temp_matrix<EXP2> b(_b);
+        //cout << "IN QP SOLVER" << endl;
+        //cout << "max eig: " << max(real_eigenvalues(Q)) << endl;
+        //cout << "min eig: " << min(real_eigenvalues(Q)) << endl;
+        //cout << "Q: \n" << Q << endl;
+        //cout << "b: \n" << b << endl;
+
+        // make sure requires clause is not broken
+        DLIB_ASSERT(Q.nr() == Q.nc() &&
+                     alpha.size() == lower.size() &&
+                     alpha.size() == upper.size() &&
+                     is_col_vector(b) &&
+                     is_col_vector(alpha) &&
+                     is_col_vector(lower) &&
+                     is_col_vector(upper) &&
+                     b.size() == alpha.size() &&
+                     b.size() == Q.nr() &&
+                     alpha.size() > 0 &&
+                     0 <= min(alpha-lower) &&
+                     0 <= max(upper-alpha) &&
+                     eps > 0 &&
+                     max_iter > 0,
+                     "\t unsigned long solve_qp_box_using_smo()"
+                     << "\n\t Invalid arguments were given to this function"
+                     << "\n\t Q.nr():               " << Q.nr()
+                     << "\n\t Q.nc():               " << Q.nc()
+                     << "\n\t is_col_vector(b):     " << is_col_vector(b)
+                     << "\n\t is_col_vector(alpha): " << is_col_vector(alpha)
+                     << "\n\t is_col_vector(lower): " << is_col_vector(lower)
+                     << "\n\t is_col_vector(upper): " << is_col_vector(upper)
+                     << "\n\t b.size():             " << b.size() 
+                     << "\n\t alpha.size():         " << alpha.size() 
+                     << "\n\t lower.size():         " << lower.size() 
+                     << "\n\t upper.size():         " << upper.size() 
+                     << "\n\t Q.nr():               " << Q.nr() 
+                     << "\n\t min(alpha-lower):     " << min(alpha-lower) 
+                     << "\n\t max(upper-alpha):     " << max(upper-alpha) 
+                     << "\n\t eps:                  " << eps 
+                     << "\n\t max_iter:             " << max_iter 
+        );
+
+
+        // Compute f'(alpha) (i.e. the gradient of f(alpha)) for the current alpha.  
+        matrix<T,NR,NC,MM,L> df = Q*alpha + b;
+        matrix<T,NR,NC,MM,L> QQ = reciprocal_max(diag(Q));
+
+
+        unsigned long iter = 0;
+        for (; iter < max_iter; ++iter)
+        {
+            T max_df = 0;
+            long best_r =0;
+            for (long r = 0; r < Q.nr(); ++r)
+            {
+                if (alpha(r) <= lower(r) && df(r) > 0)
+                    ;//alpha(r) = lower(r);
+                else if (alpha(r) >= upper(r) && df(r) < 0)
+                    ;//alpha(r) = upper(r);
+                else if (std::abs(df(r)) > max_df)
+                {
+                    best_r = r;
+                    max_df = std::abs(df(r));
+                }
+            }
+
+            //for (long r = 0; r < Q.nr(); ++r)
+            long r = best_r;
+            {
+
+                const T old_alpha = alpha(r);
+                alpha(r) = -(df(r)-Q(r,r)*alpha(r))*QQ(r);
+                if (alpha(r) < lower(r))
+                    alpha(r) = lower(r);
+                else if (alpha(r) > upper(r))
+                    alpha(r) = upper(r);
+
+                const T delta = old_alpha-alpha(r);
+
+                // Now update the gradient. We will perform the equivalent of: df = Q*alpha + b;
+                for(long k = 0; k < df.nr(); ++k)
+                    df(k) -= Q(r,k)*delta;
+            }
+
+            if (max_df < eps)
+                break;
+        }
+        //cout << "df: \n" << trans(df) << endl;
+        //cout << "objective value: " << 0.5*trans(alpha)*Q*alpha + trans(b)*alpha << endl;
+
+        return iter+1;
+    }
+
+// ----------------------------------------------------------------------------------------
+
+    namespace impl_mpc
+    {
+        template <long N>
+        void pack(
+            matrix<double,0,1>& out,
+            const std::vector<matrix<double,N,1> >& item
+        )
+        {
+            DLIB_CASSERT(item.size() != 0,"");
+            out.set_size(item.size()*item[0].size());
+            long j = 0;
+            for (unsigned long i = 0; i < item.size(); ++i)
+                for (long r = 0; r < item[i].size(); ++r)
+                    out(j++) = item[i](r);
+        }
+
+        template <long N>
+        void pack(
+            matrix<double,0,1>& out,
+            const matrix<double,N,1>& item,
+            const long num
+        )
+        {
+            out.set_size(item.size()*num);
+            long j = 0;
+            for (long r = 0; r < num; ++r)
+                for (long i = 0; i < item.size(); ++i)
+                    out(j++) = item(i);
+        }
+
+        template <long N>
+        void unpack(
+            std::vector<matrix<double,N,1> >& out,
