text: import math
  import typing
  
  from motioncontrol import utils
  
  from .utils import Point, RobotState
  
  
  class PathState(typing.NamedTuple):
      curvature: float
      goal_point: Point
      path_position: Point
      goal_direction: int
      remaining_distance: float
  
  
  class PathSegment(typing.NamedTuple):
      start: Point
      end: Point
      length: float
      angle: float
  
  
  class PathTuning(typing.NamedTuple):
      lookahead: float
      lookahead_reduction_factor: float = 1.0
      curvature_scaling: float = 1.0
  
  
  class Path:
      """Represents a path between a set of points
  
      Provides methods to calculate desired robot heading to follow path
      """
  
      def __init__(
              self,
              tuning_parameters: PathTuning,
              initial_robot_state: RobotState,
              waypoints: typing.List[Point],
      ):
          """Path starting from `initial_robot_state` following between the `waypoints`
  
          Tuning parameters:
  
          `lookahead` will be used to select a goal point, during the last segment of the path, it
          will be linearly scaled from `lookahead` to `lookahead / lookahead_reduction_factor` across
          that last segment.
  
          `curvature_scaling` should be used to tune how responsive the robot is to turning - if the
          robot fails to complete curves, increase it, if it turns too sharply decrease this value.
          """
          self.initial_state = initial_robot_state
  
          self.lookahead = tuning_parameters.lookahead
          self.lookahead_reduction = tuning_parameters.lookahead_reduction_factor
          self.curvature_scaling = tuning_parameters.curvature_scaling
  
          position = self.initial_state.position
          self.segments = []
          for waypoint in waypoints:
              length = utils.distance_between(position, waypoint)
              angle = utils.angle_between(position, waypoint)
              segment = PathSegment(start=position, end=waypoint, length=length, angle=angle)
              self.segments.append(segment)
              position = waypoint
  
          self.end = self.segments[-1].end
  
          end_stabilization_length = self.lookahead * 1.1
          end_angle = self.segments[-1].angle
          self.pseudo_end = Point(
              x=self.end.x + (math.cos(end_angle) * end_stabilization_length),
              y=self.end.y + (math.sin(end_angle) * end_stabilization_length))
          self.segments.append(
              PathSegment(
                  start=self.end,
                  end=self.pseudo_end,
                  length=end_stabilization_length,
                  angle=end_angle))
  
      def get_path_state(self, robot_state: RobotState) -> PathState:
          """Given the current pose of the robot and an optional lookahead
          distance, get a `PathState` object describing the optimal state.
          """
          closest, closest_segment_index = self._find_closest_point(robot_state.position)
          lookahead = self._compute_lookahead(closest, closest_segment_index)
  
          absolute_goal = self._find_goal_point(robot_state, lookahead) or closest
          relative_goal = utils.vehicle_coords(robot_state, absolute_goal)
  
          D = utils.distance_between(Point(), relative_goal)
          x = relative_goal.x
  
          curvature = self.curvature_scaling * ((2 * x) / (D * D))
  
          remaining_distance = utils.distance_between(robot_state.position, self.end)
  
          return PathState(
              curvature=curvature,
              goal_point=absolute_goal,
              path_position=closest,
              goal_direction=utils.signum(relative_goal.y, separate_zero=False),
              remaining_distance=remaining_distance)
  
      def _find_goal_point(self, robot_state: RobotState, lookahead: float) -> Point:
          """Find a goal point - point on path `lookahead` from robot that is closest by on-path
           distance to the end
  
          Returns `None` if no such intersection is found.
          """
          for segment in reversed(self.segments):
              intersections = utils.circle_line_intersection(robot_state.position, lookahead, segment)
              intersections = [n for n in intersections if utils.on_segment(n, segment)]
              if intersections:
                  return min(intersections, key=(lambda x: utils.distance_between(x, segment.end)))
  
          return None
  
      def _find_closest_point(self, point: Point) -> (Point, int):
          """Find the closest point on the path to the given point
  
          Returns the closest point, and the index of the path segment it is on."""
          candidates = []
  
          for i, segment in enumerate(self.segments):
              candidate = utils.closest_point_on_line(segment, point)
              distance = utils.distance_between(candidate, point)
              candidates.append((candidate, distance, i))
  
          closest = min(candidates, key=lambda x: x[1])
          return closest[0], closest[2]
  
      def _compute_lookahead(self, path_position: Point, segment_index: int) -> float:
          segment = self.segments[segment_index]
  
          on_end_segment = segment_index == len(self.segments) - 2
          on_pseudo_segment = segment_index == len(self.segments) - 1
  
          if on_pseudo_segment:
              return self.lookahead / self.lookahead_reduction
  
          if on_end_segment:
              remaining_distance = utils.distance_between(path_position, self.end)
              scale = ((segment.length + (self.lookahead_reduction - 1) * remaining_distance) /
                       (self.lookahead_reduction * segment.length))
              return self.lookahead * scale
  
          return self.lookahead
  