improve doxygen

Signed-off-by: kosuke55 <kosuke.tnp@gmail.com>

Author: kosuke55

planning/behavior_path_planner/autoware_behavior_path_planner_common/include/autoware/behavior_path_planner_common/utils/path_safety_checker/safety_check.hpp

@@ -252,15 +252,27 @@ double calc_obstacle_min_length(const Shape & shape);
 double calc_obstacle_max_length(const Shape & shape);
 
 /**
- * @brief Calculate collision roughly by comparing minimum/maximum distance with margin.
- * @param path The path of the ego vehicle.
- * @param objects The predicted objects.
- * @param min_margin_threshold threshold for collision check when the minimum distance between ego
- * @param max_margin_threshold threshold for collision check when the maximum distance between ego
- * @param parameters The common parameters used in behavior path planner.
- * @param use_offset_ego_point If true, the closest point to the object is calculated by
- * interpolating the path points.
- * @return Collision (rough) between minimum distance and maximum distance
+ * @brief Performs efficient rough collision detection between ego vehicle and objects
+ * @details
+ * This function calculates two types of distances between ego vehicle and each object:
+ * - Minimum distance: The shortest possible distance between ego and object when positioned
+ * diagonally with their corners closest to each other (uses maximum extent of both objects)
+ * - Maximum distance: The largest possible distance between ego and object when positioned parallel
+ *   to each other (uses minimum extent of both objects)
+ *
+ * A collision is detected when:
+ * - min_distance < min_margin_threshold (first element of returned pair is true)
+ * - max_distance < max_margin_threshold (second element of returned pair is true)
+ *
+ * This approach provides a computationally efficient rough collision check that can be used
+ * before performing more expensive precise collision detection algorithms.
+ * @param path The path of the ego vehicle
+ * @param objects The predicted objects to check for collision
+ * @param min_margin_threshold Threshold for minimum distance collision check
+ * @param max_margin_threshold Threshold for maximum distance collision check
+ * @param parameters The common parameters used in behavior path planner
+ * @param use_offset_ego_point If true, uses interpolated point on path closest to object
+ * @return A pair of boolean values {min_distance_collision, max_distance_collision}
  */
 std::pair<bool, bool> checkObjectsCollisionRough(
   const PathWithLaneId & path, const PredictedObjects & objects, const double min_margin_threshold,

planning/behavior_path_planner/autoware_behavior_path_planner_common/src/utils/path_safety_checker/safety_check.cpp

@@ -882,7 +882,6 @@ double calculateRoughDistanceToObjects(
 double shortest_distance_from_ego_footprint_to_objects_on_path(
   const PathWithLaneId & path, const PredictedObjects & objects,
   const BehaviorPathPlannerParameters & parameters, const bool use_offset_ego_pose)
-
 {
   const auto & p = parameters;
   double min_distance = std::numeric_limits<double>::max();