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#!/usr/bin/env python3
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"""
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飛行任務規劃模組
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支援: M-Formation, Circle, Leader-Follower (Bezier 轉彎), Grid Sweep
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"""
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import math
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from typing import List, Tuple, Optional, Dict, Any
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from enum import Enum
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class MissionType(Enum):
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"""任務類型"""
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M_FORMATION = "m_formation"
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CIRCLE_FORMATION = "circle_formation"
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LEADER_FOLLOWER = "leader_follower"
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GRID_SWEEP = "grid_sweep"
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class CoordinateConverter:
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"""GPS 座標與 Local 座標的轉換器"""
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def __init__(self, origin_lat: float, origin_lon: float, origin_alt: float = 0):
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self.origin_lat = origin_lat
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self.origin_lon = origin_lon
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self.origin_alt = origin_alt
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self.R = 6371000.0
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def gps_to_local(self, lat: float, lon: float, alt: float) -> Tuple[float, float, float]:
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lat_rad = math.radians(lat)
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lon_rad = math.radians(lon)
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origin_lat_rad = math.radians(self.origin_lat)
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origin_lon_rad = math.radians(self.origin_lon)
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dlat = lat_rad - origin_lat_rad
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dlon = lon_rad - origin_lon_rad
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x = self.R * dlon * math.cos((lat_rad + origin_lat_rad) / 2)
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y = self.R * dlat
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z = alt - self.origin_alt
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return x, y, z
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def local_to_gps(self, x: float, y: float, z: float) -> Tuple[float, float, float]:
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origin_lat_rad = math.radians(self.origin_lat)
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origin_lon_rad = math.radians(self.origin_lon)
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lat_rad = origin_lat_rad + (y / self.R)
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lon_rad = origin_lon_rad + (x / (self.R * math.cos((lat_rad + origin_lat_rad) / 2)))
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lat = math.degrees(lat_rad)
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lon = math.degrees(lon_rad)
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alt = self.origin_alt + z
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return lat, lon, alt
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class FormationPlanner:
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"""隊形規劃器"""
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def __init__(self, spacing: float = 5.0,
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base_altitude: float = 10.0,
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altitude_diff: float = 2.0):
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self.spacing = spacing
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self.base_altitude = base_altitude
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self.altitude_diff = altitude_diff
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self.current_origin = None
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self.converter = None
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def plan_formation_mission(self,
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drone_gps_positions: List[Tuple[float, float, float]],
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target_gps: Tuple[float, float, float],
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mission_type: MissionType = MissionType.M_FORMATION,
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params: Optional[Dict[str, Any]] = None
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) -> Tuple[List[List[Tuple[float, float, float]]],
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Tuple[float, float, float]]:
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if len(drone_gps_positions) == 0:
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raise ValueError("無人機位置列表不能為空")
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center_lat = sum(pos[0] for pos in drone_gps_positions) / len(drone_gps_positions)
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center_lon = sum(pos[1] for pos in drone_gps_positions) / len(drone_gps_positions)
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center_alt = sum(pos[2] for pos in drone_gps_positions) / len(drone_gps_positions)
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self.current_origin = (center_lat, center_lon, center_alt)
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self.converter = CoordinateConverter(center_lat, center_lon, center_alt)
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drone_local = [self.converter.gps_to_local(*pos) for pos in drone_gps_positions]
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target_local = self.converter.gps_to_local(*target_gps)
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if mission_type == MissionType.M_FORMATION:
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s1, s2 = self._calculate_m_formation(drone_local, target_local, params)
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waypoints_local = [[s1[i], s2[i]] for i in range(len(drone_local))]
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elif mission_type == MissionType.CIRCLE_FORMATION:
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s1, s2 = self._calculate_circle_formation(drone_local, target_local, params)
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waypoints_local = [[s1[i], s2[i]] for i in range(len(drone_local))]
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elif mission_type == MissionType.LEADER_FOLLOWER:
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params = params or {}
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route_wps_gps = params.get('route_waypoints')
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if route_wps_gps is None or len(route_wps_gps) < 2:
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raise ValueError("LEADER_FOLLOWER 需要至少 2 個路徑點")
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route_wps_local = [
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self.converter.gps_to_local(wp[0], wp[1], 0)[:2]
