Distributed Iterative Learning Control for a Team of Quadrotors (1603.05933v2)

Abstract: The goal of this work is to enable a team of quadrotors to learn how to accurately track a desired trajectory while holding a given formation. We solve this problem in a distributed manner, where each vehicle has only access to the information of its neighbors. The desired trajectory is only available to one (or few) vehicles. We present a distributed iterative learning control (ILC) approach where each vehicle learns from the experience of its own and its neighbors' previous task repetitions, and adapts its feedforward input to improve performance. Existing algorithms are extended in theory to make them more applicable to real-world experiments. In particular, we prove stability for any causal learning function with gains chosen according to a simple scalar condition. Previous proofs were restricted to a specific learning function that only depends on the tracking error derivative (D-type ILC). Our extension provides more degrees of freedom in the ILC design and, as a result, better performance can be achieved. We also show that stability is not affected by a linear dynamic coupling between neighbors. This allows us to use an additional consensus feedback controller to compensate for non-repetitive disturbances. Experiments with two quadrotors attest the effectiveness of the proposed distributed multi-agent ILC approach. This is the first work to show distributed ILC in experiment.

• The paper extends classical iterative learning control to a distributed framework, allowing quadrotors to collaboratively learn through local neighbor information.
• The approach integrates a consensus feedback controller to robustly manage non-repetitive disturbances, significantly improving overall system stability.
• Experimental validation demonstrated a 24% reduction in tracking error and a 53% decrease in error variability, confirming the method’s theoretical advancements.

Overview of Distributed Iterative Learning Control for a Team of Quadrotors

The paper presents a sophisticated approach to formation control of multi-agent systems (MAS), specifically focusing on quadrotors, using a distributed iterative learning control (ILC) framework. The primary objective is to enable a group of quadrotors to accurately track a predefined trajectory while maintaining a specific formation, all facilitated through a distributed control scheme. This goal is achieved by leveraging the iterative learning capabilities where each quadrotor in the team learns from its own experience and the observations of its neighbors.

Key Contributions

The research makes several pertinent contributions to the field of distributed control in multi-agent systems:

1. Distributed ILC Framework: The paper extends classical ILC methods to a distributed setting, allowing multiple quadrotors to collaboratively learn a task through iterations. The ILC algorithm here is not tethered to a central controller but is based on local information exchanges between neighboring quadrotors.
2. Theoretical Extensions: The authors extend existing stability proofs for D-type ILC algorithms to accommodate more general, causally defined learning functions, thereby providing additional flexibility in the design of ILC algorithms. This extension is crucial as it allows the incorporation of both position and derivative errors, enhancing convergence speed and tracking performance.
3. Stability and Convergence Analysis: A significant theoretical advancement is made by proving the stability of their extended ILC approach for any causal learning function, subject to a straightforward scalar condition involving learning gains and system dynamics.
4. Consensus Feedback Integration: It introduces a consensus-based feedback controller to handle non-repetitive disturbances, enhancing the system's robustness. The integration does not affect the ILC's stability, as demonstrated through rigorous theoretical analysis.
5. Experimental Validation: The experimental implementation involves a pair of quadrotors tasked with formation control and trajectory tracking. These experiments underscore the practical viability of the distributed ILC approach, marking a rare illustrative success of distributed ILC in physical experimentation beyond simulations.

Numerical Findings

The experimental results are particularly noteworthy. The setup exhibited significant performance improvements, with errors decreasing substantially across trials. The robustness against disturbances was quantifiably improved when consensus feedback was involved, indicating a 24% reduction in relative tracking error and a reduction of 53% in error variability post-convergence. This empirical evidence aligns well with the theoretical assertions made in the paper.

Implications and Future Directions

Practically, the research paves the way for enhanced autonomy in multi-agent robotic systems, particularly in applications requiring precise formation control such as autonomous drone fleets, cooperative transport, and surveillance tasks. Theoretically, the introduction of flexible ILC frameworks that are robust against non-repetitive disturbances sets a precedent for future research in ILC algorithms for dynamically coupled systems.

For future research, the exploration of more complex network topologies, larger teams of agents, and real-time adaptive learning rates could be valuable. Furthermore, integrating this approach with other forms of machine learning could yield more adaptive and resilient control strategies. Additionally, the inclusion of safety constraints and collision avoidance mechanisms in the distributed learning framework would enhance the applicability of the method in real-world scenarios.

In summary, this paper offers a compelling contribution to the field of distributed control for multi-agent systems, characterized by its strong theoretical foundations and validated through experimental rigor. This work not only advances the existing methodologies but also supports the broader implementation of learning-based control strategies in robotic systems.