An autonomous underwater vehicle (AUV) navigates without GPS by dead-reckoning between pre-programmed waypoints, steering its thrusters toward each target and using sonar to sense its surroundings.
heading_error = atan2(target − pos)
ω = clamp(k_turn · heading_error, ±ω_max)
v = thrust · v_max
battery(t) = battery(0) − ∫ (k1 + k2·thrust³) dt
- Thrust — sets forward propulsion speed; higher thrust drains the battery faster (drag scales with speed³).
- Turn rate — how aggressively the AUV can steer its heading toward the next waypoint.
- Sonar range — radius of the pulsing sonar cone used to "sense" the seafloor and nearby waypoints.
- Survey grid / Orbit dive — switches the waypoint pattern between a lawnmower survey transect and a spiral descent orbit.
Real AUVs like REMUS or Autosub use exactly this waypoint-and-dead-reckoning approach to map seafloors, track pollution plumes, and inspect subsea infrastructure in water far too deep or hazardous for divers.