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for wp in route_wps_gps
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]
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waypoints_local = self._calculate_leader_follower(drone_local, route_wps_local, params)
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elif mission_type == MissionType.GRID_SWEEP:
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params = params or {}
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rect_corners_gps = params.get('rect_corners')
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if rect_corners_gps is None or len(rect_corners_gps) != 4:
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raise ValueError("GRID_SWEEP 需要 4 個 GPS 角點")
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rect_corners_local = [
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self.converter.gps_to_local(c[0], c[1], 0)[:2]
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for c in rect_corners_gps
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]
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waypoints_local = self._calculate_grid_sweep(drone_local, rect_corners_local, params)
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else:
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raise ValueError(f"不支援的任務類型: {mission_type}")
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waypoints_gps = []
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for drone_wps in waypoints_local:
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gps_wps = [self.converter.local_to_gps(*wp) for wp in drone_wps]
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waypoints_gps.append(gps_wps)
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return waypoints_gps, self.current_origin
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# ------------------------------------------------------------------ M-Formation
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def _calculate_m_formation(self, drone_positions, target_point, params):
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params = params or {}
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N = len(drone_positions)
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spacing = params.get('spacing', self.spacing)
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base_altitude = params.get('base_altitude', self.base_altitude)
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altitude_diff = params.get('altitude_diff', self.altitude_diff)
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C_x = sum(pos[0] for pos in drone_positions) / N
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C_y = sum(pos[1] for pos in drone_positions) / N
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T_x, T_y, T_z = target_point
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V_x, V_y = T_x - C_x, T_y - C_y
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P_x, P_y = -V_y, V_x
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length = math.sqrt(P_x ** 2 + P_y ** 2)
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P_x_unit, P_y_unit = (P_x / length, P_y / length) if length > 0.01 else (1.0, 0.0)
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projections = [((pos[0] - C_x) * P_x_unit + (pos[1] - C_y) * P_y_unit, i)
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for i, pos in enumerate(drone_positions)]
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projections.sort()
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stage1_positions = [None] * N
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stage2_positions = [None] * N
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for rank, (_, original_idx) in enumerate(projections):
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offset = (rank - (N - 1) / 2) * spacing
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altitude = base_altitude + (altitude_diff if rank % 2 == 0 else -altitude_diff)
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stage1_positions[original_idx] = (C_x + P_x_unit * offset, C_y + P_y_unit * offset, altitude)
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stage2_positions[original_idx] = (T_x + P_x_unit * offset, T_y + P_y_unit * offset, altitude)
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return stage1_positions, stage2_positions
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# ------------------------------------------------------------------ Circle
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def _calculate_circle_formation(self, drone_positions, target_point, params):
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params = params or {}
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N = len(drone_positions)
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radius = params.get('radius', 10.0)
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altitude = params.get('altitude', 10.0)
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start_angle = params.get('start_angle', 0.0)
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center_x, center_y, center_z = target_point
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stage1_positions = []
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stage2_positions = []
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angle_step = 360.0 / N
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for i in range(N):
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angle_rad = math.radians(start_angle + angle_step * i)
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final_x = center_x + radius * math.cos(angle_rad)
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final_y = center_y + radius * math.sin(angle_rad)
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final_z = altitude
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current_x, current_y, current_z = drone_positions[i]
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stage1_positions.append((
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current_x + (final_x - current_x) * 0.5,
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current_y + (final_y - current_y) * 0.5,
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current_z + (final_z - current_z) * 0.5
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))
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stage2_positions.append((final_x, final_y, final_z))
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return stage1_positions, stage2_positions
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# ------------------------------------------------------------------ 路徑跟隨 (Bezier 轉彎)
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def _calculate_leader_follower(self, drone_positions, route_wps_local, params):
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"""
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路徑跟隨編隊 — Bezier 曲線轉彎版
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步驟:
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1. _build_center_path: 在轉折 WP 處用二次 Bezier 曲線平滑轉彎
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2. 固定排序，每架無人機沿中心路徑套用橫向+縱向偏移
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隊形 (俯視):
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| (前進方向) |
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| D1 | ← 左偏移, 後 0m
