jetson/ros2_ws/src/saltybot_accel_limiter/config/accel_limiter_config.yaml

@@ -0,0 +1,14 @@
+# Acceleration limiter configuration
+
+accel_limiter:
+  ros__parameters:
+    # Update frequency (Hz)
+    frequency: 50  # 50 Hz = 20ms cycle
+
+    # Linear acceleration limit (m/s²)
+    # Prevents jerky forward/backward and lateral motion
+    linear_accel_limit: 0.5
+
+    # Angular acceleration limit (rad/s²)
+    # Prevents jerky rotation
+    angular_accel_limit: 1.0

jetson/ros2_ws/src/saltybot_accel_limiter/launch/accel_limiter.launch.py

@@ -0,0 +1,36 @@
+"""Launch file for accel_limiter_node."""
+
+from launch import LaunchDescription
+from launch_ros.actions import Node
+from launch.substitutions import LaunchConfiguration
+from launch.actions import DeclareLaunchArgument
+import os
+from ament_index_python.packages import get_package_share_directory
+
+
+def generate_launch_description():
+    """Generate launch description for acceleration limiter node."""
+    # Package directory
+    pkg_dir = get_package_share_directory("saltybot_accel_limiter")
+
+    # Parameters
+    config_file = os.path.join(pkg_dir, "config", "accel_limiter_config.yaml")
+
+    # Declare launch arguments
+    return LaunchDescription(
+        [
+            DeclareLaunchArgument(
+                "config_file",
+                default_value=config_file,
+                description="Path to configuration YAML file",
+            ),
+            # Acceleration limiter node
+            Node(
+                package="saltybot_accel_limiter",
+                executable="accel_limiter_node",
+                name="accel_limiter",
+                output="screen",
+                parameters=[LaunchConfiguration("config_file")],
+            ),
+        ]
+    )

jetson/ros2_ws/src/saltybot_accel_limiter/package.xml

@@ -0,0 +1,21 @@
+<?xml version="1.0"?>
+<?xml-model href="http://download.ros.org/schema/package_format3.xsd" schematypens="http://www.w3.org/2001/XMLSchema"?>
+<package format="3">
+  <name>saltybot_accel_limiter</name>
+  <version>0.1.0</version>
+  <description>Smooth acceleration and deceleration limiter for velocity commands.</description>
+  <maintainer email="seb@vayrette.com">Seb</maintainer>
+  <license>Apache-2.0</license>
+
+  <buildtool_depend>ament_python</buildtool_depend>
+
+  <depend>rclpy</depend>
+  <depend>geometry_msgs</depend>
+  <depend>std_msgs</depend>
+
+  <test_depend>pytest</test_depend>
+
+  <export>
+    <build_type>ament_python</build_type>
+  </export>
+</package>

jetson/ros2_ws/src/saltybot_accel_limiter/saltybot_accel_limiter/accel_limiter_node.py

