Translational and Scaling Formation Maneuver Control via a Bearing-Based Approach (1506.05636v2)

Abstract: This paper studies distributed maneuver control of multi-agent formations in arbitrary dimensions. The objective is to control the translation and scale of the formation while maintaining the desired formation pattern. Unlike conventional approaches where the target formation is defined by relative positions or distances, we propose a novel bearing-based approach where the target formation is defined by inter-neighbor bearings. Since the bearings are invariant to the translation and scale of the formation, the bearing-based approach provides a simple solution to the problem of translational and scaling formation maneuver control. Linear formation control laws for double-integrator dynamics are proposed and the global formation stability is analyzed. This paper also studies bearing-based formation control in the presence of practical problems including input disturbances, acceleration saturation, and collision avoidance. The theoretical results are illustrated with numerical simulations.

• The paper introduces a bearing-based formation control method that guarantees convergence during translation and scaling maneuvers.
• It formulates control laws using relative position and acceleration feedback to manage leader-follower dynamics in multi-agent systems.
• It develops the bearing Laplacian matrix for stability analysis, ensuring robust performance in complex, dynamic environments.

Overview of Bearing-Based Formation Control for Multi-Agent Systems

This paper investigates the distributed maneuver control of multi-agent formations in arbitrary dimensions with a focus on maintaining desired formation patterns through translation and scaling. Traditional methods for formation control typically define target formations by relative positions or distances between agents. This paper introduces a novel bearing-based approach where target formations are defined by inter-neighbor bearings. This approach exploits the properties of bearings, which are invariant to translation and scale, allowing for a straightforward solution to translational and scaling formation maneuver control.

Problem Formulation

The paper formulates a problem of maintaining a formation defined by inter-neighbor bearings while allowing translational and scaling maneuvers. To address this, the paper defines a target formation consisting of both leaders (agents with predefined motion) and followers (agents whose motion is governed by control laws). The central task is to ensure that followers adjust their movements relative to their neighbors to achieve the desired bearing configuration, despite translational and scaling maneuvers.

Control Laws

Two linear control laws for followers modeled as double-integrator systems are proposed. The first control law is suited to scenarios where the leader velocities are constant. It utilizes relative position and velocity feedback to ensure global exponential convergence to the target formation. The second control law incorporates acceleration feedback and is designed to handle time-varying leader velocities, allowing for responsive adjustments to dynamic conditions.

Bearing Laplacian and Stability

A significant contribution of the paper is the development of the bearing Laplacian matrix, which plays a critical role in analyzing the formation’s stability. The matrix incorporates both the interconnection topology and the inter-neighbor bearings of the formation, and the global formation stability is examined through the matrix's properties. The paper leverages the larger framework of bearing rigidity theory, asserting that formations defined by inter-neighbor bearings can be uniquely determined and are stable under specified conditions.

Practical Considerations and Extensions

The paper extends the formulations to address practical issues such as input disturbances, acceleration saturation, and collision avoidance. An integral control term is introduced to handle constant input disturbances, further ensuring convergence even in the presence of disturbances. Simulation results demonstrate the efficacy of the proposed methods in complex environments, including three-dimensional spaces and scenarios requiring obstacle avoidance.

Theoretical and Practical Implications

The bearing-based approach offers theoretical implications for the broader field of distributed control systems and practical applications in environments where multi-agent systems need to dynamically adjust their formations—a common scenario in robotics and autonomous vehicle fleets. This paper’s findings suggest the potential for more nuanced control structures that can handle higher dimensional spaces and dynamic conditions, presenting a robust alternative to position-based or distance-based formation control methods.

In conclusion, the authors deliver a comprehensive framework for bearing-based formation control, validated through theoretical analysis and simulations. Future research avenues include exploring its applicability to more complex agent dynamics, such as nonholonomic systems, and further refining the conditions under which the formations maintain stability and avoid collisions in various operational contexts.