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| D2 | ← 右偏移, 後 5m
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| D3 | ← 左偏移, 後 10m
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| D4 | ← 右偏移, 後 15m
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"""
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N = len(drone_positions)
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lateral_offset = params.get('lateral_offset', 3.0)
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longitudinal_spacing = params.get('longitudinal_spacing', 5.0)
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altitude = params.get('altitude', self.base_altitude)
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turn_margin = params.get('turn_margin', 0.35) # 轉彎切入距離佔段長比例
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curve_resolution = params.get('curve_resolution', 8) # 每個彎道的插值點數
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# Step 1: 建立帶 Bezier 轉彎的中心路徑
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center_path = self._build_center_path(
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route_wps_local, turn_margin, curve_resolution
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)
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# Step 2: 固定排序
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first_dir = (center_path[0][2], center_path[0][3])
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first_perp = (-first_dir[1], first_dir[0])
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C_x = sum(p[0] for p in drone_positions) / N
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C_y = sum(p[1] for p in drone_positions) / N
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projections = [
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((pos[0] - C_x) * first_perp[0] + (pos[1] - C_y) * first_perp[1], i)
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for i, pos in enumerate(drone_positions)
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]
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projections.sort()
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# Step 3: 偏移
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all_waypoints = [None] * N
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for rank, (_, original_idx) in enumerate(projections):
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lat_sign = -1 if rank % 2 == 0 else 1
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lat = lat_sign * lateral_offset
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lon = rank * longitudinal_spacing
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waypoints = []
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for (cx, cy, dx, dy) in center_path:
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perp_x, perp_y = -dy, dx
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ox = cx + lat * perp_x - lon * dx
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oy = cy + lat * perp_y - lon * dy
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waypoints.append((ox, oy, altitude))
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all_waypoints[original_idx] = waypoints
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return all_waypoints
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def _build_center_path(self, waypoints, turn_margin, curve_resolution):
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"""
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建立帶 Bezier 曲線轉彎的中心路徑
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在每個轉折 WP 處:
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1. 計算 pre_turn = WP - d_in × T
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2. 計算 post_turn = WP + d_out × T
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3. 用二次 Bezier 曲線: B(t) = (1-t)²·pre + 2t(1-t)·WP + t²·post
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4. 方向從導數得到: B'(t) = 2(1-t)(WP-pre) + 2t(post-WP)
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Args:
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waypoints: 路徑航點 [(x, y), ...]
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turn_margin: 轉彎切入距離佔相鄰段長的比例 (0~0.5)
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curve_resolution: 每個彎道的 Bezier 插值點數
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Returns:
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[(x, y, dir_x, dir_y), ...] 中心路徑點 + 單位方向
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"""
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num_wps = len(waypoints)
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if num_wps < 2:
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return [(waypoints[0][0], waypoints[0][1], 0.0, 1.0)]
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# 計算每段方向和長度
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segments = []
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for i in range(num_wps - 1):
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dx = waypoints[i + 1][0] - waypoints[i][0]
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dy = waypoints[i + 1][1] - waypoints[i][1]
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length = math.sqrt(dx ** 2 + dy ** 2)
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if length < 0.01:
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segments.append((0.0, 1.0, length))
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else:
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segments.append((dx / length, dy / length, length))
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path = []
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# 第一個航點
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path.append((waypoints[0][0], waypoints[0][1],
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segments[0][0], segments[0][1]))
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# 中間航點 (轉彎處)
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for i in range(1, num_wps - 1):
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d_in_x, d_in_y, len_in = segments[i - 1]
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d_out_x, d_out_y, len_out = segments[i]
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# 切入距離 T: 取相鄰兩段中較短的 × turn_margin
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T = min(len_in, len_out) * turn_margin
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if T < 0.5:
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# 段太短，不插彎，直接加一個平均方向點
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avg_dx = d_in_x + d_out_x
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avg_dy = d_in_y + d_out_y
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avg_len = math.sqrt(avg_dx ** 2 + avg_dy ** 2)
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if avg_len > 0.01:
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avg_dx /= avg_len
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avg_dy /= avg_len
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else:
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avg_dx, avg_dy = d_in_x, d_in_y
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path.append((waypoints[i][0], waypoints[i][1], avg_dx, avg_dy))
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continue
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# P0 = pre_turn (弧線起始)