@@ -0,0 +1,156 @@
+#!/usr/bin/env python3
+"""Smooth acceleration limiter for velocity commands.
+
+Applies configurable acceleration and deceleration rate limits to prevent jerky motion.
+
+Subscribed topics:
+  /cmd_vel (geometry_msgs/Twist) - Target velocity command
+
+Published topics:
+  /cmd_vel_smooth (geometry_msgs/Twist) - Rate-limited velocity command
+
+Prevents sudden velocity changes by limiting rate of change to:
+  - linear: 0.5 m/s² (configurable)
+  - angular: 1.0 rad/s² (configurable)
+"""
+
+from typing import Optional
+
+import rclpy
+from rclpy.node import Node
+from rclpy.timer import Timer
+from geometry_msgs.msg import Twist
+
+
+class AccelLimiterNode(Node):
+    """ROS2 node for smooth acceleration limiting."""
+
+    def __init__(self):
+        super().__init__("accel_limiter")
+
+        # Parameters
+        self.declare_parameter("frequency", 50)  # Hz
+        frequency = self.get_parameter("frequency").value
+        self.declare_parameter("linear_accel_limit", 0.5)  # m/s²
+        self.declare_parameter("angular_accel_limit", 1.0)  # rad/s²
+
+        self.linear_accel_limit = self.get_parameter("linear_accel_limit").value
+        self.angular_accel_limit = self.get_parameter("angular_accel_limit").value
+
+        self.period = 1.0 / frequency
+
+        # Latest target velocity from subscription
+        self.target_vel: Optional[Twist] = None
+
+        # Current smoothed velocity (published)
+        self.current_vel = Twist()
+
+        # Subscription to target velocity
+        self.create_subscription(Twist, "/cmd_vel", self._on_cmd_vel, 10)
+
+        # Publisher for smoothed velocity
+        self.pub_smooth = self.create_publisher(Twist, "/cmd_vel_smooth", 10)
+
+        # Timer for rate limiting at configured frequency
+        self.timer: Timer = self.create_timer(self.period, self._timer_callback)
+
+        self.get_logger().info(
+            f"Acceleration limiter initialized at {frequency}Hz. "
+            f"Linear accel limit: {self.linear_accel_limit} m/s². "
+            f"Angular accel limit: {self.angular_accel_limit} rad/s²"
+        )
+
+    def _on_cmd_vel(self, msg: Twist) -> None:
+        """Update target velocity from cmd_vel subscription."""
+        self.target_vel = msg
+
+    def _timer_callback(self) -> None:
+        """Apply rate limiting and publish smoothed velocity."""
+        if self.target_vel is None:
+            # No target yet, publish zero velocity
+            self.pub_smooth.publish(self.current_vel)
+            return
+
+        # Create new velocity with rate-limited changes
+        limited_vel = Twist()
+
+        # Rate limit linear components
+        limited_vel.linear.x = self._limit_component(
+            self.current_vel.linear.x,
+            self.target_vel.linear.x,
+            self.linear_accel_limit,
+        )
+        limited_vel.linear.y = self._limit_component(
+            self.current_vel.linear.y,
+            self.target_vel.linear.y,
+            self.linear_accel_limit,
+        )
+        limited_vel.linear.z = self._limit_component(
+            self.current_vel.linear.z,
+            self.target_vel.linear.z,
+            self.linear_accel_limit,
+        )
+
+        # Rate limit angular components
+        limited_vel.angular.x = self._limit_component(
+            self.current_vel.angular.x,
+            self.target_vel.angular.x,
+            self.angular_accel_limit,
+        )
+        limited_vel.angular.y = self._limit_component(
+            self.current_vel.angular.y,
+            self.target_vel.angular.y,
+            self.angular_accel_limit,
+        )
+        limited_vel.angular.z = self._limit_component(
+            self.current_vel.angular.z,
+            self.target_vel.angular.z,
+            self.angular_accel_limit,
+        )
+
+        # Update current velocity and publish
+        self.current_vel = limited_vel
+        self.pub_smooth.publish(self.current_vel)
+
+    def _limit_component(
+        self, current: float, target: float, accel_limit: float
+    ) -> float:
+        """Apply acceleration limit to a single velocity component.
+
+        Args:
+            current: Current velocity value (m/s or rad/s)
+            target: Target velocity value (m/s or rad/s)
+            accel_limit: Maximum acceleration (m/s² or rad/s²)
+
+        Returns:
+            Rate-limited velocity value
+        """
+        # Compute desired change
+        change = target - current
+
+        # Maximum change allowed in this time period: accel_limit * dt
+        max_change = accel_limit * self.period
+
+        # Clamp change to limits
+        if change > max_change:
+            return current + max_change
+        elif change < -max_change:
+            return current - max_change
+        else:
+            return target
+
+
+def main(args=None):
+    rclpy.init(args=args)
+    node = AccelLimiterNode()
+    try:
+        rclpy.spin(node)
+    except KeyboardInterrupt:
+        pass
+    finally:
+        node.destroy_node()
+        rclpy.shutdown()
+
+
+if __name__ == "__main__":
+    main()

jetson/ros2_ws/src/saltybot_accel_limiter/setup.cfg

@@ -0,0 +1,4 @@
+[develop]
+script-dir=$base/lib/saltybot_accel_limiter
+[install]
+install-scripts=$base/lib/saltybot_accel_limiter

