diff --git a/src/Evolution/Systems/CurvedScalarWave/Worldtube/CMakeLists.txt b/src/Evolution/Systems/CurvedScalarWave/Worldtube/CMakeLists.txt
index 99bebd7da777..fd839cd32032 100644
--- a/src/Evolution/Systems/CurvedScalarWave/Worldtube/CMakeLists.txt
+++ b/src/Evolution/Systems/CurvedScalarWave/Worldtube/CMakeLists.txt
@@ -36,6 +36,7 @@ spectre_target_headers(
 target_link_libraries(
   ${LIBRARY}
   PUBLIC
+  ControlSystem
   DataStructures
   Domain
   GeneralRelativity
diff --git a/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/CMakeLists.txt b/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/CMakeLists.txt
index d9a1fa4cefb7..533ae0ca4597 100644
--- a/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/CMakeLists.txt
+++ b/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/CMakeLists.txt
@@ -20,4 +20,5 @@ spectre_target_headers(
   ReceiveElementData.hpp
   SendToElements.hpp
   UpdateAcceleration.hpp
+  UpdateFunctionsOfTime.hpp
 )
diff --git a/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/UpdateFunctionsOfTime.hpp b/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/UpdateFunctionsOfTime.hpp
new file mode 100644
index 000000000000..42d35c60760b
--- /dev/null
+++ b/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/UpdateFunctionsOfTime.hpp
@@ -0,0 +1,155 @@
+// Distributed under the MIT License.
+// See LICENSE.txt for details.
+
+#pragma once
+
+#include <cstddef>
+#include <memory>
+#include <unordered_map>
+#include <utility>
+
+#include "ControlSystem/UpdateFunctionOfTime.hpp"
+#include "DataStructures/DataBox/DataBox.hpp"
+#include "DataStructures/DataBox/Prefixes.hpp"
+#include "Domain/Creators/Tags/Domain.hpp"
+#include "Evolution/Systems/CurvedScalarWave/Worldtube/Inboxes.hpp"
+#include "Evolution/Systems/CurvedScalarWave/Worldtube/RadiusFunctions.hpp"
+#include "Evolution/Systems/CurvedScalarWave/Worldtube/Tags.hpp"
+#include "Evolution/Systems/CurvedScalarWave/Worldtube/Worldtube.hpp"
+#include "Parallel/AlgorithmExecution.hpp"
+#include "Parallel/GlobalCache.hpp"
+#include "ParallelAlgorithms/EventsAndTriggers/Tags.hpp"
+#include "ParallelAlgorithms/Initialization/MutateAssign.hpp"
+#include "Time/Tags/TimeStepId.hpp"
+#include "Time/TimeStepId.hpp"
+#include "Time/TimeSteppers/TimeStepper.hpp"
+#include "Utilities/Gsl.hpp"
+#include "Utilities/TMPL.hpp"
+
+namespace CurvedScalarWave::Worldtube::Actions {
+
+/*!
+ * \brief Updates the functions of time according to the motion of the
+ * worldtube.
+ *
+ * \details We demand that the scalar charge is always in the center of the
+ * worldtube and therefore deform the grid to the track the particle's motion.
+ * In addition, the worldtube and black hole excision sphere radii are adjusted
+ * according to smooth_broken_power_law.