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p0_x = waypoints[i][0] - d_in_x * T
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p0_y = waypoints[i][1] - d_in_y * T
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# P1 = WP 本身 (控制點)
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p1_x = waypoints[i][0]
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p1_y = waypoints[i][1]
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# P2 = post_turn (弧線結束)
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p2_x = waypoints[i][0] + d_out_x * T
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p2_y = waypoints[i][1] + d_out_y * T
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# 加入 pre_turn 點 (方向 = incoming)
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path.append((p0_x, p0_y, d_in_x, d_in_y))
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# 加入 Bezier 插值點
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for j in range(1, curve_resolution):
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t = j / curve_resolution
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# B(t) = (1-t)²·P0 + 2t(1-t)·P1 + t²·P2
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one_minus_t = 1.0 - t
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bx = one_minus_t * one_minus_t * p0_x + \
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2 * t * one_minus_t * p1_x + \
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t * t * p2_x
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by = one_minus_t * one_minus_t * p0_y + \
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2 * t * one_minus_t * p1_y + \
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t * t * p2_y
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# B'(t) = 2(1-t)(P1-P0) + 2t(P2-P1) → 切線方向
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tdx = 2 * one_minus_t * (p1_x - p0_x) + 2 * t * (p2_x - p1_x)
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tdy = 2 * one_minus_t * (p1_y - p0_y) + 2 * t * (p2_y - p1_y)
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# 正規化
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t_len = math.sqrt(tdx ** 2 + tdy ** 2)
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if t_len > 0.01:
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tdx /= t_len
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tdy /= t_len
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else:
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tdx, tdy = d_in_x, d_in_y
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path.append((bx, by, tdx, tdy))
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# 加入 post_turn 點 (方向 = outgoing)
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path.append((p2_x, p2_y, d_out_x, d_out_y))
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# 最後一個航點
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path.append((waypoints[-1][0], waypoints[-1][1],
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segments[-1][0], segments[-1][1]))
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return path
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# ------------------------------------------------------------------ 柵狀掃描
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def _calculate_grid_sweep(self, drone_positions, rect_corners_local, params):
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"""柵狀掃描：掃描方向沿矩形長邊，切割方向沿短邊"""
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N = len(drone_positions)
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line_spacing = params.get('line_spacing', 5.0)
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altitude = params.get('altitude', self.base_altitude)
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c0, c1, c2, c3 = rect_corners_local
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edge_a = (c1[0] - c0[0], c1[1] - c0[1])
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len_a = math.sqrt(edge_a[0] ** 2 + edge_a[1] ** 2)
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edge_b = (c3[0] - c0[0], c3[1] - c0[1])
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len_b = math.sqrt(edge_b[0] ** 2 + edge_b[1] ** 2)
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if len_a >= len_b:
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sweep_vec = edge_a
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sweep_len = len_a
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cut_vec = edge_b
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cut_len = len_b
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sweep_start_mid = ((c0[0] + c3[0]) / 2, (c0[1] + c3[1]) / 2)
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sweep_end_mid = ((c1[0] + c2[0]) / 2, (c1[1] + c2[1]) / 2)
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cut_start_corner = c0
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else:
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sweep_vec = edge_b
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sweep_len = len_b
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cut_vec = edge_a
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cut_len = len_a
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sweep_start_mid = ((c0[0] + c1[0]) / 2, (c0[1] + c1[1]) / 2)
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sweep_end_mid = ((c3[0] + c2[0]) / 2, (c3[1] + c2[1]) / 2)
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cut_start_corner = c0
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sweep_dir = (sweep_vec[0] / sweep_len, sweep_vec[1] / sweep_len)
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cut_dir = (cut_vec[0] / cut_len, cut_vec[1] / cut_len)
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C_x = sum(p[0] for p in drone_positions) / N
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C_y = sum(p[1] for p in drone_positions) / N
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dist_to_start = math.sqrt(
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(C_x - sweep_start_mid[0]) ** 2 + (C_y - sweep_start_mid[1]) ** 2
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)
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dist_to_end = math.sqrt(
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(C_x - sweep_end_mid[0]) ** 2 + (C_y - sweep_end_mid[1]) ** 2
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)
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if dist_to_start <= dist_to_end:
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near_corner_a = cut_start_corner
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else:
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sweep_dir = (-sweep_dir[0], -sweep_dir[1])
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near_corner_a = (cut_start_corner[0] + sweep_vec[0],
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cut_start_corner[1] + sweep_vec[1])
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projections = [
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((pos[0] - C_x) * cut_dir[0] + (pos[1] - C_y) * cut_dir[1], i)
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for i, pos in enumerate(drone_positions)
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]
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projections.sort()
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strip_width = cut_len / N
