Ejemplo n.º 1
0
    def test_constructors_initialisations(self):
        ps = copra.PreviewSystem()
        ps.system(self.A, self.B, self.c, self.x0, self.nbStep)

        controller = copra.LMPC(ps)

        copra.LMPC()
        copra.LMPC(copra.SolverFlag.QuadProgDense)
        copra.LMPC(ps, copra.SolverFlag.QuadProgDense)

        controller.initialize_controller(ps)
Ejemplo n.º 2
0
    def test_lmpc_ineq(self):
        ps = copra.PreviewSystem()
        ps.system(self.A, self.B, self.c, self.x0, self.nbStep)

        controller = copra.LMPC(ps)
        xCost = copra.TargetCost(self.M, -self.xd)
        uCost = copra.ControlCost(self.N, -self.ud)
        trajConstr = copra.TrajectoryConstraint(self.Eineq, self.fineq)
        contConstr = copra.ControlConstraint(self.Gineq, self.hineq)
        xCost.weights(self.wx)
        uCost.weights(self.wu)

        controller.add_cost(xCost)
        controller.add_cost(uCost)
        controller.add_constraint(trajConstr)
        controller.add_constraint(contConstr)

        self.assertTrue(controller.solve())
        control = controller.control()
        fullTraj = controller.trajectory()
        fTLen = int(len(fullTraj) / 2)
        posTraj = [0.] * fTLen
        velTraj = [0.] * fTLen
        for i in range(fTLen):
            posTraj[i] = fullTraj[2 * i]
            velTraj[i] = fullTraj[2 * i + 1]

        self.assertAlmostEqual(self.xd[1], velTraj[-1], places=3)
        self.assertLessEqual(max(posTraj), self.x0[0])
        self.assertLessEqual(np.amax(control), self.hineq[0])

        print("Test lmpc with inequalities")
        print(controller.solve_time(), "s")
        print(controller.solve_and_build_time(), "s")
        print()
Ejemplo n.º 3
0
    def test_throw_handler(self):
        ps = copra.PreviewSystem()
        ps.system(self.A, self.B, self.c, self.x0, self.nbStep)

        controller = copra.LMPC(ps)
        # Test trajectory constraint throws
        with self.assertRaises(RuntimeError):
            constr = copra.TrajectoryConstraint(np.identity(5), np.ones((2, )))
            controller.add_constraint(constr)

        # Test control constraint throws
        with self.assertRaises(RuntimeError):
            constr = copra.ControlConstraint(np.identity(5), np.ones((2, )))
            controller.add_constraint(constr)

        # Test mixed constraint throws
        with self.assertRaises(RuntimeError):
            constr = copra.MixedConstraint(np.identity(5), np.identity(5),
                                           np.ones((2, )))
            controller.add_constraint(constr)

        # Test trajectory bound constraint throws
        with self.assertRaises(RuntimeError):
            constr = copra.TrajectoryBoundConstraint(np.ones((3, )),
                                                     np.ones((2, )))
            controller.add_constraint(constr)

        # Test control bound constraint throws
        with self.assertRaises(RuntimeError):
            constr = copra.ControlBoundConstraint(np.ones((3, )), np.ones(
                (2, )))
            controller.add_constraint(constr)
Ejemplo n.º 4
0
    def test_preview_systeme_still_exist(self):
        ps = copra.PreviewSystem()
        ps.system(self.A, self.B, self.c, self.x0, self.nbStep)

        controller = copra.LMPC(ps)
        del ps
        trajConstr = copra.TrajectoryConstraint(self.Eineq, self.fineq)
        contConstr = copra.ControlConstraint(self.Gineq, self.hineq)
        targetCost = copra.TargetCost(self.M, -self.xd)
        controlCost = copra.ControlCost(self.N, -self.ud)
        targetCost.weights(self.wx)
        controlCost.weights(self.wu)

        controller.add_constraint(trajConstr)
        controller.add_constraint(contConstr)
        controller.add_cost(targetCost)
        controller.add_cost(controlCost)

        self.assertTrue(controller.solve())
        control = controller.control()
        fullTraj = controller.trajectory()
        fTLen = int(len(fullTraj) / 2)
        posTraj = [0.] * fTLen
        velTraj = [0.] * fTLen
        for i in range(fTLen):
            posTraj[i] = fullTraj[2 * i]
            velTraj[i] = fullTraj[2 * i + 1]