+ */
+struct UpdateFunctionsOfTime {
+  template <typename DbTagsList, typename... InboxTags, typename Metavariables,
+            typename ArrayIndex, typename ActionList,
+            typename ParallelComponent>
+  static Parallel::iterable_action_return_t apply(
+      db::DataBox<DbTagsList>& box,
+      tuples::TaggedTuple<InboxTags...>& /*inboxes*/,
+      Parallel::GlobalCache<Metavariables>& cache,
+      const ArrayIndex& /*array_index*/, ActionList /*meta*/,
+      const ParallelComponent* const /*meta*/) {
+    const double current_expiration_time = db::get<Tags::ExpirationTime>(box);
+    const double time = db::get<::Tags::Time>(box);
+    const auto& particle_pos_vel =
+        db::get<Tags::ParticlePositionVelocity<3>>(box);
+    const double& x = get<0>(particle_pos_vel[0]);
+    const double& y = get<1>(particle_pos_vel[0]);
+    const double& xdot = get<0>(particle_pos_vel[1]);
+    const double& ydot = get<1>(particle_pos_vel[1]);
+    const double r = hypot(x, y);
+    const double radial_vel = (xdot * x + ydot * y) / r;
+    const auto& excision_sphere = db::get<Tags::ExcisionSphere<3>>(box);
+    const double grid_radius_particle =
+        get(magnitude(excision_sphere.center()));
+
+    DataVector angular_update(2);
+    DataVector expansion_update(2);
+    DataVector size_a_update(2);
+    DataVector size_b_update(2);
+
+    angular_update[0] = atan2(y, x);
+    angular_update[1] = (x * ydot - y * xdot) / square(r);
+    expansion_update[0] = r / grid_radius_particle;
+    expansion_update[1] = radial_vel / grid_radius_particle;
+
+    const auto& wt_radius_params =
+        db::get<Tags::WorldtubeRadiusParameters>(box);
+    const auto& bh_radius_params =
+        db::get<Tags::BlackHoleRadiusParameters>(box);
+    const double wt_radius_grid = excision_sphere.radius();
+    const double wt_radius_inertial =
+        smooth_broken_power_law(r, wt_radius_params[0], wt_radius_params[1],
+                                wt_radius_params[2], wt_radius_params[3]);
+    const double wt_radius_derivative = smooth_broken_power_law_derivative(
+        r, wt_radius_params[0], wt_radius_params[1], wt_radius_params[2],
+        wt_radius_params[3]);
+    const double wt_radius_time_derivative = wt_radius_derivative * radial_vel;
+
+    const auto& bh_excision_sphere =
+        db::get<domain::Tags::Domain<3>>(box).excision_spheres().at(
+            "ExcisionSphereB");
+    const double bh_excision_radius_grid = bh_excision_sphere.radius();
+    const double bh_excision_radius_inertial =
+        smooth_broken_power_law(r, bh_radius_params[0], bh_radius_params[1],
+                                bh_radius_params[2], bh_radius_params[3]);
+    const double bh_excision_radius_derivative =
+        smooth_broken_power_law_derivative(
+            r, bh_radius_params[0], bh_radius_params[1], bh_radius_params[2],
+            bh_radius_params[3]);
+    const double bh_excision_radius_time_derivative =
+        bh_excision_radius_derivative * radial_vel;
+
+    const double sqrt_4_pi = sqrt(4. * M_PI);
+    // The expansion map has already stretched the excision spheres and we need
+    // to account for that.
+    size_a_update[0] =
+        sqrt_4_pi * (wt_radius_grid - wt_radius_inertial / expansion_update[0]);
+    size_a_update[1] = sqrt_4_pi *
+                       (wt_radius_inertial * expansion_update[1] -
+                        wt_radius_time_derivative * expansion_update[0]) /
+                       square(expansion_update[0]);
+
+    size_b_update[0] =
+        sqrt_4_pi * (bh_excision_radius_grid -
+                     bh_excision_radius_inertial / expansion_update[0]);
+    size_b_update[1] =
+        sqrt_4_pi *
+        (bh_excision_radius_inertial * expansion_update[1] -
+         bh_excision_radius_time_derivative * expansion_update[0]) /
+        square(expansion_update[0]);
+
+    // we set the new expiration time to 1/100th of a time step next to the
+    // current time. This is small enough that it can handle rapid time step
+    // decreases but large enough to avoid floating point precision issues.
