diff --git a/cartographer/transform/rigid_transform_test.cc b/cartographer/transform/rigid_transform_test.cc
new file mode 100644
index 0000000..c33e569
--- /dev/null
+++ b/cartographer/transform/rigid_transform_test.cc
@@ -0,0 +1,100 @@
+/*
+ * Copyright 2017 The Cartographer Authors
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+#include "cartographer/transform/rigid_transform.h"
+
+#include <random>
+
+#include "cartographer/transform/rigid_transform_test_helpers.h"
+#include "cartographer/transform/transform.h"
+#include "gtest/gtest.h"
+
+namespace cartographer {
+namespace transform {
+namespace {
+
+template <typename T>
+class RigidTransformTest : public ::testing::Test {
+ protected:
+  T eps() {
+    return std::numeric_limits<T>::epsilon();
+  }
+
+  Rigid2<T> GetRandomRigid2() {
+    const T x = T(0.7) * distribution_(prng_);
+    const T y = T(0.7) * distribution_(prng_);
+    const T theta = T(0.2) * distribution_(prng_);
+    return transform::Rigid2<T>(typename Rigid2<T>::Vector(x, y), theta);
+  }
+
+  Rigid3<T> GetRandomRigid3() {
+    const T x = T(0.7) * distribution_(prng_);
+    const T y = T(0.7) * distribution_(prng_);
+    const T z = T(0.7) * distribution_(prng_);
+    const T ax = T(0.7) * distribution_(prng_);
+    const T ay = T(0.7) * distribution_(prng_);
+    const T az = T(0.7) * distribution_(prng_);
+    return transform::Rigid3<T>(typename Rigid3<T>::Vector(x, y, z),
+                                AngleAxisVectorToRotationQuaternion(
+                                    typename Rigid3<T>::Vector(ax, ay, az)));
+  }
+
+  std::mt19937 prng_ = std::mt19937(42);
+  std::uniform_real_distribution<T> distribution_ =
+      std::uniform_real_distribution<T>(-1., 1.);
+};
+
+using ScalarTypes = ::testing::Types<float, double>;
+TYPED_TEST_CASE(RigidTransformTest, ScalarTypes);
+
+TYPED_TEST(RigidTransformTest, Identity2DTest) {
+  const auto pose = this->GetRandomRigid2();
+  EXPECT_THAT(pose * Rigid2<TypeParam>(), IsNearly(pose, this->eps()));
+  EXPECT_THAT(Rigid2<TypeParam>() * pose, IsNearly(pose, this->eps()));
+  EXPECT_THAT(pose * Rigid2<TypeParam>::Identity(),
+              IsNearly(pose, this->eps()));
+  EXPECT_THAT(Rigid2<TypeParam>::Identity() * pose,
+              IsNearly(pose, this->eps()));
+}
+
+TYPED_TEST(RigidTransformTest, Inverse2DTest) {
+  const auto pose = this->GetRandomRigid2();
+  EXPECT_THAT(pose.inverse() * pose,
+              IsNearly(Rigid2<TypeParam>::Identity(), this->eps()));
+  EXPECT_THAT(pose * pose.inverse(),
+              IsNearly(Rigid2<TypeParam>::Identity(), this->eps()));
+}
+
+TYPED_TEST(RigidTransformTest, Identity3DTest) {
+  const auto pose = this->GetRandomRigid3();
+  EXPECT_THAT(pose * Rigid3<TypeParam>(), IsNearly(pose, this->eps()));
+  EXPECT_THAT(Rigid3<TypeParam>() * pose, IsNearly(pose, this->eps()));
+  EXPECT_THAT(pose * Rigid3<TypeParam>::Identity(),
+              IsNearly(pose, this->eps()));
+  EXPECT_THAT(Rigid3<TypeParam>::Identity() * pose,
+              IsNearly(pose, this->eps()));
+}
+
+TYPED_TEST(RigidTransformTest, Inverse3DTest) {
+  const auto pose = this->GetRandomRigid3();
+  EXPECT_THAT(pose.inverse() * pose,
+              IsNearly(Rigid3<TypeParam>::Identity(), this->eps()));
+  EXPECT_THAT(pose * pose.inverse(),
+              IsNearly(Rigid3<TypeParam>::Identity(), this->eps()));
+}
+
+}  // namespace
+}  // namespace transform
+}  // namespace cartographer