        self.assertAlmostEqual(self.xd[1], velTraj[-1], places=3)
        self.assertLessEqual(max(posTraj), self.x0[0])
        self.assertLessEqual(np.amax(control), self.hineq[0])
Ejemplo n.º 5
0
    def test_lmpc_eq(self):
        print "test_lmpc_eq"
        ps = pyCopra.PreviewSystem()
        ps.system(self.A, self.B, self.c, self.x0Eq, self.nbStep)

        controller = pyCopra.LMPC(ps)
        xCost = pyCopra.TargetCost(self.M, -self.xdEq)
        uCost = pyCopra.ControlCost(self.N, -self.ud)
        trajConstr = pyCopra.TrajectoryConstraint(self.Eeq, self.feq, False)
        xCost.weights(self.wx)
        uCost.weights(self.wu)

        controller.add_cost(xCost)
        controller.add_cost(uCost)
        controller.add_constraint(trajConstr)

        self.assertTrue(controller.solve())
        control = controller.control()
        fullTraj = controller.trajectory()
        fTLen = len(fullTraj) / 2
        posTraj = [0.] * fTLen
        velTraj = [0.] * fTLen
        for i in xrange(fTLen):
            posTraj[i] = fullTraj[2 * i]
            velTraj[i] = fullTraj[2 * i + 1]

        self.assertAlmostEqual(self.xd[1], velTraj[-1], places=3)
        self.assertLessEqual(max(posTraj), self.x0[0] + 1e-6)
        self.assertLessEqual(max(velTraj), self.feq[0] + 1e-6)

        print "Test lmpc with equalities"
        print controller.solve_time(), "s"
        print controller.solve_and_build_time(), "s"
        print
Ejemplo n.º 6
0
    def test_constraint_and_cost_deletion(self):
        print("Testing 'test_constraint_deletion'.")
        print(
            "In order to see the outputs, the copra must be installed under Debug mode."
        )

        ps = copra.PreviewSystem()
        ps.system(self.A, self.B, self.c, self.x0, self.nbStep)

        controller = copra.LMPC(ps)
        trajConstr = copra.TrajectoryConstraint(self.Eineq, self.fineq)
        contConstr = copra.ControlConstraint(self.Gineq, self.hineq)
        trajEqConstr = copra.TrajectoryConstraint(self.Eeq, self.feq, False)
        contEqConstr = copra.ControlConstraint(self.Geq, self.heq, False)
        trajBdConstr = copra.TrajectoryBoundConstraint(self.xLower,
                                                       self.xUpper)
        contBdConstr = copra.ControlBoundConstraint(self.uLower, self.uUpper)
        targetCost = copra.TargetCost(self.M, -self.xd)
        trajectoryCost = copra.TrajectoryCost(self.M, -self.xd)
        controlCost = copra.ControlCost(self.N, -self.ud)
        M_mixed = np.ones((1, 2))
        mixedCost = copra.MixedCost(M_mixed, self.N, -self.ud)

        controller.add_constraint(trajConstr)
        controller.add_constraint(contConstr)
        controller.add_constraint(trajEqConstr)
        controller.add_constraint(contEqConstr)
        controller.add_constraint(trajBdConstr)
        controller.add_constraint(contBdConstr)
        controller.add_cost(targetCost)
        controller.add_cost(trajectoryCost)
        controller.add_cost(controlCost)
        controller.add_cost(mixedCost)

        del trajConstr

        targetCost.weights(self.wx)
        controlCost.weights(self.wu)

        del trajEqConstr
        del contEqConstr
        del trajBdConstr
        del contBdConstr
        del trajectoryCost
        del mixedCost

        self.assertFalse(controller.solve())
        self.assertTrue(controller.solve())  # Has kept the contConstr only
Ejemplo n.º 7
0
    def test_constructors_initialisations(self):
        print "test_constructors_initialisations"
        ps = pyCopra.PreviewSystem()
        ps.system(self.A, self.B, self.c, self.x0, self.nbStep)

        controller = pyCopra.LMPC(ps)

        pyCopra.LMPC()
        if hasattr(pyCopra.SolverFlag, 'QuadProgDense'):
            pyCopra.LMPC(pyCopra.SolverFlag.QuadProgDense)
            pyCopra.LMPC(ps, pyCopra.SolverFlag.QuadProgDense)
        elif hasattr(pyCopra.SolverFlag, 'QLD'):
            pyCopra.LMPC(pyCopra.SolverFlag.QLD)
            pyCopra.LMPC(ps, pyCopra.SolverFlag.QLD)
        else:
            pyCopra.LMPC(pyCopra.SolverFlag.Default)
            pyCopra.LMPC(ps, pyCopra.SolverFlag.Default)