+    const double new_expiration_time =
+        time +
+        0.01 * (db::get<::Tags::Next<::Tags::TimeStepId>>(box).substep_time() -
+                time);
+
+    db::mutate<Tags::ExpirationTime>(
+        [&new_expiration_time](const auto expiration_time) {
+          *expiration_time = new_expiration_time;
+        },
+        make_not_null(&box));
+    db::mutate<Tags::WorldtubeRadius>(
+        [&wt_radius_inertial](const auto wt_radius) {
+          *wt_radius = wt_radius_inertial;
+        },
+        make_not_null(&box));
+    std::unordered_map<std::string, std::pair<DataVector, double>>
+        all_updates{};
+    all_updates["Rotation"] =
+        std::make_pair(std::move(angular_update), new_expiration_time);
+    all_updates["Expansion"] =
+        std::make_pair(std::move(expansion_update), new_expiration_time);
+    all_updates["SizeA"] = std::make_pair(size_a_update, new_expiration_time);
+    all_updates["SizeB"] =
+        std::make_pair(std::move(size_b_update), new_expiration_time);
+
+    Parallel::mutate<::domain::Tags::FunctionsOfTime,
+                     control_system::UpdateMultipleFunctionsOfTime>(
+        cache, current_expiration_time, all_updates);
+
+    return {Parallel::AlgorithmExecution::Continue, std::nullopt};
+  }
+};
+}  // namespace CurvedScalarWave::Worldtube::Actions
diff --git a/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/CMakeLists.txt b/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/CMakeLists.txt
index 242493c661ec..9c8d3e7f077e 100644
--- a/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/CMakeLists.txt
+++ b/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/CMakeLists.txt
@@ -20,6 +20,7 @@ set(LIBRARY_SOURCES
   SingletonActions/Test_InitializeEvolvedVariables.cpp
   SingletonActions/Test_ObserveWorldtubeSolution.cpp
   SingletonActions/Test_UpdateAcceleration.cpp
+  SingletonActions/Test_UpdateFunctionsOfTime.cpp
   )
 
 add_test_library(${LIBRARY} "${LIBRARY_SOURCES}")
diff --git a/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/Test_UpdateFunctionsOfTime.cpp b/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/Test_UpdateFunctionsOfTime.cpp
new file mode 100644
index 000000000000..436fff6b5e3a
--- /dev/null
+++ b/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/Test_UpdateFunctionsOfTime.cpp
@@ -0,0 +1,205 @@
+// Distributed under the MIT License.
+// See LICENSE.txt for details.
+
+#include "Framework/TestingFramework.hpp"
+
+#include <array>
+#include <cstddef>
+#include <random>
+
+#include "DataStructures/DataBox/DataBox.hpp"
+#include "DataStructures/DataBox/Tag.hpp"
+#include "DataStructures/DataVector.hpp"
+#include "DataStructures/Tensor/Tensor.hpp"
+#include "Domain/Block.hpp"
+#include "Domain/Creators/Tags/Domain.hpp"
+#include "Domain/Creators/Tags/FunctionsOfTime.hpp"
+#include "Domain/Domain.hpp"
+#include "Domain/FunctionsOfTime/FunctionOfTime.hpp"
+#include "Domain/FunctionsOfTime/RegisterDerivedWithCharm.hpp"
+#include "Domain/FunctionsOfTime/Tags.hpp"
+#include "Domain/Tags.hpp"
+#include "Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/UpdateFunctionsOfTime.hpp"
+#include "Evolution/Systems/CurvedScalarWave/Worldtube/SingletonChare.hpp"
+#include "Framework/ActionTesting.hpp"
+#include "Framework/TestHelpers.hpp"
+#include "Helpers/Evolution/Systems/CurvedScalarWave/Worldtube/TestHelpers.hpp"
+#include "Parallel/Phase.hpp"
+#include "Parallel/PhaseDependentActionList.hpp"
+#include "ParallelAlgorithms/Actions/FunctionsOfTimeAreReady.hpp"
+#include "Time/Tags/TimeStepId.hpp"
+#include "Time/Time.hpp"
+#include "Time/TimeStepId.hpp"
+#include "Utilities/Gsl.hpp"
+#include "Utilities/TMPL.hpp"
+
+namespace CurvedScalarWave::Worldtube {
+namespace {
+
+template <typename Metavariables>
+struct MockWorldtubeSingleton {
