diff --git a/include/pyhpp/core/problem.hh b/include/pyhpp/core/problem.hh
index c582e23..b8d64ab 100644
--- a/include/pyhpp/core/problem.hh
+++ b/include/pyhpp/core/problem.hh
@@ -147,10 +147,9 @@ struct Problem {
 
   boost::python::tuple directPath(ConfigurationIn_t start,
                                   ConfigurationIn_t end, bool validate);
-  hpp::core::ConstraintSetPtr_t constraints_;
   PyWPathValidationPtr_t pathValidation_;
-  value_type errorThreshold_;
-  size_type maxIterProjection_;
+  value_type errorThreshold_{1e-4};
+  size_type maxIterProjection_{20};
 };
 
 }  // namespace core
diff --git a/src/pyhpp/core/problem.cc b/src/pyhpp/core/problem.cc
index 494175b..92b4b3c 100644
--- a/src/pyhpp/core/problem.cc
+++ b/src/pyhpp/core/problem.cc
@@ -117,11 +117,9 @@ namespace core {
 using namespace boost::python;
 
 Problem::Problem(const DevicePtr_t& robot)
-    : obj(hpp::core::Problem::create(robot)),
-      errorThreshold_(1e-4),
-      maxIterProjection_(20) {
-  constraints_ =
-      hpp::core::ConstraintSet::create(robot, "Default constraint set");
+    : obj(hpp::core::Problem::create(robot)) {
+  obj->constraints(
+      hpp::core::ConstraintSet::create(robot, "Default constraint set"));
 }
 
 const DevicePtr_t& Problem::robot() const { return obj->robot(); }
@@ -393,9 +391,9 @@ boost::python::tuple Problem::applyConstraints(ConfigurationIn_t config) {
   double residualError = 0.0;
   try {
     Configuration_t output = config;
-    success = constraints_->apply(output);
+    success = obj->constraints()->apply(output);
     if (hpp::core::ConfigProjectorPtr_t configProjector =
-            constraints_->configProjector()) {
+            obj->constraints()->configProjector()) {
       residualError = configProjector->residualError();
     }
     return boost::python::make_tuple(success, output, residualError);
@@ -427,10 +425,7 @@ boost::python::tuple Problem::isConfigValid(ConfigurationIn_t dofArray) {
 
 void Problem::setConstraints(hpp::core::ConstraintSetPtr_t constraints) {
   try {
-    constraints_ =
-        hpp::core::ConstraintSet::create(robot(), "Default constraint set");
-    constraints_->addConstraint(constraints);
-    obj->constraints(constraints_);
+    obj->constraints(constraints);
   } catch (const std::exception& exc) {
     throw std::logic_error(exc.what());
   }
@@ -447,7 +442,7 @@ hpp::core::ConstraintSetPtr_t Problem::getConstraints() {
 void Problem::setRightHandSideFromConfig(ConfigurationIn_t configIn) {
   try {
     hpp::core::ConfigProjectorPtr_t configProjector(
-        constraints_->configProjector());
+        obj->constraints()->configProjector());
     if (!configProjector) {
       throw std::runtime_error("No constraint has been set.");
     }
@@ -466,12 +461,12 @@ void Problem::addNumericalConstraintsToConfigProjector1(
         extract_vector<hpp::constraints::ImplicitPtr_t>(constraints);
     auto prioritiesVec = extract_vector<std::size_t>(priorities);
     hpp::core::ConfigProjectorPtr_t configProjector =
-        constraints_->configProjector();
+        obj->constraints()->configProjector();
     for (unsigned int i = 0; i < constraintsVec.size(); ++i) {
       if (!configProjector) {
         configProjector = hpp::core::ConfigProjector::create(
             robot(), configProjName, errorThreshold_, maxIterProjection_);
-        constraints_->addConstraint(configProjector);
+        obj->constraints()->addConstraint(configProjector);
       }
       configProjector->add(constraintsVec[i], prioritiesVec[i]);
     }
@@ -486,12 +481,12 @@ void Problem::addNumericalConstraintsToConfigProjector2(
     auto constraintsVec =
         extract_vector<hpp::constraints::ImplicitPtr_t>(constraints);
     hpp::core::ConfigProjectorPtr_t configProjector =
-        constraints_->configProjector();
+        obj->constraints()->configProjector();
     for (unsigned int i = 0; i < constraintsVec.size(); ++i) {
       if (!configProjector) {
         configProjector = hpp::core::ConfigProjector::create(
             robot(), configProjName, errorThreshold_, maxIterProjection_);
-        constraints_->addConstraint(configProjector);
+        obj->constraints()->addConstraint(configProjector);
       }
       configProjector->add(constraintsVec[i], 0);
     }
diff --git a/tests/unit/test_problem.py b/tests/unit/test_problem.py
index 8c71377..00e0897 100644
--- a/tests/unit/test_problem.py
+++ b/tests/unit/test_problem.py
@@ -7,7 +7,8 @@
 import unittest
 import numpy as np
 from pinocchio import SE3
-from unit.conftest import create_ur5_problem
+from pyhpp.manipulation import Problem as ManipulationProblem
+from unit.conftest import create_ur3_robot, create_ur5_problem
 
 
 class TestProblemAccessors(unittest.TestCase):
@@ -109,6 +110,34 @@ def test_apply_constraints_returns_tuple(self):
         self.assertIsInstance(success, bool)
         self.assertEqual(len(output), len(q))
 
+    def test_add_numerical_constraints_updates_active_constraint_set(self):
+        problem, robot = create_ur5_problem()
+        active_constraints = problem.getConstraints()
+        constraint = problem.createTransformationConstraint(
+            "test_constraint",
+            "",
+            "ur5/ee_fixed_joint",
+            SE3.Identity(),
+            [True, True, True, True, True, True],
+        )
+
+        problem.addNumericalConstraintsToConfigProjector("test-projector", [constraint])
+
+        projector = active_constraints.configProjector()
+        self.assertIsNotNone(projector)
+        self.assertEqual(len(projector.numericalConstraints()), 1)
+        self.assertIsNotNone(problem.getConstraints().configProjector())
+
+
+class TestManipulationProblemProjectionDefaults(unittest.TestCase):
+    def test_projection_defaults_match_core_problem(self):
+        robot = create_ur3_robot()
+
+        problem = ManipulationProblem(robot)
+
+        self.assertAlmostEqual(problem.errorThreshold, 1e-4)
+        self.assertEqual(problem.maxIterProjection, 20)
+
 
 class TestProblemTransformationConstraints(unittest.TestCase):
     def test_create_transformation_constraint(self):