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Group-Control Motion Planning Framework for Microrobot Swarms in a Global Field

Siyu Li, Afagh Mehri Shervedani, Miloš Žefran, Igor Paprotny

TL;DR

This work introduces a group-control framework for coordinating large microrobot swarms in a global (uniform) field, enabling STLC in positions with $m = \log_2(n+2) + 1$ groups. It builds on onboard Physical Finite-State Machines (PFSMs) to assign robots to multiple groups, constructively translating some while rotating others and ultimately achieving independent motion through bilateral vector fields and Lie-bracket-inspired motions. The paper analyzes controllability (including unilateral-to-bilateral conversion and orientation limits) and develops a motion-planning approximation scheme that trades off between the number of moving robots per primitive and planning complexity, with complexity bounds tied to the primitive order $k$ relative to $k_{max}$ for STLC. Simulations and instantiations demonstrate scalability and show how subgroups and Lie-bracket primitives can substantially reduce planning complexity while increasing path length and execution time, highlighting practical implications for microassembly and targeted drug delivery in dense microrobot swarms.

Abstract

This paper investigates how a novel paradigm called group-control can be effectively used for motion planning for microrobot swarms in a global field. We prove that Small-Time Local Controllability (STLC) in robot positions is achievable through group-control, with the minimum number of groups required for STLC being $\log_2(n + 2) + 1$ for $n$ robots. We then discuss the trade-offs between control complexity, motion planning complexity, and motion efficiency. We show how motion planning can be simplified if appropriate primitives can be achieved through more complex control actions. We identify motion planning problems that balance the number of motion primitives with planning complexity. Various instantiations of these motion planning problems are explored, with simulations used to demonstrate the effectiveness of group-control.

Group-Control Motion Planning Framework for Microrobot Swarms in a Global Field

TL;DR

This work introduces a group-control framework for coordinating large microrobot swarms in a global (uniform) field, enabling STLC in positions with groups. It builds on onboard Physical Finite-State Machines (PFSMs) to assign robots to multiple groups, constructively translating some while rotating others and ultimately achieving independent motion through bilateral vector fields and Lie-bracket-inspired motions. The paper analyzes controllability (including unilateral-to-bilateral conversion and orientation limits) and develops a motion-planning approximation scheme that trades off between the number of moving robots per primitive and planning complexity, with complexity bounds tied to the primitive order relative to for STLC. Simulations and instantiations demonstrate scalability and show how subgroups and Lie-bracket primitives can substantially reduce planning complexity while increasing path length and execution time, highlighting practical implications for microassembly and targeted drug delivery in dense microrobot swarms.

Abstract

This paper investigates how a novel paradigm called group-control can be effectively used for motion planning for microrobot swarms in a global field. We prove that Small-Time Local Controllability (STLC) in robot positions is achievable through group-control, with the minimum number of groups required for STLC being for robots. We then discuss the trade-offs between control complexity, motion planning complexity, and motion efficiency. We show how motion planning can be simplified if appropriate primitives can be achieved through more complex control actions. We identify motion planning problems that balance the number of motion primitives with planning complexity. Various instantiations of these motion planning problems are explored, with simulations used to demonstrate the effectiveness of group-control.
Paper Structure (14 sections, 5 theorems, 8 equations, 1 figure, 1 table)

This paper contains 14 sections, 5 theorems, 8 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. MicroStressBot
  4. Physical FSM Robots
  5. Group-Control
  6. Modeling
  7. Dynamics
  8. Switched and Embedded Systems
  9. Controllability Analysis
  10. Unilateral Control to Bilateral Control
  11. Control of Robot Orientation
  12. Small-Time Local Controllability (STLC)
  13. Motion Planning
  14. Motion Planning Approximation Scheme

Key Result

proposition thmcounterproposition

The control sequence $(f_i(d), f_m(\pi),f_i(d), f_m(\pi))$, where $f_i(d)$ corresponds to the activation of group $G_i$ so the robots in the group translate for $d$, corresponds to a vector field $h_i(\frac{2 d}{r})$ that rotates the robots that do not belong to the group $i$ by $\frac{2 d}{r}$ and

Figures (1)

  • Figure 1: The schematic of a MicroStressBot.

Theorems & Definitions (17)

  • definition thmcounterdefinition
  • remark thmcounterremark
  • proposition thmcounterproposition
  • proof
  • remark thmcounterremark
  • proposition thmcounterproposition
  • remark thmcounterremark
  • proposition thmcounterproposition
  • remark thmcounterremark
  • proof
  • ...and 7 more