+  using metavariables = Metavariables;
+  using mutable_global_cache_tags =
+      tmpl::list<domain::Tags::FunctionsOfTimeInitialize>;
+  static constexpr size_t Dim = metavariables::volume_dim;
+  using chare_type = ActionTesting::MockSingletonChare;
+  using array_index = int;
+  using phase_dependent_action_list = tmpl::list<
+      Parallel::PhaseActions<
+          Parallel::Phase::Initialization,
+          tmpl::list<ActionTesting::InitializeDataBox<
+              db::AddSimpleTags<::Tags::Time,
+                                Tags::ParticlePositionVelocity<Dim>,
+                                ::Tags::Next<::Tags::TimeStepId>,
+                                Tags::WorldtubeRadius, Tags::ExpirationTime>,
+              db::AddComputeTags<>>>>,
+      Parallel::PhaseActions<
+          Parallel::Phase::Testing,
+          tmpl::list<Actions::UpdateFunctionsOfTime,
+                     domain::Actions::CheckFunctionsOfTimeAreReady<Dim>>>>;
+  using component_being_mocked = WorldtubeSingleton<Metavariables>;
+};
+
+template <size_t Dim>
+struct MockMetavariables {
+  static constexpr size_t volume_dim = Dim;
+  using component_list = tmpl::list<MockWorldtubeSingleton<MockMetavariables>>;
+  using const_global_cache_tags =
+      tmpl::list<Tags::ExcisionSphere<Dim>, domain::Tags::Domain<3>,
+                 Tags::WorldtubeRadiusParameters,
+                 Tags::BlackHoleRadiusParameters>;
+};
+
+void test_particle_motion() {
+  static constexpr size_t Dim = 3;
+  using metavars = MockMetavariables<Dim>;
+  domain::creators::register_derived_with_charm();
+  using worldtube_chare = MockWorldtubeSingleton<metavars>;
+  const double initial_worldtube_radius = 0.456;
+
+  const auto bco_domain_creator =
+      TestHelpers::CurvedScalarWave::Worldtube::worldtube_binary_compact_object<
+          true>(6., initial_worldtube_radius, 0.1);
+  domain::FunctionsOfTime::register_derived_with_charm();
+
+  const auto domain = bco_domain_creator->create_domain();
+  const auto wt_excision_sphere =
+      domain.excision_spheres().at("ExcisionSphereA");
+  const auto bh_excision_sphere =
+      domain.excision_spheres().at("ExcisionSphereB");
+
+  const std::array<double, 4> wt_radius_options{{0.1, 5., 1e-2, 2.3}};
+  const std::array<double, 4> bh_radius_options{{0.1, 5., 1e-2, 0.123}};
+
+  ActionTesting::MockRuntimeSystem<metavars> runner{
+      {
+          wt_excision_sphere,
+          bco_domain_creator->create_domain(),
+          wt_radius_options,
+          bh_radius_options,
+      },
+      bco_domain_creator->functions_of_time()};
+
+  const double current_time = 1.;
+  const Time next_time{{current_time, 2.}, {1, 2}};
+  const TimeStepId next_time_step_id{true, 123, next_time};
+  std::array<tnsr::I<double, Dim, Frame::Inertial>, 2> particle_pos_vel{};
+  MAKE_GENERATOR(gen);
+  std::uniform_real_distribution<double> pos_dist(-10., 10.);
+  std::uniform_real_distribution<double> vel_dist(-0.2, 0.2);
+  particle_pos_vel.at(0) =
+      tnsr::I<double, Dim, Frame::Inertial>{{pos_dist(gen), pos_dist(gen), 0.}};
+  particle_pos_vel.at(1) =
+      tnsr::I<double, Dim, Frame::Inertial>{{vel_dist(gen), vel_dist(gen), 0.}};
+  const double initial_expiration_time = 1e-10;
+  ActionTesting::emplace_singleton_component_and_initialize<worldtube_chare>(
+      &runner, ActionTesting::NodeId{0}, ActionTesting::LocalCoreId{0},
+      {1., particle_pos_vel, next_time_step_id, initial_worldtube_radius,
+       initial_expiration_time});
+  const auto& global_cache = ActionTesting::cache<worldtube_chare>(runner, 0);
+
+  const auto& fots = get<domain::Tags::FunctionsOfTime>(global_cache);
+  CHECK(fots.at("Rotation")->time_bounds()[1] ==
+        approx(initial_expiration_time));
+  CHECK(fots.at("Expansion")->time_bounds()[1] ==