jetson/ros2_ws/src/saltybot_accel_limiter/setup.py

@@ -0,0 +1,27 @@
+from setuptools import find_packages, setup
+
+package_name = "saltybot_accel_limiter"
+
+setup(
+    name=package_name,
+    version="0.1.0",
+    packages=find_packages(exclude=["test"]),
+    data_files=[
+        ("share/ament_index/resource_index/packages", ["resource/" + package_name]),
+        ("share/" + package_name, ["package.xml"]),
+        ("share/" + package_name + "/launch", ["launch/accel_limiter.launch.py"]),
+        ("share/" + package_name + "/config", ["config/accel_limiter_config.yaml"]),
+    ],
+    install_requires=["setuptools"],
+    zip_safe=True,
+    maintainer="Seb",
+    maintainer_email="seb@vayrette.com",
+    description="Smooth acceleration and deceleration rate limiting for velocity commands",
+    license="Apache-2.0",
+    tests_require=["pytest"],
+    entry_points={
+        "console_scripts": [
+            "accel_limiter_node = saltybot_accel_limiter.accel_limiter_node:main",
+        ],
+    },
+)

jetson/ros2_ws/src/saltybot_accel_limiter/test/test_accel_limiter.py

@@ -0,0 +1,442 @@
+"""Unit tests for accel_limiter_node."""
+
+import pytest
+import math
+from geometry_msgs.msg import Twist, Vector3
+
+import rclpy
+
+# Import the node under test
+from saltybot_accel_limiter.accel_limiter_node import AccelLimiterNode
+
+
+@pytest.fixture
+def rclpy_fixture():
+    """Initialize and cleanup rclpy."""
+    rclpy.init()
+    yield
+    rclpy.shutdown()
+
+
+@pytest.fixture
+def node(rclpy_fixture):
+    """Create an acceleration limiter node instance."""
+    node = AccelLimiterNode()
+    yield node
+    node.destroy_node()
+
+
+class TestNodeInitialization:
+    """Test suite for node initialization."""
+
+    def test_node_initialization(self, node):
+        """Test that node initializes with correct defaults."""
+        assert node.linear_accel_limit == 0.5
+        assert node.angular_accel_limit == 1.0
+        assert node.target_vel is None
+        assert node.current_vel.linear.x == 0.0
+        assert node.current_vel.linear.y == 0.0
+        assert node.current_vel.linear.z == 0.0
+        assert node.current_vel.angular.x == 0.0
+        assert node.current_vel.angular.y == 0.0
+        assert node.current_vel.angular.z == 0.0
+
+    def test_frequency_parameter(self, node):
+        """Test frequency parameter is set correctly."""
+        frequency = node.get_parameter("frequency").value
+        assert frequency == 50
+
+    def test_linear_accel_parameter(self, node):
+        """Test linear acceleration limit parameter."""
+        limit = node.get_parameter("linear_accel_limit").value
+        assert limit == 0.5
+
+    def test_angular_accel_parameter(self, node):
+        """Test angular acceleration limit parameter."""
+        limit = node.get_parameter("angular_accel_limit").value
+        assert limit == 1.0
+
+    def test_period_calculation(self, node):
+        """Test that time period is correctly calculated from frequency."""
+        # 50 Hz = 20ms = 0.02s
+        assert node.period == pytest.approx(0.02)
+
+
+class TestLimitComponent:
+    """Test suite for _limit_component method."""
+
+    def test_no_change_needed(self, node):
+        """Test when target equals current (no acceleration needed)."""
+        result = node._limit_component(1.0, 1.0, 0.5)
+        assert result == pytest.approx(1.0)
+
+    def test_zero_acceleration(self, node):
+        """Test when current is zero and target is zero."""
+        result = node._limit_component(0.0, 0.0, 0.5)
+        assert result == pytest.approx(0.0)
+
+    def test_small_change_within_limit(self, node):
+        """Test small change that is within acceleration limit."""
+        # Max change in 20ms at 0.5 m/s²: 0.5 * 0.02 = 0.01 m/s
+        # Desired change: 0.005 m/s (less than limit)
+        result = node._limit_component(0.0, 0.005, 0.5)
+        assert result == pytest.approx(0.005)
+
+    def test_acceleration_exceeds_limit(self, node):
+        """Test acceleration that exceeds the limit."""
+        # Max change in 20ms at 0.5 m/s²: 0.5 * 0.02 = 0.01 m/s
+        # Desired change: 0.1 m/s (much greater than limit)