        controller.initialize_controller(ps)
Ejemplo n.º 8
0
    def test_lmpc_mixed(self):
        print "test_lmpc_mixed"
        ps = pyCopra.PreviewSystem()
        ps.system(self.A, self.B, self.c, self.x0, self.nbStep)

        controller = pyCopra.LMPC(ps)
        xCost = pyCopra.TargetCost(self.M, -self.xd)
        uCost = pyCopra.ControlCost(self.N, -self.ud)
        mixedConstr = pyCopra.MixedConstraint(self.Eineq, self.Gineq,
                                              self.hineq)
        xCost.weights(self.wx)
        uCost.weights(self.wu)

        controller.add_cost(xCost)
        controller.add_cost(uCost)
        controller.add_constraint(mixedConstr)

        self.assertTrue(controller.solve())
        control = controller.control()
        fullTraj = controller.trajectory()
        fTLen = len(fullTraj) / 2
        posTraj = [0.] * fTLen
        velTraj = [0.] * fTLen
        for i in xrange(fTLen):
            posTraj[i] = fullTraj[2 * i]
            velTraj[i] = fullTraj[2 * i + 1]

        self.assertAlmostEqual(self.xd[1], velTraj[-1], places=3)
        self.assertLessEqual(max(posTraj), self.x0[0])
        for i in xrange(self.Eineq.shape[0]):
            res = 0
            for j in xrange(self.Eineq.shape[1]):
                res += self.Eineq[i, j] * fullTraj[i * self.Eineq.shape[1] + j]
            for j in xrange(self.Gineq.shape[1]):
                res += self.Gineq[i, j] * control[i * self.Gineq.shape[1] + j]
            self.assertLessEqual(res, self.hineq[0])

        print "Test lmpc with inequalities"
        print controller.solve_time(), "s"
        print controller.solve_and_build_time(), "s"
        print
Ejemplo n.º 9
0
    def test_dynamic_walk(self):
        A = np.array([[1, 0, 0, 0.11699999999999999, 0, 0],
                      [0, 1, 0, 0, 0.11699999999999999, 0],
                      [0, 0, 1, 0, 0, 0.11699999999999999], [0, 0, 0, 1, 0, 0],
                      [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]])
        B = np.array([[0.006844499999999999, 0,
                       0], [0, 0.006844499999999999, 0],
                      [0, 0, 0.006844499999999999],
                      [0.11699999999999999, 0, 0], [0, 0.11699999999999999, 0],
                      [0, 0, 0.11699999999999999]])