+        approx(initial_expiration_time));
+  CHECK(fots.at("SizeA")->time_bounds()[1] == approx(initial_expiration_time));
+  CHECK(fots.at("SizeB")->time_bounds()[1] == approx(initial_expiration_time));
+  ActionTesting::set_phase(make_not_null(&runner), Parallel::Phase::Testing);
+  // UpdateFunctionsOfTime
+  CHECK(ActionTesting::next_action_if_ready<worldtube_chare>(
+      make_not_null(&runner), 0));
+  // CheckFunctionsOfTimeAreReady
+  CHECK(ActionTesting::next_action_if_ready<worldtube_chare>(
+      make_not_null(&runner), 0));
+
+  const double new_expiration_time_expected = 1.005;
+
+  CHECK(fots.at("Rotation")->time_bounds()[1] ==
+        approx(new_expiration_time_expected));
+  CHECK(fots.at("Expansion")->time_bounds()[1] ==
+        approx(new_expiration_time_expected));
+  CHECK(fots.at("SizeA")->time_bounds()[1] ==
+        approx(new_expiration_time_expected));
+  CHECK(fots.at("SizeB")->time_bounds()[1] ==
+        approx(new_expiration_time_expected));
+
+  const auto& expiration_time_tag =
+      ActionTesting::get_databox_tag<worldtube_chare, Tags::ExpirationTime>(
+          runner, 0);
+  CHECK(expiration_time_tag == approx(new_expiration_time_expected));
+
+  const auto& wt_neighbor_block = domain.blocks()[1];
+  // does not include shape map
+  const auto& grid_to_inertial_map_particle =
+      wt_excision_sphere.moving_mesh_grid_to_inertial_map();
+  // includes worldtube shape map
+  const auto& grid_to_inertial_map_wt_boundary =
+      wt_neighbor_block.moving_mesh_grid_to_inertial_map();
+  const auto mapped_particle =
+      grid_to_inertial_map_particle.coords_frame_velocity_jacobians(
+          wt_excision_sphere.center(), 0.5, fots);
+  CHECK_ITERABLE_APPROX(std::get<0>(mapped_particle), particle_pos_vel.at(0));
+  CHECK_ITERABLE_APPROX(std::get<3>(mapped_particle), particle_pos_vel.at(1));
+  const double orbit_radius = get(magnitude(particle_pos_vel[0]));
+
+  auto wt_boundary_point = wt_excision_sphere.center();
+  wt_boundary_point[0] += wt_excision_sphere.radius();
+  const auto mapped_wt_boundary_data =
+      grid_to_inertial_map_wt_boundary.coords_frame_velocity_jacobians(
+          wt_boundary_point, 0.5, fots);
+  const auto& mapped_wt_boundary_point = std::get<0>(mapped_wt_boundary_data);
+  const double wt_radius = get(magnitude(tenex::evaluate<ti::I>(
+      mapped_wt_boundary_point(ti::I) - particle_pos_vel.at(0)(ti::I))));
+  const double wt_radius_expected = smooth_broken_power_law(
+      orbit_radius, wt_radius_options[0], wt_radius_options[1],
+      wt_radius_options[2], wt_radius_options[3]);
+  CHECK(wt_radius == approx(wt_radius_expected));
+
+  const auto& wt_radius_tag =
+      ActionTesting::get_databox_tag<worldtube_chare, Tags::WorldtubeRadius>(
+          runner, 0);
+  CHECK(wt_radius_tag == approx(wt_radius_expected));
+
+  const auto& bh_neighbor_block = domain.blocks()[12];
+  // includes bh shape map
+  const auto& grid_to_inertial_map_bh_boundary =
+      bh_neighbor_block.moving_mesh_grid_to_inertial_map();
+  auto bh_boundary_point = bh_excision_sphere.center();
+  bh_boundary_point[0] += bh_excision_sphere.radius();
+  const auto mapped_bh_boundary_point = std::get<0>(
+      grid_to_inertial_map_bh_boundary.coords_frame_velocity_jacobians(
+          bh_boundary_point, 0.5, fots));
+  const double bh_radius = get(magnitude(mapped_bh_boundary_point));
+  const double bh_radius_expected = smooth_broken_power_law(
+      orbit_radius, bh_radius_options[0], bh_radius_options[1],
+      bh_radius_options[2], bh_radius_options[3]);
+  CHECK(bh_radius == approx(bh_radius_expected));
+}
+
+SPECTRE_TEST_CASE("Unit.CurvedScalarWave.Worldtube.UpdateFunctionsOfTime",
+                  "[Unit]") {
+  test_particle_motion();
+}
+}  // namespace
+}  // namespace CurvedScalarWave::Worldtube