+        result = node._limit_component(0.0, 0.1, 0.5)
+        assert result == pytest.approx(0.01)
+
+    def test_deceleration_exceeds_limit(self, node):
+        """Test deceleration that exceeds the limit."""
+        # Max change in 20ms at 0.5 m/s²: -0.5 * 0.02 = -0.01 m/s
+        # Desired change: -0.1 m/s (much more negative than limit)
+        result = node._limit_component(0.1, 0.0, 0.5)
+        assert result == pytest.approx(0.09)
+
+    def test_negative_to_positive_acceleration(self, node):
+        """Test acceleration from negative to positive velocity."""
+        result = node._limit_component(-0.1, 0.1, 0.5)
+        # Max change: 0.01, so -0.1 + 0.01 = -0.09
+        assert result == pytest.approx(-0.09)
+
+    def test_positive_to_negative_deceleration(self, node):
+        """Test deceleration from positive to negative velocity."""
+        result = node._limit_component(0.1, -0.1, 0.5)
+        # Max change: -0.01, so 0.1 - 0.01 = 0.09
+        assert result == pytest.approx(0.09)
+
+    def test_angular_acceleration_limit(self, node):
+        """Test with angular acceleration limit."""
+        # Max change in 20ms at 1.0 rad/s²: 1.0 * 0.02 = 0.02 rad/s
+        # Desired change: 0.1 rad/s (exceeds limit)
+        result = node._limit_component(0.0, 0.1, 1.0)
+        assert result == pytest.approx(0.02)
+
+    def test_large_acceleration_value(self, node):
+        """Test with large acceleration limit."""
+        # Max change in 20ms at 10.0 m/s²: 10.0 * 0.02 = 0.2 m/s
+        # Desired change: 0.1 m/s (within limit)
+        result = node._limit_component(0.0, 0.1, 10.0)
+        assert result == pytest.approx(0.1)
+
+
+class TestSubscriptionHandling:
+    """Test suite for cmd_vel subscription."""
+
+    def test_cmd_vel_subscription(self, node):
+        """Test that cmd_vel subscription updates target velocity."""
+        cmd = Twist()
+        cmd.linear.x = 1.0
+        cmd.linear.y = 0.5
+        cmd.angular.z = 0.2
+
+        node._on_cmd_vel(cmd)
+
+        assert node.target_vel is cmd
+        assert node.target_vel.linear.x == 1.0
+        assert node.target_vel.linear.y == 0.5
+        assert node.target_vel.angular.z == 0.2
+
+    def test_multiple_cmd_vel_updates(self, node):
+        """Test that subscription updates replace previous command."""
+        cmd1 = Twist()
+        cmd1.linear.x = 1.0
+
+        cmd2 = Twist()
+        cmd2.linear.x = 2.0
+
+        node._on_cmd_vel(cmd1)
+        assert node.target_vel.linear.x == 1.0
+
+        node._on_cmd_vel(cmd2)
+        assert node.target_vel.linear.x == 2.0
+
+
+class TestTimerCallback:
+    """Test suite for timer callback and rate limiting."""
+
+    def test_timer_callback_no_target(self, node):
+        """Test timer callback when no target velocity received yet."""
+        # Should publish current velocity (zero)
+        node._timer_callback()
+        assert node.current_vel.linear.x == 0.0
+        assert node.current_vel.angular.z == 0.0
+
+    def test_timer_callback_linear_acceleration(self, node):
+        """Test linear acceleration limiting."""
+        # Target: 1.0 m/s
+        target = Twist()
+        target.linear.x = 1.0
+        node._on_cmd_vel(target)
+
+        # First callback: current should move towards target, limited
+        node._timer_callback()
+        # Max acceleration: 0.5 m/s², period: 0.02s = 0.01 m/s change
+        assert node.current_vel.linear.x == pytest.approx(0.01)
+
+        # Second callback: should continue accelerating
+        node._timer_callback()
+        assert node.current_vel.linear.x == pytest.approx(0.02)
+
+    def test_timer_callback_linear_deceleration(self, node):
+        """Test linear deceleration limiting."""
+        # Start with velocity
+        node.current_vel.linear.x = 1.0
+
+        # Target: 0 m/s (deceleration)
+        target = Twist()
+        target.linear.x = 0.0
+        node._on_cmd_vel(target)
+
+        # Callback should decelerate limited by rate limit
+        node._timer_callback()
+        # Max deceleration: -0.01 m/s, so 1.0 - 0.01 = 0.99
+        assert node.current_vel.linear.x == pytest.approx(0.99)
+
