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

arXiv: https://arxiv.org/abs/2406.05309 · HTML: https://mlsanity.com/paper/2406.05309/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2024.

## Built on by (most cited first, 30 of 33)

- [Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2412.19948/) (2024)
- [HardFlow: Hard-Constrained Sampling for Flow-Matching Models via Trajectory Optimization](https://mlsanity.com/paper/2511.08425/) (2025)
- [Demystifying Diffusion Policies: Action Memorization and Simple Lookup Table Alternatives](https://mlsanity.com/paper/2505.05787/) (2025)
- [STLCG++: A Masking Approach for Differentiable Signal Temporal Logic Specification](https://mlsanity.com/paper/2501.04194/) (2025)
- [Generative AI Agents in Autonomous Machines: A Safety Perspective](https://mlsanity.com/paper/2410.15489/) (2024)
- [Zero-Shot Trajectory Planning for Signal Temporal Logic Tasks](https://mlsanity.com/paper/2501.13457/) (2025)
- [UniConFlow: A Unified Constrained Flow-Matching Framework for Certified Motion Planning](https://mlsanity.com/paper/2506.02955/) (2025)
- [A Review On Safe Reinforcement Learning Using Lyapunov and Barrier Functions](https://mlsanity.com/paper/2508.09128/) (2025)
- [Learning responsibility allocations for multi-agent interactions: A differentiable optimization approach with control barrier functions](https://mlsanity.com/paper/2410.07409/) (2024)
- [Pick-and-place Manipulation Across Grippers Without Retraining: A Learning-optimization Diffusion Policy Approach](https://mlsanity.com/paper/2502.15613/) (2025)
- [Unifying Model Predictive Path Integral Control, Reinforcement Learning, and Diffusion Models for Optimal Control and Planning](https://mlsanity.com/paper/2502.20476/) (2025)
- [Generative AI for Autonomous Driving: A Review](https://mlsanity.com/paper/2505.15863/) (2025)
- [SAD-Flower: Flow Matching for Safe, Admissible, and Dynamically Consistent Planning](https://mlsanity.com/paper/2511.05355/) (2025)
- [Implicit Maximum Likelihood Estimation for Real-time Generative Model Predictive Control](https://mlsanity.com/paper/2603.13733/) (2026)
- [Inference-stage Adaptation-projection Strategy Adapts Diffusion Policy to Cross-manipulators Scenarios](https://mlsanity.com/paper/2509.11621/) (2025)
- [Formal Safety Verification and Refinement for Generative Motion Planners via Certified Local Stabilization](https://mlsanity.com/paper/2509.19688/) (2025)
- [Provably Safe Generative Sampling with Constricting Barrier Functions](https://mlsanity.com/paper/2602.21429/) (2026)
- [DiRecT: Safe Diffusion-Based Planning via Receding-Horizon Denoising](https://mlsanity.com/paper/2606.15359/) (2026)
- [Safe Vision Language Action Models via Barrier Enhanced Flow Matching](https://mlsanity.com/paper/2607.29569/) (2026)
- [Knowledge Integration Strategies in Autonomous Vehicle Prediction and Planning: A Comprehensive Survey](https://mlsanity.com/paper/2502.10477/) (2025)
- [Unified Generation-Refinement Planning: Bridging Guided Flow Matching and Sampling-Based MPC for Social Navigation](https://mlsanity.com/paper/2508.01192/) (2025)
- [Contractive Diffusion Policies: Robust Action Diffusion via Contractive Score-Based Sampling with Differential Equations](https://mlsanity.com/paper/2601.01003/) (2026)
- [DualShield: Safe Model Predictive Diffusion via Reachability Analysis for Interactive Autonomous Driving](https://mlsanity.com/paper/2601.15729/) (2026)
- [PC-Diffuser: Path-Consistent Capsule CBF Safety Filtering for Diffusion-Based Trajectory Planner](https://mlsanity.com/paper/2603.10330/) (2026)
- [Safe Probabilistic Planning for Human-Robot Interaction using Conformal Risk Control](https://mlsanity.com/paper/2603.10392/) (2026)
- [Train-Small Deploy-Large: Leveraging Diffusion-Based Multi-Robot Planning](https://mlsanity.com/paper/2604.06598/) (2026)
- [JPPD: Joint Prediction_Planning Diffusion with Differentiable Safety Guidance for Dynamic Obstacle Avoidance in Intelligent Transportation Systems](https://mlsanity.com/paper/2606.20686/) (2026)
- [D-SafeMPC: Diffusion-Driven Safe Model Predictive Control with Discrete-Time Control Barrier Functions](https://mlsanity.com/paper/2607.10842/) (2026)
- [Denoising as Projection: Constrained Optimization with Gradient-Guided Diffusion](https://mlsanity.com/paper/2608.29507/) (2026)
- [SoGuDiff: Socially Guided Diffusion for Steerable, Norm-Grounded Robot Navigation](https://mlsanity.com/paper/2609.30560/) (2026)

## Abstract (arXiv)

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.