+            const matrix<double,0,1>& item 
+        )
+        {
+            DLIB_CASSERT(out.size() != 0,"");
+            DLIB_CASSERT((long)out.size()*out[0].size() == item.size(),"");
+            long j = 0;
+            for (unsigned long i = 0; i < out.size(); ++i)
+                for (long r = 0; r < out[i].size(); ++r)
+                    out[i](r) = item(j++);
+        }
+    }
+
+    template <long S, long I>
+    unsigned long solve_linear_mpc (
+        const matrix<double,S,S>& A,
+        const matrix<double,S,I>& B,
+        const matrix<double,S,1>& C,
+        const matrix<double,S,1>& Q,
+        const matrix<double,I,1>& R,
+        const matrix<double,I,1>& _lower,
+        const matrix<double,I,1>& _upper,
+        const std::vector<matrix<double,S,1> >& target, 
+        const matrix<double,S,1>& initial_state,
+        std::vector<matrix<double,I,1> >& controls // input and output
+    )
+    {
+        using namespace impl_mpc;
+        DLIB_CASSERT(target.size() == controls.size(),"");
+
+        matrix<double> K(B.nr()*controls.size(), B.nc()*controls.size());
+        matrix<double,0,1> M(B.nr()*controls.size());
+
+        // compute powers of A: Apow[i] == A^i
+        std::vector<matrix<double,S,S> > Apow(controls.size());
+        Apow[0] = identity_matrix(A);
+        for (unsigned long i = 1; i < Apow.size(); ++i)
+            Apow[i] = A*Apow[i-1];
+
+        // fill in K
+        K = 0;
+        for (unsigned long r = 0; r < controls.size(); ++r)
+            for (unsigned long c = 0; c <= r; ++c)
+                set_subm(K,r*B.nr(),c*B.nc(), B.nr(), B.nc()) = Apow[r-c]*B;
+
+        // fill in M
+        set_subm(M,0*A.nr(),0,A.nr(),1) = A*initial_state + C;
+        for (unsigned long i = 1; i < controls.size(); ++i)
+            set_subm(M,i*A.nr(),0,A.nr(),1) = A*subm(M,(i-1)*A.nr(),0,A.nr(),1) + C;
+
+        //cout << "M: \n" << M << endl;
+        //cout << "K: \n" << K << endl;
+
+        matrix<double,0,1> t, v, lower, upper;
+        pack(t, target);
+        pack(v, controls);
+        pack(lower, _lower, controls.size());
+        pack(upper, _upper, controls.size());
+
+
+        matrix<double> QQ(K.nr(),K.nr()), RR(K.nc(),K.nc());
+        QQ = 0;
+        RR = 0;
+        for (unsigned long c = 0; c < controls.size(); ++c)
+        {
+            set_subm(QQ,c*Q.nr(),c*Q.nr(),Q.nr(),Q.nr()) = diagm(Q);
+            set_subm(RR,c*R.nr(),c*R.nr(),R.nr(),R.nr()) = diagm(R);
+        }
+
+        matrix<double> m1 = trans(K)*QQ*K+RR;
+        matrix<double> m2 = trans(K)*QQ*(M-t);
+
+
+        // run the solver...
+        unsigned long iter;
+        iter = solve_qp_box_using_smo(
+            m1,
+            m2,
+            v,
+            lower,
+            upper,
+            0.00000001,
+            100000);
+
+        //cout << "iterations: " << iter << endl;
+
+        unpack(controls, v);
+        return iter;
+    }
+
+
+
+    class test_mpc : public tester
+    {
+    public:
+        test_mpc (
+        ) :
+            tester ("test_mpc",
+                    "Runs tests on the mpc object.")
+        {}
+
+        void perform_test (
+        )
+        {
+            // a basic position + velocity model
+            matrix<double,2,2> A;
+            A = 1, 1,
+            0, 1;
+            matrix<double,2,1> B, C;
+            B = 0,
+            1;
+
+            C = 0.02,0.1; // no constant bias
+
+            matrix<double,2,1> Q;
+            Q = 2, 0; // only care about getting the position right
+            matrix<double,1,1> R, lower, upper;
+            R = 1;
+
+            lower = -0.2;
+            upper =  0.2;
+
+            std::vector<matrix<double,1,1> > controls(30);
+            std::vector<matrix<double,2,1> > target(30);
+            for (unsigned long i = 0; i < controls.size(); ++i)
+            {
+                controls[i] = 0;
+                target[i] = 0;
+            }
+
+            mpc<2,1,30> solver(A,B,C,Q,R,lower,upper);
+            solver.set_epsilon(0.00000001);
+            solver.set_max_iterations(10000);
+            matrix<double,2,1> initial_state;
+            initial_state = 0;
+            initial_state(0) = 5;
+            for (int i = 0; i < 30; ++i)
+            {
+                print_spinner();
+                matrix<double,1,1> control = solver(initial_state);
+
+                for (unsigned long i = 1; i < controls.size(); ++i)
+                    controls[i-1] = controls[i];
+
+                // Compute the correct control via SMO and make sure it matches.
+                solve_linear_mpc(A,B,C,Q,R,lower,upper, target, initial_state, controls);
+                dlog << LINFO << "ERROR: " << length(control-controls[0]);
+                DLIB_TEST(length(control-controls[0]) < 1e-7);
+
+                initial_state = A*initial_state + B*control + C;
+                //cout << control(0) << "\t" << trans(initial_state);
+            }
+        }
+    } a;
+
+}
+
+
+
+