chore: rename libs→common_libs, all bot dirs to _garage suffix, fix all path refs

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

common_libs/radar_lock/radar_lock.nim

@@ -0,0 +1,38 @@
+## Standalone radar lock module for Robocode Tank Royale (1v1).
+## No bot-specific imports — takes plain floats, returns radarTurnRate.
+##
+## Tank Royale radar uses standard math convention: 0° = east, CCW positive.
+## Angles are in degrees.
+
+import std/math
+
+const
+  MaxRadarTurn* = 45.0
+  DefaultOvershootDeg* = 5.0
+
+var overShootDeg* = DefaultOvershootDeg
+
+proc init*() =
+  ## Reset module to defaults.
+  ## In your bot's constructor set:
+  ##   adjustRadarForBodyTurn = true
+  ##   adjustRadarForGunTurn  = true
+  overShootDeg = DefaultOvershootDeg
+
+proc normalizeRelative(angle: float64): float64 {.inline.} =
+  result = angle mod 360.0
+  if result >= 180.0: result -= 360.0
+  elif result < -180.0: result += 360.0
+
+proc doRadar*(currentRadarHeading, enemyBearing: float64): float64 =
+  ## Returns radarTurnRate (degrees/tick, positive = clockwise).
+  ##
+  ## currentRadarHeading: current radar direction in degrees (0=east, CCW+).
+  ## enemyBearing:        absolute bearing to enemy in same coordinate system.
+  ##
+  ## Handles angle wrapping, clamps to [-45, +45], adds overshoot sweep.
+  var turn = normalizeRelative(enemyBearing - currentRadarHeading)
+  # Add overshoot in the same direction as the turn to maintain lock
+  if turn < 0.0: turn -= overShootDeg
+  else:          turn += overShootDeg
+  result = turn.clamp(-MaxRadarTurn, MaxRadarTurn)