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Self-navigation in crowds: An invariant set-based approach

Veejay Karthik J, Leena Vachhani

TL;DR

This work tackles safe self-navigation for non-holonomic robots in crowded, non-cooperative environments using only onboard sensing. It introduces an invariant-set-based controller that yields guaranteed safety and enables direct computation of safe control inputs without explicit trajectory planning, by shaping state-constrained regions around a moving target. The approach combines a Lyapunov-based feedback law with a planning strategy that identifies disc-shaped invariant sets and greedily latched targets toward the final destination, all while handling perception uncertainties. Hardware experiments with Turtlebot3s and extensive simulations demonstrate real-time feasibility and parallelizable computations, achieving collision-free convergence with substantial speedups from parallelization. The methodology offers a practical, sensor-driven alternative to optimization- and learning-based planners for rapid, safe navigation in dynamic crowds, with potential extensions to learning-augmented planning.

Abstract

Self-navigation in non-coordinating crowded environments is formidably challenging within multi-agent systems consisting of non-holonomic robots operating through local sensing. Our primary objective is the development of a novel, rapid, sensor-driven, self-navigation controller that directly computes control commands to enable safe maneuvering while coexisting with other agents. We propose an input-constrained feedback controller meticulously crafted for non-holonomic mobile robots and the characterization of associated invariant sets. The invariant sets are the key to maintaining stability and safety amidst the non-cooperating agents. We then propose a planning strategy that strategically guides the generation of invariant sets toward the agent's intended target. This enables the agents to directly compute theoretically safe control inputs without explicitly requiring pre-planned paths/trajectories to reliably navigate through crowded multi-agent environments. The practicality of our technique is demonstrated through hardware experiments, and the ability to parallelize computations to shorten computational durations for synthesizing safe control commands. The proposed approach finds potential applications in crowded multi-agent scenarios that require rapid control computations based on perceived safety bounds during run-time.

Self-navigation in crowds: An invariant set-based approach

TL;DR

This work tackles safe self-navigation for non-holonomic robots in crowded, non-cooperative environments using only onboard sensing. It introduces an invariant-set-based controller that yields guaranteed safety and enables direct computation of safe control inputs without explicit trajectory planning, by shaping state-constrained regions around a moving target. The approach combines a Lyapunov-based feedback law with a planning strategy that identifies disc-shaped invariant sets and greedily latched targets toward the final destination, all while handling perception uncertainties. Hardware experiments with Turtlebot3s and extensive simulations demonstrate real-time feasibility and parallelizable computations, achieving collision-free convergence with substantial speedups from parallelization. The methodology offers a practical, sensor-driven alternative to optimization- and learning-based planners for rapid, safe navigation in dynamic crowds, with potential extensions to learning-augmented planning.

Abstract

Self-navigation in non-coordinating crowded environments is formidably challenging within multi-agent systems consisting of non-holonomic robots operating through local sensing. Our primary objective is the development of a novel, rapid, sensor-driven, self-navigation controller that directly computes control commands to enable safe maneuvering while coexisting with other agents. We propose an input-constrained feedback controller meticulously crafted for non-holonomic mobile robots and the characterization of associated invariant sets. The invariant sets are the key to maintaining stability and safety amidst the non-cooperating agents. We then propose a planning strategy that strategically guides the generation of invariant sets toward the agent's intended target. This enables the agents to directly compute theoretically safe control inputs without explicitly requiring pre-planned paths/trajectories to reliably navigate through crowded multi-agent environments. The practicality of our technique is demonstrated through hardware experiments, and the ability to parallelize computations to shorten computational durations for synthesizing safe control commands. The proposed approach finds potential applications in crowded multi-agent scenarios that require rapid control computations based on perceived safety bounds during run-time.
Paper Structure (15 sections, 2 theorems, 21 equations, 10 figures, 2 tables, 1 algorithm)

This paper contains 15 sections, 2 theorems, 21 equations, 10 figures, 2 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Problem Formulation
  3. Contributions and Organization
  4. FEEDBACK CONTROL DESIGN
  5. THE PROPOSED SELF-NAVIGATOR
  6. Identifying the set of candidate $L_i(\mathcal{F}_i^k)$ around $\mathcal{R}_i$
  7. The Planning Strategy
  8. The self-navigation algorithm
  9. RESULTS & ANALYSIS
  10. Hardware Experiments
  11. Simulation Results
  12. Comparisons
  13. Discussion - Measurement uncertainties
  14. EXPERIMENTS ON PARALLELIZATION
  15. CONCLUSIONS & FUTURE WORK

Key Result

Theorem 1

The control design in $(eqn:ControlDesign)$ accomplishes $\mathcal{O}_1$, while the input $\omega_i$ is constrained within $|\omega_i|\leq K_2\left(\frac{\pi}{2}\right) + K_1$.

Figures (10)

  • Figure 1: The Problem Formulation
  • Figure 2: Describing the invariant set ${L}^k_i$ associated with $\mathcal{F}^k_i$ within the bounds of safety perceived during runtime.
  • Figure 3: The Planning Strategy. A visualization of $\mathcal{D}^k_i$ at each planning instance in the ego-centric frame of the $\mathcal{R}_i$.
  • Figure 4: The experimental setup - Schematic
  • Figure 5: Experiments to demonstrate the self-navigator deployed on Turtlebot3 robots
  • ...and 5 more figures

Theorems & Definitions (7)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Remark 1
  • Remark 2
  • Remark 3