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drone_sweep_proj = C_x * sweep_dir[0] + C_y * sweep_dir[1]
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near_sweep_proj = near_corner_a[0] * sweep_dir[0] + near_corner_a[1] * sweep_dir[1]
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gather_sweep_proj = (drone_sweep_proj + near_sweep_proj) / 2
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all_waypoints = [None] * N
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for rank, (_, original_idx) in enumerate(projections):
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strip_center_offset = (rank + 0.5) * strip_width
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base_x = near_corner_a[0] + cut_dir[0] * strip_center_offset
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base_y = near_corner_a[1] + cut_dir[1] * strip_center_offset
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waypoints_list = []
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gather_offset = gather_sweep_proj - near_sweep_proj
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gx = base_x + sweep_dir[0] * gather_offset
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gy = base_y + sweep_dir[1] * gather_offset
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waypoints_list.append((gx, gy, altitude))
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num_lines = max(1, int(strip_width / line_spacing))
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actual_spacing = strip_width / num_lines
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first_line_offset = (rank * strip_width) + actual_spacing / 2
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entry_x = near_corner_a[0] + cut_dir[0] * first_line_offset
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entry_y = near_corner_a[1] + cut_dir[1] * first_line_offset
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waypoints_list.append((entry_x, entry_y, altitude))
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current_cut_offset = first_line_offset
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for line_idx in range(num_lines):
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line_near_x = near_corner_a[0] + cut_dir[0] * current_cut_offset
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line_near_y = near_corner_a[1] + cut_dir[1] * current_cut_offset
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line_far_x = line_near_x + sweep_dir[0] * sweep_len
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line_far_y = line_near_y + sweep_dir[1] * sweep_len
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if line_idx % 2 == 0:
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waypoints_list.append((line_far_x, line_far_y, altitude))
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else:
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waypoints_list.append((line_near_x, line_near_y, altitude))
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if line_idx < num_lines - 1:
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next_cut_offset = current_cut_offset + actual_spacing
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next_near_x = near_corner_a[0] + cut_dir[0] * next_cut_offset
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next_near_y = near_corner_a[1] + cut_dir[1] * next_cut_offset
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next_far_x = next_near_x + sweep_dir[0] * sweep_len
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next_far_y = next_near_y + sweep_dir[1] * sweep_len
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if line_idx % 2 == 0:
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waypoints_list.append((next_far_x, next_far_y, altitude))
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else:
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waypoints_list.append((next_near_x, next_near_y, altitude))
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current_cut_offset = next_cut_offset
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all_waypoints[original_idx] = waypoints_list
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return all_waypoints
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# ================================================================================
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# 測試
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|
|
# ================================================================================
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|
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if __name__ == "__main__":
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|
planner = FormationPlanner()
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|
|
drones = [
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(24.123450, 120.567800, 0.0),
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(24.123470, 120.567820, 0.0),
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(24.123440, 120.567810, 0.0),
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(24.123460, 120.567830, 0.0),
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]
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target = (24.12400, 120.56795, 10.0)
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|
|
# M-Formation
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|
|
wps, origin = planner.plan_formation_mission(drones, target, MissionType.M_FORMATION)
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|
|
print("M-Formation:")
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|
|
for i, wp_list in enumerate(wps):
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|
|
print(f" Drone {i}: {len(wp_list)} waypoints")
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|
|
|
|
# Leader-Follower (Bezier 轉彎)
|
|
|
route = [
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|
|
(24.12345, 120.56780),
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|
(24.12370, 120.56800),
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|
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(24.12390, 120.56820),
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|
|
(24.12400, 120.56800),
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|
|
(24.12420, 120.56790),
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|
|
]
|
|
|
wps_lf, origin_lf = planner.plan_formation_mission(
|
|
|
drones, target, MissionType.LEADER_FOLLOWER,
|
|
|
params={
|
|
|
'route_waypoints': route,
|
|
|
'lateral_offset': 3.0,
|
|
|
'longitudinal_spacing': 5.0,
|
|
|
'turn_margin': 0.35,
|
|
|
'curve_resolution': 8,
|
|
|
'altitude': 10.0
|
|
|
}
|
|
|
)
|
|
|
print(f"\nLeader-Follower (Bezier turns):")
|
|
|
for i, wp_list in enumerate(wps_lf):
|
|
|
print(f" Drone {i}: {len(wp_list)} waypoints")
|
|
|
for j, wp in enumerate(wp_list):
|
|
|
print(f" WP{j}: ({wp[0]:.6f}, {wp[1]:.6f}, {wp[2]:.1f})")
|
|
|
|
|
|
# Grid Sweep
|
|
|
rect = [
|
|
|
(24.1237, 120.5679),
|
|
|
(24.1237, 120.5683),
|
|
|
(24.1240, 120.5683),
|
|
|
(24.1240, 120.5679)
|
|
|
]
|
|
|
wps2, origin2 = planner.plan_formation_mission(
|
|
|
drones, target, MissionType.GRID_SWEEP,
|
|
|
params={'rect_corners': rect, 'line_spacing': 5.0, 'altitude': 10.0}
|
|
|
)
|
|
|
print(f"\nGrid Sweep:")
|
|
|
for i, wp_list in enumerate(wps2):
|
|
|
print(f" Drone {i}: {len(wp_list)} waypoints") |