Mixed Reality Environment and High-Dimensional Continuification Control for Swarm Robotics

TL;DR

This work addresses validating continuum-based density control for large swarms using a mixed reality platform that blends real differential-drive robots with virtual agents. It extends the continuification framework to higher dimensions, deriving a PDE mass-balance model $\rho_t + \nabla \cdot [\rho \mathbf{V}] = q$ with $\mathbf{V} = (\mathbf{f}*\rho)$, and a macroscopic controller that drives the error $e = \rho^d - \rho$ to zero, complemented by a discretization via a Poisson closure $\nabla^2 \varphi = q$ to produce microscopic inputs $\mathbf{u}_i = \mathbf{U}(\mathbf{x}_i,t)$. Validation on the platform includes monomodal and multimodal density targets and tracking scenarios, revealing promising regulation performance (low residual errors) but more modest tracking convergence due to finite agent numbers, kinematic constraints, and domain adaptations. The results demonstrate the platform’s viability for scalable swarm robotics experiments and provide practical insights into bridging theory and real-world implementation of continuum-based swarm controls. The work lays a foundation for larger-scale, more accurate experimental studies and informs future improvements in both theory and hardware deployment.

Abstract

Many new methodologies for the control of large-scale multi-agent systems are based on macroscopic representations of the emerging system dynamics, in the form of continuum approximations of large ensembles. These techniques, that are developed in the limit case of an infinite number of agents, are usually validated only through numerical simulations. In this paper, we introduce a mixed reality set-up for testing swarm robotics techniques, focusing on the macroscopic collective motion of robotic swarms. This hybrid apparatus combines both real differential drive robots and virtual agents to create a heterogeneous swarm of tunable size. We also extend continuification-based control methods for swarms to higher dimensions, and assess experimentally their validity in the new platform. Our study demonstrates the effectiveness of the platform for conducting large-scale swarm robotics experiments, and it contributes new theoretical insights into control algorithms exploiting continuification approaches.

Figures (7)

• Figure 1: Continuification control scheme (inspired by nikitin2021continuation). The schemes describes all the stages of the solution: ($i$) continuification, ($ii$) macroscopic control design, and ($iii$) discretization.
• Figure 2: (a) Render of a differential drive robot, and (b) inner view of the robot.
• Figure 3: Experimental platform. (a) A render of the real set-up, with 4 robots moving in the arena, and (b) a sketch of the platform, assuming virtual agents to be the black dots and real robots to be concentric circles.
• Figure 4: Control scheme for robot $i$. By measuring the overall density of the swarm, the continuification control inputs can be used to give the robots a desired position and velocity to track.
• Figure 5: Monomodal regulation. (a) Desired density, (b) steady-state configuration of the swarm, (c) percentage error in time, (d) KL divergence in time.

Theorems & Definitions (6)

• Remark
• Theorem 1: Macroscopic convergence
• proof
• Remark
• Remark
• Remark