diff --git a/cartographer/mapping/sparse_pose_graph.cc b/cartographer/mapping/sparse_pose_graph.cc
index 8fa6f75..6bb0474 100644
--- a/cartographer/mapping/sparse_pose_graph.cc
+++ b/cartographer/mapping/sparse_pose_graph.cc
@@ -93,9 +93,9 @@ proto::SparsePoseGraph SparsePoseGraph::ToProto() {
         constraint.pose.sqrt_Lambda_ij;
 
     constraint_proto->mutable_submap_id()->set_trajectory_id(
-        constraint.i.trajectory_id);
+        constraint.submap_id.trajectory_id);
     constraint_proto->mutable_submap_id()->set_submap_index(
-        constraint.i.submap_index);
+        constraint.submap_id.submap_index);
 
     constraint_proto->mutable_scan_id()->set_trajectory_id(
         grouped_node_indices[constraint.j].first);
diff --git a/cartographer/mapping/sparse_pose_graph.h b/cartographer/mapping/sparse_pose_graph.h
index 5758d46..abe2441 100644
--- a/cartographer/mapping/sparse_pose_graph.h
+++ b/cartographer/mapping/sparse_pose_graph.h
@@ -58,9 +58,7 @@ class SparsePoseGraph {
       Eigen::Matrix<double, 6, 6> sqrt_Lambda_ij;
     };
 
-    // TODO(hrapp): Rename to 'submap_id' and mention that the paper calls this
-    // 'i'.
-    mapping::SubmapId i;
+    mapping::SubmapId submap_id; // 'i' in the paper.
 
     // Scan index.
     int j;
diff --git a/cartographer/mapping_2d/sparse_pose_graph/optimization_problem.cc b/cartographer/mapping_2d/sparse_pose_graph/optimization_problem.cc
index b4578b7..6df19c4 100644
--- a/cartographer/mapping_2d/sparse_pose_graph/optimization_problem.cc
+++ b/cartographer/mapping_2d/sparse_pose_graph/optimization_problem.cc
@@ -139,8 +139,8 @@ void OptimizationProblem::Solve(const std::vector<Constraint>& constraints) {
         constraint.tag == Constraint::INTER_SUBMAP
             ? new ceres::HuberLoss(options_.huber_scale())
             : nullptr,
-        C_submaps.at(constraint.i.trajectory_id)
-            .at(constraint.i.submap_index)
+        C_submaps.at(constraint.submap_id.trajectory_id)
+            .at(constraint.submap_id.submap_index)
             .data(),
         C_point_clouds[constraint.j].data());
   }
diff --git a/cartographer/mapping_3d/sparse_pose_graph/optimization_problem.cc b/cartographer/mapping_3d/sparse_pose_graph/optimization_problem.cc
index 6e6263a..63b685d 100644
--- a/cartographer/mapping_3d/sparse_pose_graph/optimization_problem.cc
+++ b/cartographer/mapping_3d/sparse_pose_graph/optimization_problem.cc
@@ -175,11 +175,11 @@ void OptimizationProblem::Solve(const std::vector<Constraint>& constraints) {
         constraint.tag == Constraint::INTER_SUBMAP
             ? new ceres::HuberLoss(options_.huber_scale())
             : nullptr,
-        C_submaps.at(constraint.i.trajectory_id)
-            .at(constraint.i.submap_index)
+        C_submaps.at(constraint.submap_id.trajectory_id)
+            .at(constraint.submap_id.submap_index)
             .rotation(),
-        C_submaps.at(constraint.i.trajectory_id)
-            .at(constraint.i.submap_index)
+        C_submaps.at(constraint.submap_id.trajectory_id)
+            .at(constraint.submap_id.submap_index)
             .translation(),
         C_point_clouds[constraint.j].rotation(),
         C_point_clouds[constraint.j].translation());