diff --git a/cartographer/mapping/id.h b/cartographer/mapping/id.h
index 1f772ef..b7dadaa 100644
--- a/cartographer/mapping/id.h
+++ b/cartographer/mapping/id.h
@@ -18,6 +18,7 @@
 #define CARTOGRAPHER_MAPPING_ID_H_
 
 #include <algorithm>
+#include <iostream>
 #include <iterator>
 #include <limits>
 #include <map>
@@ -28,6 +29,7 @@
 
 #include "cartographer/common/make_unique.h"
 #include "cartographer/common/port.h"
+#include "cartographer/common/time.h"
 #include "glog/logging.h"
 
 namespace cartographer {
@@ -322,6 +324,35 @@ class MapById {
 
   bool empty() const { return begin() == end(); }
 
+  // Returns an iterator to the the first element in the container belonging to
+  // trajectory 'trajectory_id' whose time is not considered to go before
+  // 'time', or EndOfTrajectory(trajectory_id) if all keys are considered to go
+  // before 'time'.
+  ConstIterator lower_bound(const int trajectory_id, const common::Time& time) {
+    if (SizeOfTrajectoryOrZero(trajectory_id) == 0) {
+      return EndOfTrajectory(trajectory_id);
+    }
+
+    const std::map<int, DataType>& trajectory =
+        trajectories_.at(trajectory_id).data_;
+    if (std::prev(trajectory.end())->second.time() < time) {
+      return EndOfTrajectory(trajectory_id);
+    }
+    auto left = trajectory.begin();
+    auto right = std::prev(trajectory.end());
+    while (left != right) {
+      const int middle = left->first + (right->first - left->first) / 2;
+      const auto lower_bound_middle = trajectory.lower_bound(middle);
+      if (lower_bound_middle->second.time() < time) {
+        left = std::next(lower_bound_middle);
+      } else {
+        right = lower_bound_middle;
+      }
+    }
+
+    return ConstIterator(*this, IdType{trajectory_id, left->first});
+  }
+
  private:
   struct MapByIndex {
     bool can_append_ = true;
diff --git a/cartographer/mapping/id_test.cc b/cartographer/mapping/id_test.cc
index 8a6b23a..fce3fc9 100644
--- a/cartographer/mapping/id_test.cc
+++ b/cartographer/mapping/id_test.cc
@@ -16,16 +16,35 @@
 
 #include "cartographer/mapping/id.h"
 
+#include <algorithm>
 #include <deque>
 #include <iterator>
+#include <random>
 #include <utility>
 
+#include "cartographer/common/time.h"
 #include "gtest/gtest.h"
 
 namespace cartographer {
 namespace mapping {
 namespace {
 
+common::Time CreateTime(const int milliseconds) {
+  return common::Time(common::FromMilliseconds(milliseconds));
+}
+
+class Data {
+ public:
+  Data(int milliseconds) : time_(CreateTime(milliseconds)) {}
+
+  const common::Time& time() const {
+    return time_;
+  }
+
+ private:
+  const common::Time time_;
+};
+
 template <typename IdType>
 static MapById<IdType, int> CreateTestMapById() {
   MapById<IdType, int> map_by_id;
@@ -145,6 +164,65 @@ TEST(IdTest, FindSubmapId) {
   EXPECT_TRUE(map_by_id.find(SubmapId{42, 3}) == map_by_id.end());
 }
 
+TEST(IdTest, LowerBoundEdgeCases) {
+  MapById<SubmapId, Data> map_by_id;
+  map_by_id.Append(0, Data(1));
+  map_by_id.Append(2, Data(2));
+  CHECK(map_by_id.lower_bound(1, CreateTime(10)) ==
+        map_by_id.EndOfTrajectory(1));
+  CHECK(map_by_id.lower_bound(2, CreateTime(3)) ==
+        map_by_id.EndOfTrajectory(2));
+  CHECK(map_by_id.lower_bound(2, CreateTime(1)) ==
+        map_by_id.BeginOfTrajectory(2));
+}
+
+TEST(IdTest, LowerBound) {
+  MapById<SubmapId, Data> map_by_id;
+  map_by_id.Append(0, Data(1));
+  map_by_id.Append(0, Data(2));
+  map_by_id.Append(0, Data(4));
+  map_by_id.Append(0, Data(5));
+  CHECK(map_by_id.lower_bound(0, CreateTime(3)) ==
+        (MapById<SubmapId, Data>::ConstIterator(map_by_id, SubmapId{0, 2})));
+  CHECK(map_by_id.lower_bound(0, CreateTime(2)) ==
+        (MapById<SubmapId, Data>::ConstIterator(map_by_id, SubmapId{0, 1})));
+  CHECK(map_by_id.lower_bound(0, CreateTime(4)) ==
+        (MapById<SubmapId, Data>::ConstIterator(map_by_id, SubmapId{0, 2})));
+}
+
+TEST(IdTest, LowerBoundFuzz) {
+  constexpr int kMaxTimeIncrement = 20;
+  constexpr int kMaxNumNodes = 20;
+  constexpr int kNumTests = 100;
+  constexpr int kTrajectoryId = 1;
+
+  std::mt19937 rng;
+  std::uniform_int_distribution<int> dt_dist(1, kMaxTimeIncrement);
+  std::uniform_int_distribution<int> N_dist(1, kMaxNumNodes);
+
+  for (int i = 0; i < kNumTests; ++i) {
+    const int N = N_dist(rng);
+    int t = 0;
+    MapById<SubmapId, Data> map_by_id;
+    for (int j = 0; j < N; ++j) {
+      t = t + dt_dist(rng);
+      map_by_id.Append(kTrajectoryId, Data(t));
+    }
+    std::uniform_int_distribution<int> t0_dist(1, N * kMaxTimeIncrement + 1);
+    int t0 = t0_dist(rng);
+    auto it = map_by_id.lower_bound(kTrajectoryId, CreateTime(t0));
+
+    auto ground_truth = std::lower_bound(
+        map_by_id.BeginOfTrajectory(kTrajectoryId),
+        map_by_id.EndOfTrajectory(kTrajectoryId), CreateTime(t0),
+        [](MapById<SubmapId, Data>::IdDataReference a, const common::Time& t) {
+          return a.data.time() < t;
+        });
+
+    CHECK(ground_truth == it);
+  }
+}
+
 }  // namespace
 }  // namespace mapping
 }  // namespace cartographer