+    def test_timer_callback_angular_acceleration(self, node):
+        """Test angular acceleration limiting."""
+        target = Twist()
+        target.angular.z = 1.0
+        node._on_cmd_vel(target)
+
+        node._timer_callback()
+        # Max angular acceleration: 1.0 rad/s², period: 0.02s = 0.02 rad/s
+        assert node.current_vel.angular.z == pytest.approx(0.02)
+
+    def test_timer_callback_all_components(self, node):
+        """Test rate limiting across all velocity components."""
+        target = Twist()
+        target.linear.x = 1.0
+        target.linear.y = 0.5
+        target.linear.z = 0.2
+        target.angular.x = 0.1
+        target.angular.y = 0.2
+        target.angular.z = 1.0
+
+        node._on_cmd_vel(target)
+        node._timer_callback()
+
+        # All linear components should be limited by linear_accel_limit
+        assert node.current_vel.linear.x == pytest.approx(0.01)
+        assert node.current_vel.linear.y == pytest.approx(0.005)
+        assert node.current_vel.linear.z == pytest.approx(0.002)
+
+        # All angular components should be limited by angular_accel_limit
+        assert node.current_vel.angular.x == pytest.approx(0.002)
+        assert node.current_vel.angular.y == pytest.approx(0.004)
+        assert node.current_vel.angular.z == pytest.approx(0.02)
+
+    def test_timer_reaches_target(self, node):
+        """Test that velocity eventually reaches target after multiple callbacks."""
+        target = Twist()
+        target.linear.x = 0.1
+        node._on_cmd_vel(target)
+
+        # Max change per callback: 0.01
+        # Target: 0.1, so needs 10 callbacks to reach it
+        for _ in range(5):
+            node._timer_callback()
+
+        # After 5 callbacks: 0.05
+        assert node.current_vel.linear.x == pytest.approx(0.05)
+
+        # Continue for 5 more callbacks
+        for _ in range(5):
+            node._timer_callback()
+
+        # Should be at target now or very close
+        assert node.current_vel.linear.x == pytest.approx(0.1)
+
+    def test_timer_stops_at_target(self, node):
+        """Test that velocity stops changing once target is reached."""
+        target = Twist()
+        target.linear.x = 0.01
+        node._on_cmd_vel(target)
+
+        node._timer_callback()
+        assert node.current_vel.linear.x == pytest.approx(0.01)
+
+        # Next callback should stay at target
+        node._timer_callback()
+        assert node.current_vel.linear.x == pytest.approx(0.01)
+
+
+class TestRateLimit:
+    """Test suite for rate limiting behavior."""
+
+    def test_linear_vs_angular_different_limits(self, node):
+        """Test that linear and angular limits are independent."""
+        target = Twist()
+        target.linear.x = 1.0
+        target.angular.z = 1.0
+
+        node._on_cmd_vel(target)
+        node._timer_callback()
+
+        # Linear limited by 0.5 m/s²: 0.5 * 0.02 = 0.01
+        assert node.current_vel.linear.x == pytest.approx(0.01)
+
+        # Angular limited by 1.0 rad/s²: 1.0 * 0.02 = 0.02
+        assert node.current_vel.angular.z == pytest.approx(0.02)
+
+    def test_emergency_stop(self, node):
+        """Test emergency deceleration from high speed."""
+        # Start at high speed
+        node.current_vel.linear.x = 2.0
+
+        # Sudden stop command
+        target = Twist()
+        target.linear.x = 0.0
+        node._on_cmd_vel(target)
+
+        # Should decelerate gradually, not instantly
+        node._timer_callback()
+        assert node.current_vel.linear.x == pytest.approx(1.99)
+        assert node.current_vel.linear.x > 0.0  # Not zero yet
+
+    def test_alternating_direction(self, node):
+        """Test rapid direction changes are smoothed."""
+        # Accelerate forward
+        target1 = Twist()
+        target1.linear.x = 0.5
+        node._on_cmd_vel(target1)
+
+        for _ in range(10):
+            node._timer_callback()
+
+        vel_forward = node.current_vel.linear.x
+
+        # Suddenly reverse
+        target2 = Twist()
+        target2.linear.x = -0.5
+        node._on_cmd_vel(target2)
+
+        node._timer_callback()
+        vel_after_reverse = node.current_vel.linear.x
+
