Distributed Model Predictive Control for Cooperative Multirotor Landing on Uncrewed Surface Vessel in Waves

TL;DR

This work addresses autonomous landing of a multirotor on a USV in wave environments using a sequential distributed MPC framework. The key idea is to augment standard tracking MPCs with artificial intermediate goals exchanged between the UAV and USV, enabling consensus landing without full trajectory sharing, and to integrate a spatial-temporal wave map $f_W(\cdot)$ to time the landing while minimizing USV tilt via a tilt-cost. The approach yields three concrete benefits: (1) robust coordination under limited bandwidth and potential comms loss, (2) real-time optimization of a safe landing location and timing, and (3) a practical mechanism to prefer calmer water regions before touchdown. The simulations compare 'Cooperative', 'Calm', and 'Ride the Wave' strategies, showing that steering toward calmer waters ('Calm') reduces tilt and improves safety, with a tunable trade-off between tilt minimization and landing speed controlled by $\lambda_m$. Future work includes online learning of the wave map $f_W(\cdot)$ and experimental validation on physical UAV-USV platforms.

Abstract

Heterogeneous autonomous robot teams consisting of multirotor and uncrewed surface vessels (USVs) have the potential to enable various maritime applications, including advanced search-and-rescue operations. A critical requirement of these applications is the ability to land a multirotor on a USV for tasks such as recharging. This paper addresses the challenge of safely landing a multirotor on a cooperative USV in harsh open waters. To tackle this problem, we propose a novel sequential distributed model predictive control (MPC) scheme for cooperative multirotor-USV landing. Our approach combines standard tracking MPCs for the multirotor and USV with additional artificial intermediate goal locations. These artificial goals enable the robots to coordinate their cooperation without prior guidance. Each vehicle solves an individual optimization problem for both the artificial goal and an input that tracks it but only communicates the former to the other vehicle. The artificial goals are penalized by a suitable coupling cost. Furthermore, our proposed distributed MPC scheme utilizes a spatial-temporal wave model to coordinate in real-time a safer landing location and time the multirotor's landing to limit severe tilt of the USV.

Figures (6)

• Figure 1: Block diagram of our proposed distributed model predictive control (MPC): Our approach uses standard tracking MPCs for a multirotor and USV augmented with artificial goal locations. Each vehicle solves an individual optimization problem for both the artificial goal and an input that tracks it but only communicates the former. Our proposed distributed MPC simultaneously finds a consensus landing location between the UAV and USV (through cooperation cost $J^{\text{co-op}}(\cdot)$), tracks it (through a tracking cost $J^{\text{track}}(\cdot)$), and leverages a spatial-temporal wave model $f_W(\cdot)$ to optimize a location and time that aids safe landing by minimizing large tilt angles of the USV (through a tilt cost $J^{\text{tilt}}(\cdot)$).
• Figure 2: Visualization of multirotor trajectory (solid red), multirotor goal (dashed red), USV trajectory (solid yellow) and USV goal (dashed yellow) using a distributed MPC framework with no tilt cost $J^{\text{tilt}}(\cdot)$ for either vehicle in (a) "Cooperative" Strategy, our proposed $J^{\text{tilt}}_S(\cdot)$ in (b) "Calm" Strategy and an alternative tilt cost in (c) "Ride the Wave" Strategy. Our proposed "Calm" Strategy leads to a lower tilt of the USV before reaching a consensus on the final landing location.
• Figure 3: Trade-off between average tilt at the landing location vs the distance the USV travels. As we increase the weight on $\lambda_S$, the tilt at landing decreases but the USV has to travel further to enable this.
• Figure 4: Visualization of multirotor trajectory (solid red), multirotor goal (dashed red), USV trajectory (solid yellow) and USV goal (dashed yellow) using a distributed MPC framework our proposed $J^{\text{tilt}}_S(\cdot)$ where there is a $10$ s communication loss between the vehicles at (a) $0.02$ s and (b) $5$ s. Our proposed approach is robust to communication breaks.
• Figure 5: Visualization of multirotor altitude as it descends to land for increasing $\lambda_m$. For $\lambda_m > 10000$ (dashed and dotted black), the multirotor is very sensitive to small changes in the tilt at landing and, therefore, takes longer to land. We propose $\lambda_m \approx 10000$ (solid red) to balance this trade-off.