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Scale-free vision-based aerial control of a ground formation with hybrid topology

Miguel Aranda, Youcef Mezouar, Gonzalo López-Nicolás, Carlos Sagüés

TL;DR

The paper tackles bearing-based formation control for ground robots using a vision-based, infrastructure-free approach with multiple UAVs that observe partial subsets of the team. It introduces a two-layer hybrid topology, computes ground-track goals via image-space similarity transforms, and fuses multi-camera commands into scale-consistent ground motions governed by a Lyapunov-stability framework. The key contributions are a scale-free, non-centralized control method that tolerates switching topology, a formal stability analysis, and simulations showing successful formation convergence for both small and larger teams. This work offers a scalable, robust framework for flexible aerial-ground coordination without requiring camera calibration or a shared reference frame, enabling practical deployment in dynamic environments.

Abstract

We present a novel vision-based control method to make a group of ground mobile robots achieve a specified formation shape with unspecified size. Our approach uses multiple aerial control units equipped with downward-facing cameras, each observing a partial subset of the multirobot team. The units compute the control commands from the ground robots' image projections, using neither calibration nor scene scale information, and transmit them to the robots. The control strategy relies on the calculation of image similarity transformations, and we show it to be asymptotically stable if the overlaps between the subsets of controlled robots satisfy certain conditions. The presence of the supervisory units, which coordinate their motions to guarantee a correct control performance, gives rise to a hybrid system topology. All in all, the proposed system provides relevant practical advantages in simplicity and flexibility. Within the problem of controlling a team shape, our contribution lies in addressing several simultaneous challenges: the controller needs only partial information of the robotic group, does not use distance measurements or global reference frames, is designed for unicycle agents, and can accommodate topology changes. We present illustrative simulation results.

Scale-free vision-based aerial control of a ground formation with hybrid topology

TL;DR

The paper tackles bearing-based formation control for ground robots using a vision-based, infrastructure-free approach with multiple UAVs that observe partial subsets of the team. It introduces a two-layer hybrid topology, computes ground-track goals via image-space similarity transforms, and fuses multi-camera commands into scale-consistent ground motions governed by a Lyapunov-stability framework. The key contributions are a scale-free, non-centralized control method that tolerates switching topology, a formal stability analysis, and simulations showing successful formation convergence for both small and larger teams. This work offers a scalable, robust framework for flexible aerial-ground coordination without requiring camera calibration or a shared reference frame, enabling practical deployment in dynamic environments.

Abstract

We present a novel vision-based control method to make a group of ground mobile robots achieve a specified formation shape with unspecified size. Our approach uses multiple aerial control units equipped with downward-facing cameras, each observing a partial subset of the multirobot team. The units compute the control commands from the ground robots' image projections, using neither calibration nor scene scale information, and transmit them to the robots. The control strategy relies on the calculation of image similarity transformations, and we show it to be asymptotically stable if the overlaps between the subsets of controlled robots satisfy certain conditions. The presence of the supervisory units, which coordinate their motions to guarantee a correct control performance, gives rise to a hybrid system topology. All in all, the proposed system provides relevant practical advantages in simplicity and flexibility. Within the problem of controlling a team shape, our contribution lies in addressing several simultaneous challenges: the controller needs only partial information of the robotic group, does not use distance measurements or global reference frames, is designed for unicycle agents, and can accommodate topology changes. We present illustrative simulation results.
Paper Structure (9 sections, 8 theorems, 16 equations, 5 figures, 1 algorithm)

This paper contains 9 sections, 8 theorems, 16 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System description and operating assumptions
  3. Similarity-based motion goals computation
  4. Coordinated ground robot control scheme
  5. Stability analysis
  6. Stability with changes in topology
  7. Motion and coordination of the aerial units
  8. Simulation results
  9. Practical Discussion and Conclusion

Key Result

Lemma 1

For any $p \in \mathcal{P}$, the robots form the desired shape if and only if $\mathbf{X}=\mathbf{0}$, which occurs if and only if $V=0$.

Figures (5)

  • Figure 1: Overview of the multirobot control system. Multiple (three, in this example) moving aerial units are used. Each computes (Section \ref{['ssimila']}) and transmits (a) motion commands for a set of ground robots in its camera's field of view (c). The robots that are controlled by multiple cameras combine the multiple received commands (d) to obtain their motion input, as described in Section \ref{['smulti']}. The UAVs can communicate (b) to coordinate their actions. The control task is for the ground robots' positions to form a specified shape.
  • Figure 2: Each UAV (i.e., 1 or 2) sees and controls only a partial subset of robots, using the corresponding partial set of template and current image points to compute the desired image points via a least-squares similarity.
  • Figure 3: Left: geometric variables and control vector computed for robot $i$ by camera $j$, defined in its image. Right-top: representation of $i's$ global motion vector computed from image information received from two cameras $j_1$ and $j_2$. Right-bottom: state of the robot on the ground plane.
  • Figure 4: One-camera simulation results. Top: robot paths (final positions joined by dashed lines) and projection of camera path on ground plane (initial point marked as square, final as circle). Row 2: linear (left), angular (right) robot velocities. Row 3: image traces of robots --initial and final point sets joined by dashed lines-- (left) and cost function (right). Row 4: scale (left) and rotation (right) of desired formation. Row 5: camera height (left) and rotation (right).
  • Figure 5: Simulation results. Top-left: Robot paths --final positions joined by dashed lines--, final camera fields of view --circles--, and paths of the three cameras; Top-right panel: evolution of linear and angular velocities of the ground robots (top), scales and rotations of the partial desired formations (bottom). Second row: template image (left), and image traces of the robots in $S_{j}^{c}$ for the three cameras (initial points marked as squares, final points as circles, joined by dashed lines). Bottom row: evolution of $V$ (highest-valued curve) and the three $V^{j}$ (left), camera heights (center) and camera velocity norms (right).

Theorems & Definitions (10)

  • Remark 1
  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Corollary 1
  • Corollary 2
  • Corollary 3
  • Corollary 4
  • Remark 2
  • Proposition 1