+        # Should still be positive but decreasing
+        assert vel_after_reverse < vel_forward
+        assert vel_after_reverse > -0.5
+
+
+class TestScenarios:
+    """Integration-style tests for realistic scenarios."""
+
+    def test_scenario_gradual_acceleration(self, node):
+        """Scenario: Smooth acceleration from stop to cruising speed."""
+        target = Twist()
+        target.linear.x = 0.5  # Cruise at 0.5 m/s
+
+        node._on_cmd_vel(target)
+
+        velocities = []
+        for _ in range(100):
+            node._timer_callback()
+            velocities.append(node.current_vel.linear.x)
+
+        # Velocities should be monotonically increasing
+        for i in range(1, len(velocities)):
+            assert velocities[i] >= velocities[i - 1]
+
+        # Should reach target
+        assert velocities[-1] == pytest.approx(0.5)
+
+    def test_scenario_smooth_stop(self, node):
+        """Scenario: Smooth deceleration to stop."""
+        # Start at cruising speed
+        node.current_vel.linear.x = 0.5
+
+        # Command to stop
+        target = Twist()
+        target.linear.x = 0.0
+        node._on_cmd_vel(target)
+
+        velocities = []
+        for _ in range(100):
+            node._timer_callback()
+            velocities.append(node.current_vel.linear.x)
+
+        # Velocities should be monotonically decreasing
+        for i in range(1, len(velocities)):
+            assert velocities[i] <= velocities[i - 1]
+
+        # Should reach zero
+        assert velocities[-1] == pytest.approx(0.0)
+
+    def test_scenario_turn_while_moving(self, node):
+        """Scenario: Robot turns while moving forward."""
+        node.current_vel.linear.x = 0.5
+        node.current_vel.linear.y = 0.0
+
+        target = Twist()
+        target.linear.x = 0.5
+        target.linear.y = 0.2
+        target.angular.z = 0.5
+
+        node._on_cmd_vel(target)
+
+        # Multiple iterations to see smooth change
+        for _ in range(50):
+            node._timer_callback()
+
+        # Forward velocity unchanged (same target)
+        assert node.current_vel.linear.x == pytest.approx(0.5)
+
+        # Lateral velocity increased toward target
+        assert node.current_vel.linear.y > 0.0
+        assert node.current_vel.linear.y <= 0.2
+
+        # Angular velocity increased
+        assert node.current_vel.angular.z > 0.0
+        assert node.current_vel.angular.z <= 0.5
+
+    def test_scenario_obstacle_avoidance(self, node):
+        """Scenario: Quick lateral movement due to obstacle."""
+        target = Twist()
+        target.linear.x = 0.5
+        target.linear.y = 0.3  # Quick dodge sideways
+        node._on_cmd_vel(target)
+
+        # Y velocity should increase gradually, not jump to 0.3
+        accelerations = []
+        for _ in range(10):
+            node._timer_callback()
+            accelerations.append(node.current_vel.linear.y)
+
+        # Each step should be limited
+        for i in range(1, len(accelerations)):
+            delta = accelerations[i] - accelerations[i - 1]
+            max_delta = 0.5 * 0.02  # linear_accel_limit * period
+            assert abs(delta) <= max_delta + 1e-6  # Small tolerance
+
+    def test_scenario_continuous_motion(self, node):
+        """Scenario: Continuous velocity updates (tracking)."""
+        for i in range(100):
+            # Gradually increasing target
+            target = Twist()
+            target.linear.x = i * 0.001
+
+            node._on_cmd_vel(target)
+            node._timer_callback()
+
+        # Current velocity should lag behind target
+        assert node.current_vel.linear.x < 0.1
+
+    def test_scenario_oscillating_command(self, node):
+        """Scenario: Target velocity oscillates."""
+        oscillations = []
+
+        for i in range(200):
+            # Sinusoidal target
+            target = Twist()
+            target.linear.x = 0.5 * (1 + math.sin(i * 0.05))
+
+            node._on_cmd_vel(target)
+            node._timer_callback()
+            oscillations.append(node.current_vel.linear.x)
+
+        # Velocity should lag behind target but not diverge
+        assert all(0.0 <= v <= 1.0 for v in oscillations)