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CoBL-Diffusion: Diffusion-Based Conditional Robot Planning in Dynamic Environments Using Control Barrier and Lyapunov Functions

Kazuki Mizuta, Karen Leung

TL;DR

CoBL-Diffusion is proposed, a novel diffusion-based safe robot planner for dynamic environments that generates smooth trajectories that enable the robot to reach goal locations while maintaining a low collision rate with dynamic obstacles.

Abstract

Equipping autonomous robots with the ability to navigate safely and efficiently around humans is a crucial step toward achieving trusted robot autonomy. However, generating robot plans while ensuring safety in dynamic multi-agent environments remains a key challenge. Building upon recent work on leveraging deep generative models for robot planning in static environments, this paper proposes CoBL-Diffusion, a novel diffusion-based safe robot planner for dynamic environments. CoBL-Diffusion uses Control Barrier and Lyapunov functions to guide the denoising process of a diffusion model, iteratively refining the robot control sequence to satisfy the safety and stability constraints. We demonstrate the effectiveness of the proposed model using two settings: a synthetic single-agent environment and a real-world pedestrian dataset. Our results show that CoBL-Diffusion generates smooth trajectories that enable the robot to reach goal locations while maintaining a low collision rate with dynamic obstacles.

CoBL-Diffusion: Diffusion-Based Conditional Robot Planning in Dynamic Environments Using Control Barrier and Lyapunov Functions

TL;DR

CoBL-Diffusion is proposed, a novel diffusion-based safe robot planner for dynamic environments that generates smooth trajectories that enable the robot to reach goal locations while maintaining a low collision rate with dynamic obstacles.

Abstract

Equipping autonomous robots with the ability to navigate safely and efficiently around humans is a crucial step toward achieving trusted robot autonomy. However, generating robot plans while ensuring safety in dynamic multi-agent environments remains a key challenge. Building upon recent work on leveraging deep generative models for robot planning in static environments, this paper proposes CoBL-Diffusion, a novel diffusion-based safe robot planner for dynamic environments. CoBL-Diffusion uses Control Barrier and Lyapunov functions to guide the denoising process of a diffusion model, iteratively refining the robot control sequence to satisfy the safety and stability constraints. We demonstrate the effectiveness of the proposed model using two settings: a synthetic single-agent environment and a real-world pedestrian dataset. Our results show that CoBL-Diffusion generates smooth trajectories that enable the robot to reach goal locations while maintaining a low collision rate with dynamic obstacles.
Paper Structure (23 sections, 2 theorems, 27 equations, 10 figures, 2 tables, 1 algorithm)

This paper contains 23 sections, 2 theorems, 27 equations, 10 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Preliminaries
  4. Diffusion Models
  5. Trajectory Generation Using Diffusion Models
  6. Control Barrier Function (CBF)
  7. Control Lyapunov Function (CLF)
  8. Conditional Motion Planning with Diffusion
  9. Problem Setting
  10. Model Architecture
  11. U-Net Conditioning on Trajectories
  12. Loss Function for Trajectory Error
  13. Temporal Weighting for Covariance
  14. Reward Function
  15. Control Barrier Function Reward
  16. ...and 8 more sections

Key Result

Theorem 1

Let $\mathcal{C} \subseteq \mathcal{D} \subseteq \mathbb{R}^n$ be the set defined in eq:safe_set. If $h$ is a CBF on $D$ and $\frac{\partial h}{\partial \mathbf{x}}(\mathbf{x})\ne 0$ for all $\mathbf{x} \in \partial C$, then any Lipschitz continuous controller $\mathbf{u}:\mathcal{D}\rightarrow\math

Figures (10)

  • Figure 1: CoBL-Diffusion uses control barrier and Lyapunov functions to guide a diffusion process to generate a robot controller for goal-reaching while avoiding dynamic obstacles.
  • Figure 2: Illustration of planning with CoBL-Diffusion. The left figure depicts the reverse diffusion process of the proposed model. The right figure illustrates the U-Net architecture employed in the proposed model.
  • Figure 3: CoBL-Diffusion.
  • Figure 4: CBF-QP and VO.
  • Figure 5: dCoBL-Diffusion.
  • ...and 5 more figures

Theorems & Definitions (4)

  • Definition 1: Control Barrier Function AmesCooganEtAl2019
  • Theorem 1: AmesCooganEtAl2019
  • Definition 2: Control Lyapunov Function
  • Theorem 2