Plug-and-Play Cooperative Navigation: From Single-Agent Navigation Fields to Graph- Maintaining Distributed MAS Controllers

A class of closed-form distributed controllers achieving leader-following in a multiagent system (MAS) with distance-limited communications in a compact obstructed environment is developed: given a user-provided navigation field for a single point agent as an input, the desired MAS PnP (“Plug-and-Play”) controller is obtained through a closed-form expression. In particular, cooperative navigation in an environment of arbitrary complexity is achievable whenever an adequate single-agent navigation solution is available. Sufficient conditions on the navigation field in relation to the communication radius are developed, guaranteeing that a prescribed initial graph of agents retains all of its edges while following a leader. In contrast with existing work, the standard radial symmetric interactions among agents are replaced with an asymmetrically rescaled version of the provided navigation field, removing the need for assumptions such as the sphericity or convexity of obstacles, and enabling the switching of the attractive interactions between neighbors on and off as needed. This approach elucidates the tradeoffs between communication range, the size of the MAS, the control effort required for cooperation, and the complexity of navigating in the provided environment. The reliance of the approach on navigation fields enables the use of state-of-the-art sensing-based reactive navigation methods designed for settings with incomplete prior knowledge of the environment and based on a sphere-world model layer. For this reason, two case studies are provided—one of sphere worlds, and the other of topological sphere worlds with star-convex obstacles—comparing different variations of the PnP controller derived from state-of-the-art single-agent navigation fields.

I. Introduction

Mobile robotic platforms are increasingly expected to operate in cooperative settings, which creates a need for efficient distributed navigation methods mindful of communication constraints. Nonconvex obstacles in real-life settings increase the tension between task execution and the need for maintaining a connected communication structure by introducing nonconvex inequality constraints into the problem. Safety requirements such as collision-avoidance among agents complicate the problem even further. A standard assumption in the literature on distributed multiagent system (MAS) navigation with connectivity maintenance is that any pair of agents may communicate state information to each other, provided the distance between them does not exceed a prescribed threshold . Such pairs are often referred to as available edges. Despite many advances, the MAS literature has stuck to a set of conservative assumptions simplifying the geometry of obstacles or removing them altogether, while focusing on other aspects and extensions of the problem. Over time, the initial smooth controllers for holonomic single-integrator agents requiring continuous communication [1], [2], [3], [4], [5] gave way to general discussions of graph maintenance such as [6]; to solutions allowing for complex behaviors such as formation reconfiguration [7]; and to challenging contexts such as intermittent communication and actuation [8], [9], [10]; and second order agent dynamics [11]—just to name a few. At the same time, new advances in the literature on single agent reactive navigation based on a recent broad extension [12] of the Rimon-Koditschek navigation paradigm [13] have made reactive navigation possible even with multiple nonconvex obstacles [14], [15]. More refined methods, specialized for the plane, using harmonic functions have also been developed [16], [17]. Following a preliminary conference version [18], this article develops a framework for directly harnessing the capabilities of arbitrary single-agent navigation methods for the purpose of cooperative navigation of a connected MAS, while removing the need for advanced knowledge of the environment beyond what is required for navigation by a single agent using the provided method. The framework introduces a class of extensions of a provided single-agent navigation solution to a multiagent one, along with formal guarantees of communication graph maintenance, making any future single-agent navigation methods immediately applicable in the distributed MAS setting. This “future-proofing” feature is of particular importance in dimension 3 and higher, where single-agent navigation methods are currently largely unavailable for domains that are not topological sphere worlds.¹

With the notable exception of [19], where navigation functions are constructed for topologically complex domains in such as knot complements, subject to specific curvature conditions.