Cooperative distributed model predictive control for embedded systems: Experiments with hovercraft formations

TL;DR

This work addresses forming and controlling a robotic swarm under inter-robot coupling and obstacle constraints by applying cooperative DMPC. A decentralized Real-Time Iteration (dRTI) scheme with inner ADMM iterations and neighbor-to-neighbor copies enables solving a centralized OCP in a distributed fashion, with optional onboard or offboard deployment. Experimental results with four hovercraft demonstrate real-time operation at about $20\ \mathrm{Hz}$, including point-to-point transitions, trajectory tracking, and dynamic obstacle avoidance, while highlighting the impact of communication delays on consensus and performance. The findings show that dRTI can achieve near-centralized performance under realistic constraints and identify wireless communication as a key factor for future improvements and scalability to larger swarms.

Abstract

This paper presents experiments for embedded cooperative distributed model predictive control applied to a team of hovercraft floating on an air hockey table. The hovercraft collectively solve a centralized optimal control problem in each sampling step via a stabilizing decentralized real-time iteration scheme using the alternating direction method of multipliers. The efficient implementation does not require a central coordinator, executes onboard the hovercraft, and facilitates sampling intervals in the millisecond range. The formation control experiments showcase the flexibility of the approach on scenarios with point-to-point transitions, trajectory tracking, collision avoidance, and moving obstacles.

Figures (4)

• Figure 1: Schematic overview of our experimental setup. We compare onboard and offboard execution of our DMPC algorithm where coupled hovercraft exchange predicted state trajectories in each control step. For onboard execution, the position measurements are sent to the hovercraft that run the state estimation and DMPC algorithm. In offboard experiments, the observer and DMPC algorithm run on external computers that communicate via Ethernet and send the control signals to the hovercraft via Wi-Fi.
• Figure 2: Optimizer execution times per MPC step for five point-to-point transition experiments. Black vertical lines indicate the minimum, median, lower and upper quartiles, and maximum and colored areas highlight probability densities. All OCP solve times lie well below the control sampling interval and can thus be compensated, except for outliers in the onboard experiments with sampling interval $\Delta t = 50\,$ms. Figure produced with daviolinplot Karvelis2024.
• Figure 3: Hovercraft motion in the 2D plane for three maneuvers with onboard computation and sampling interval $\Delta t = 50\,$ms. Solid and dotted lines show closed-loop and predicted trajectories, respectively. Circles are the current hovercraft positions and crosses mark the setpoints. The top row depicts an abrupt setpoint change with a reconfiguration from a line into a rectangular formation. The center row shows a switch in position between neighbors while avoiding collisions. In the bottom row, the four hovercraft cross the table from left to right while dodging a dynamic obstacle shown in red. The red dashed line is the future obstacle trajectory which is unknown to the hovercraft and which is plotted for better visualization of the experiment.
• Figure 4: Trajectory tracking experiment with dynamic obstacle avoidance, offboard computation, and sampling interval $\Delta t = 50\,$ms. Areas shaded in gray mark stages where the obstacle inteferes with the tracking task. The DMPC controllers avoid collisions and continue tracking the trajectory once the obstacle has passed.

Theorems & Definitions (6)

• Remark 1: Compensation of computational delay
• Remark 2: Asynchronous decentralized ADMM
• Remark 3: Closed-loop stability Stomberg2024
• Remark 4: Linearized collision avoidance
• Remark 5: Parameter tuning
• Remark 6: Soft state constraints