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Collision-Free Platooning of Mobile Robots through a Set-Theoretic Predictive Control Approach

Suryaprakash Rajkumar, Cristian Tiriolo, Walter Lucia

TL;DR

This work tackles collision-free platooning for input-constrained mobile robots using a leader–follower architecture where the leader tracks a reference path and followers track the leader with time-varying delays. It combines input–output feedback linearization with a set-theoretic model predictive control (STMPC) framework and introduces a set-based collision-avoidance policy based on forward reachability to guarantee safety. Key contributions include deriving linearized error dynamics with bounded disturbances, characterizing orientation-dependent input constraints with robust inner/outer approximations, offline ROSC-based terminal sets, and online convex optimizations that ensure Uniformly Ultimately Bounded tracking; plus a collision-avoidance mechanism that adaptively adjusts inter-vehicle delays. The approach is validated experimentally on a three-robot Khepera IV setup, demonstrating bounded tracking errors, adherence to input limits, and successful collision avoidance, indicating practical applicability for real-time platooning with guaranteed safety.

Abstract

This paper proposes a control solution to achieve collision-free platooning control of input-constrained mobile robots. The platooning policy is based on a leader-follower approach where the leader tracks a reference trajectory while followers track the leader's pose with an inter-agent delay. First, the leader and the follower kinematic models are feedback linearized and the platoon's error dynamics and input constraints characterized. Then, a set-theoretic model predictive control strategy is proposed to address the platooning trajectory tracking control problem. An ad-hoc collision avoidance policy is also proposed to guarantee collision avoidance amongst the agents. Finally, the effectiveness of the proposed control architecture is validated through experiments performed on a formation of Khepera IV differential drive robots

Collision-Free Platooning of Mobile Robots through a Set-Theoretic Predictive Control Approach

TL;DR

This work tackles collision-free platooning for input-constrained mobile robots using a leader–follower architecture where the leader tracks a reference path and followers track the leader with time-varying delays. It combines input–output feedback linearization with a set-theoretic model predictive control (STMPC) framework and introduces a set-based collision-avoidance policy based on forward reachability to guarantee safety. Key contributions include deriving linearized error dynamics with bounded disturbances, characterizing orientation-dependent input constraints with robust inner/outer approximations, offline ROSC-based terminal sets, and online convex optimizations that ensure Uniformly Ultimately Bounded tracking; plus a collision-avoidance mechanism that adaptively adjusts inter-vehicle delays. The approach is validated experimentally on a three-robot Khepera IV setup, demonstrating bounded tracking errors, adherence to input limits, and successful collision avoidance, indicating practical applicability for real-time platooning with guaranteed safety.

Abstract

This paper proposes a control solution to achieve collision-free platooning control of input-constrained mobile robots. The platooning policy is based on a leader-follower approach where the leader tracks a reference trajectory while followers track the leader's pose with an inter-agent delay. First, the leader and the follower kinematic models are feedback linearized and the platoon's error dynamics and input constraints characterized. Then, a set-theoretic model predictive control strategy is proposed to address the platooning trajectory tracking control problem. An ad-hoc collision avoidance policy is also proposed to guarantee collision avoidance amongst the agents. Finally, the effectiveness of the proposed control architecture is validated through experiments performed on a formation of Khepera IV differential drive robots
Paper Structure (12 sections, 1 theorem, 29 equations, 2 figures, 2 algorithms)

This paper contains 12 sections, 1 theorem, 29 equations, 2 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Robot Modelling
  4. Formation Setup and Problem Formulation
  5. Proposed Solution
  6. Linearized Vehicle Kinematics via Input-Output Linearization
  7. Agents' Error Dynamics
  8. Input Constraints Characterization
  9. Set-Theoretic Receding Horizon Control for Trajectory Tracking
  10. Proposed Predictive Platooning Tracking Control
  11. Experimental Results
  12. Conclusions

Key Result

Lemma 1

wang2003fullIf a control law $u(\cdot)$ is such that eq:error-dynamics is stable, the point $\bf B^i$ tracks any bounded reference trajectory with a bounded internal dynamic. Consequently, also the tracking error $\tilde{q}(k)$ is bounded. $\Box$

Figures (2)

  • Figure 1: Vehicle to Vehicle (V2V) communication graph
  • Figure 2: Experimental results: performed trajectory, wheel's angular velocity, and tracking error for agents $i=0,1,2$.

Theorems & Definitions (12)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • ...and 2 more