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Motion Control of Two Mobile Robots under Allowable Collisions

Li Tan, Wei Ren, Xi-Ming Sun, Junlin Xiong

TL;DR

This work addresses motion control for two mobile robots in a shared workspace where collisions are allowed if non-damaging. It introduces a hybrid dynamical model that captures collision onset and impulse-induced state changes, revealing that standard CLF/CBF-based controllers may fail under allowable collisions. A three-step impulsive-control redesign—impose an impulse to change direction, drive away along a computed ray, then revert to the predefined controller—guarantees task accomplishment while preventing re-collision, chattering, and deadlock. Numerical results illustrate finite collisions and successful target convergence, underscoring practical impact for multi-robot systems operating in tight environments.

Abstract

This letter investigates the motion control problem of two mobile robots under allowable collisions. Here, the allowable collisions mean that the collisions do not damage the mobile robots. The occurrence of the collisions is discussed and the effects of the collisions on the mobile robots are analyzed to develop a hybrid model of each mobile robot under allowable collisions. Based on the effects of the collisions, we show the necessity of redesigning the motion control strategy for mobile robots. Furthermore, impulsive control techniques are applied to redesign the motion control strategy to guarantee the task accomplishment for each mobile robot. Finally, an example is used to illustrate the redesigned motion control strategy.

Motion Control of Two Mobile Robots under Allowable Collisions

TL;DR

This work addresses motion control for two mobile robots in a shared workspace where collisions are allowed if non-damaging. It introduces a hybrid dynamical model that captures collision onset and impulse-induced state changes, revealing that standard CLF/CBF-based controllers may fail under allowable collisions. A three-step impulsive-control redesign—impose an impulse to change direction, drive away along a computed ray, then revert to the predefined controller—guarantees task accomplishment while preventing re-collision, chattering, and deadlock. Numerical results illustrate finite collisions and successful target convergence, underscoring practical impact for multi-robot systems operating in tight environments.

Abstract

This letter investigates the motion control problem of two mobile robots under allowable collisions. Here, the allowable collisions mean that the collisions do not damage the mobile robots. The occurrence of the collisions is discussed and the effects of the collisions on the mobile robots are analyzed to develop a hybrid model of each mobile robot under allowable collisions. Based on the effects of the collisions, we show the necessity of redesigning the motion control strategy for mobile robots. Furthermore, impulsive control techniques are applied to redesign the motion control strategy to guarantee the task accomplishment for each mobile robot. Finally, an example is used to illustrate the redesigned motion control strategy.
Paper Structure (15 sections, 3 theorems, 24 equations, 5 figures)

This paper contains 15 sections, 3 theorems, 24 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Formulation
  4. Workspace
  5. Robot Controller
  6. Problem Statement
  7. Collision Model
  8. Collision Between Two Rigid Bodies
  9. Modelling of Rigid Body Collision
  10. Control Redesign
  11. Necessity and Strategy of Control Redesign
  12. Design of Imposed Impulse and Local Controller
  13. Task Accomplishment
  14. Numerical Results
  15. Conclusion

Key Result

Theorem 1

Consider two rigid bodies with their distance $\mathbf{d}_{ij}$ and local linear velocities $\mathbf{v}_{i},\mathbf{v}_{j}$. If $\mathbf{d}_{ij}=r_{i}+r_{j}$ and $\mathbf{v}_{i\mathbf{y}}>\mathbf{v}_{j\mathbf{y}}$, then the RBC occurs.

Figures (5)

  • Figure 1: Illustration of the trajectories starting from different initial states.
  • Figure 2: Illustration of the construction of the local coordinate frame.
  • Figure 3: Illustration of designing the imposed impulse and local controller. (Left) The selection of the motion direction $\theta_{is}^{j}$. (Middle) The exclusion of the chattering phenomenon. (Right) The exclusion of the deadlock phenomenon. The pink disk is robot $i$, the grey disk is $\mathcal{R}_{j}$ and the grey dashed circle is the positions where robot $i$ collides with $\mathcal{R}_{j}$.
  • Figure 4: Illustration of the position trajectories of the two mobile robots in the workspace. The blue and magenta indicate robot 1 and robot 2, respectively. In (a), the black solid segments are the coordinate axes of the $lcf$. In (b), the grey segments are the tangent lines at collision positions.
  • Figure 5: Illustration of the motion directions and control inputs of the two mobile robots with the proposed control strategy in $t\in[0,18]$.

Theorems & Definitions (9)

  • Definition 1: CBFforU
  • Definition 2: CBFforU
  • Example 1
  • Definition 3
  • Theorem 1
  • Corollary 1
  • Remark 1
  • Remark 2
  • Theorem 2