Buoyancy Compensation for Underwater Robots (2D)

Depth & Ballast Control

Target hover depth 25 m

Pressure-compression strength 1.0×

Ballast controller gain 1.0×

Uncontrolled ROV

Depth

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Depth error

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Buoyancy-controlled AUV

Depth

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Depth error

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Ballast tank volume

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Why buoyancy alone is unstable at depth

Water pressure grows with depth (P ≈ P₀·(1 + d/10 m)). Any gas-filled space in a robot's housing — trapped air, foam syntactic buoyancy, a sealed void — obeys Boyle's law and shrinks as pressure rises: V_gas(d) = V_gas0·P₀/P(d). Less gas volume means less displaced water, so buoyant force drops exactly where the robot needs it most: deeper.

F_net(d) = m·g − ρ·g·[V_hull + V_gas(d) + V_ballast]
V_gas(d) = V_gas0 · P₀ / P(d)      (Boyle's law)

Trim a robot neutrally buoyant at one depth and this becomes a positive-feedback loop: sink a little → pressure rises → gas compresses → buoyancy drops → sink more. The same loop runs in reverse if it drifts shallower, so the equilibrium is unstable in both directions — without correction the robot runs away from its target depth rather than settling.

Uncontrolled ROV — fixed buoyant volume, trimmed neutral at the target depth. A small disturbance is all it takes to trigger the runaway.
Buoyancy-controlled AUV — a pump continuously senses depth error and moves water in or out of a ballast tank, adding or removing buoyant volume to cancel the compression effect in real time.
Compression strength — how sharply gas volume falls off with depth; higher values make the uncontrolled runaway faster and more dramatic.
Controller gain — how aggressively the ballast pump reacts to depth error; too low and it can't keep up, too high and it overshoots.

Depth vs. time

Uncontrolled ROV Buoyancy-controlled AUV Target depth