        c = np.array([0., 0., 0., 0., 0., 0.])
        x_init = np.array([
            1.5842778860957882, 0.3422260214935311, 2.289067474385933, 0., 0.,
            0.
        ])
        x_goal = np.array([
            1.627772868473883, 0.4156386515475985, 2.3984423755527136,
            0.06745225960685897, 0.3882830795737303, 0.06845759848745198
        ])
        nb_steps = 10
        G = np.array([
            [
                -1, 9.946646523934742, -4.870790074510924, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                -18.826459196882055, 3.4468275392859393, -1, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                -1.374181960437557, -8.028252906078723, -1, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                -9.936224732113594, 5.000580301294253, -1, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                8.750597187695343, -4.7538557382857105, -1, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                18.65430148414319, 1, -5.084871935334947, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                2.1775137248880574e-15, -5.443784312220143e-16, 1, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0
            ],
            [
                0, 0, 0, -1, 9.946646523934742, -4.870790074510924, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, -18.826459196882055, 3.4468275392859393, -1, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, -1.374181960437557, -8.028252906078723, -1, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, -9.936224732113594, 5.000580301294253, -1, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 8.750597187695343, -4.7538557382857105, -1, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 18.65430148414319, 1, -5.084871935334947, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 2.1775137248880574e-15, -5.443784312220143e-16, 1, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, -1, 9.946646523934742, -4.870790074510924, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, -18.826459196882055, 3.4468275392859393, -1,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, -1.374181960437557, -8.028252906078723, -1,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, -9.936224732113594, 5.000580301294253, -1, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 8.750597187695343, -4.7538557382857105, -1,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 18.65430148414319, 1, -5.084871935334947, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 2.1775137248880574e-15,
                -5.443784312220143e-16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 9.946646523934742,
                -4.870790074510924, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, -18.826459196882055,
                3.4468275392859393, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, -1.374181960437557,
                -8.028252906078723, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, -9.936224732113594,
                5.000580301294253, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 8.750597187695343,
                -4.7538557382857105, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 18.65430148414319, 1,
                -5.084871935334947, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 2.1775137248880574e-15,
                -5.443784312220143e-16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 9.946646523934742,
                -4.870790074510924, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18.826459196882055,
                3.4468275392859393, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.374181960437557,
                -8.028252906078723, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9.936224732113594,
                5.000580301294253, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8.750597187695343,
                -4.7538557382857105, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18.65430148414319, 1,
                -5.084871935334947, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2.1775137248880574e-15,
                -5.443784312220143e-16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1,
                9.946646523934742, -4.870790074510924, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                -18.826459196882055, 3.4468275392859393, -1, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                -1.374181960437557, -8.028252906078723, -1, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                -9.936224732113594, 5.000580301294253, -1, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8.750597187695343,
                -4.7538557382857105, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18.65430148414319,
                1, -5.084871935334947, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                2.1775137248880574e-15, -5.443784312220143e-16, 1, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                8.750597218241072, -4.753855754313641, -1, 0, 0, 0, 0, 0, 0, 0,
                0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                -1.3741819771739483, -8.028252929943818, -1, 0, 0, 0, 0, 0, 0,
                0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                -18.82645925631406, 3.4468275193254927, -1, 0, 0, 0, 0, 0, 0,
                0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                1.1824397341134247, 7.4638136184143935, -1, 0, 0, 0, 0, 0, 0,
                0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                14.006645137157978, -2.2569159229140494, -1, 0, 0, 0, 0, 0, 0,
                0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                2.1775137248880578e-15, -5.443784312220144e-16, 1, 0, 0, 0, 0,
                0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                8.750597218241072, -4.753855754313641, -1, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                -1.3741819771739483, -8.028252929943818, -1, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                -18.82645925631406, 3.4468275193254927, -1, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                1.1824397341134247, 7.4638136184143935, -1, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                14.006645137157978, -2.2569159229140494, -1, 0, 0, 0, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                2.1775137248880578e-15, -5.443784312220144e-16, 1, 0, 0, 0, 0,
                0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 8.750597218241072, -4.753855754313641, -1, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, -1.3741819771739483, -8.028252929943818, -1, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, -18.82645925631406, 3.4468275193254927, -1, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 1.1824397341134247, 7.4638136184143935, -1, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 14.006645137157978, -2.2569159229140494, -1, 0, 0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 2.1775137248880578e-15, -5.443784312220144e-16, 1, 0,
                0, 0
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 8.750597218241072, -4.753855754313641, -1
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, -1.3741819771739483, -8.028252929943818, -1
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, -18.82645925631406, 3.4468275193254927, -1
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 1.1824397341134247, 7.4638136184143935, -1
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 14.006645137157978, -2.2569159229140494, -1
            ],
            [
                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                0, 0, 0, 0, 0, 0, 2.1775137248880578e-15,
                -5.443784312220144e-16, 1
            ]
        ])

        h = np.array([
            47.76613348420254, 9.80665, 9.80665, 9.80665, 9.806649999999998,
            49.86555936465245, 9.806649999999994, 47.76613348420254, 9.80665,
            9.80665, 9.80665, 9.806649999999998, 49.86555936465245,
            9.806649999999994, 47.76613348420254, 9.80665, 9.80665, 9.80665,
            9.806649999999998, 49.86555936465245, 9.806649999999994,
            47.76613348420254, 9.80665, 9.80665, 9.80665, 9.806649999999998,
            49.86555936465245, 9.806649999999994, 47.76613348420254, 9.80665,
            9.80665, 9.80665, 9.806649999999998, 49.86555936465245,
            9.806649999999994, 47.76613348420254, 9.80665, 9.80665, 9.80665,
            9.806649999999998, 49.86555936465245, 9.806649999999994,
            9.806650000000007, 9.806650000000008, 9.80665, 9.806650000000001,
            9.806650000000007, 9.806649999999996, 9.806650000000007,
            9.806650000000008, 9.80665, 9.806650000000001, 9.806650000000007,
            9.806649999999996, 9.806650000000007, 9.806650000000008, 9.80665,
            9.806650000000001, 9.806650000000007, 9.806649999999996,
            9.806650000000007, 9.806650000000008, 9.80665, 9.806650000000001,
            9.806650000000007, 9.806649999999996
        ])

        ps = copra.PreviewSystem()
        ps.system(A, B, c, x_init, nb_steps)

        controller = copra.LMPC(ps)
        contConstr = copra.ControlConstraint(G, h)
        M_cost = np.identity(6)
        targetCost = copra.TargetCost(M_cost, -x_goal)

        controller.add_constraint(contConstr)
        controller.add_cost(targetCost)

        controller.solve()
        print(controller.solve_time(), "s")