Impact-Aware MPC for UAV Landings on Heaving Platforms

> Paper: Impact-Aware Model Predictive Control for UAV Landing on a Heaving Platform > Authors: Jess Stephenson, Melissa Greeff > arXiv: 2604.21078 | 2026-04-28

The challenge of landing on a moving deck

Imagine a UAV trying to land on a naval vessel while waves make the deck heave up and down. If the UAV descends as if landing on fixed ground:

• A rising deck can collide with it → huge impact forces
• A falling deck can cause it to miss entirely → crashing into the sea
• Contact rebound can toss the UAV back up, losing control

Landing on a heaving platform is one of the hardest challenges in robot control.

MPC: control by predicting the future

Model Predictive Control (MPC) does not make decisions from the current state alone. It predicts system behavior over a future horizon and optimizes the whole trajectory — like a driver looking tens of meters ahead at curves, vehicles, and pedestrians, then planning the entire driving path.

But conventional MPC has a blind spot: it does not model impacts.

The impact-aware breakthrough

The key innovation of this research is explicitly modeling the impact process within the MPC framework:

1. Landing is modeled as a rigid-body impact at the velocity level 2. Newton's restitution law describes the rebound behavior after contact 3. The impact constraints are embedded as a linear complementarity problem (LCP) 4. MPC optimizes the trajectory considering both flight dynamics and impact dynamics

This means the UAV, when deciding *when, where, and at what speed* to land, is already anticipating the physics of the contact instant.

Why this is harder than a 'soft landing'

'Soft landing' usually means reducing contact velocity. On a heaving deck:

• Descending too slowly may miss the deck if it sinks before contact
• Descending too fast risks damaging the UAV or the deck
• The optimal strategy may be to follow the deck's motion and touch down at the instant of minimal relative velocity

Impact-aware MPC finds this dynamic optimum — not minimizing absolute speed, but minimizing the relative impact at the moment of contact.

Physical constraints cannot be bypassed

Echoing Feynman's lesson that *"Nature cannot be fooled"*:

• You can optimize trajectories with algorithms
• You can sense the environment with sensors
• But you cannot violate Newton's laws

The success of impact-aware MPC lies in not trying to bypass physics, but incorporating physical constraints directly into the optimization problem.

Takeaways for control system design

If you design robotic control systems, ask yourself:

1. Does my control framework account for all relevant physical processes? 2. Do I model unavoidable constraints (like impacts) as part of the optimization problem? 3. Is my prediction horizon long enough to capture key dynamic interactions? 4. Have I validated robustness under varying environmental conditions?

Impact-aware MPC shows that in the physical world, the best control doesn't avoid all difficulties — it understands and leverages physical laws to handle them gracefully.

Once a UAV learns to *anticipate* impact, it can land safely in the most turbulent environments.