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Neural Control Barrier Functions for Safe Navigation

Marvin Harms, Mihir Kulkarni, Nikhil Khedekar, Martin Jacquet, Kostas Alexis

TL;DR

The paper tackles map-less safe navigation in unknown environments by learning neural Control Barrier Functions (CBFs) and corresponding safe controllers using an SDRE-inspired framework. It introduces a neural CBF formulation that depends on instantaneous LiDAR observations and current state, plus a switching mechanism to handle unknown observation dynamics, enabling a reactive safety filter that does not require a global map. The authors jointly train a safety controller and a CBF via a matrix-valued SDRE-based objective, with a multi-objective loss that promotes obstacle avoidance, safe-set expansion, and consistency with the CBF condition. They implement and evaluate the approach on a quadrotor using simulated data and real-world experiments, demonstrating reliable collision avoidance and safe behavior in cluttered, unknown environments. The results indicate practical significance for safe autonomous navigation in GPS-denied or feature-sparse settings using only local range observations.

Abstract

Autonomous robot navigation can be particularly demanding, especially when the surrounding environment is not known and safety of the robot is crucial. This work relates to the synthesis of Control Barrier Functions (CBFs) through data for safe navigation in unknown environments. A novel methodology to jointly learn CBFs and corresponding safe controllers, in simulation, inspired by the State Dependent Riccati Equation (SDRE) is proposed. The CBF is used to obtain admissible commands from any nominal, possibly unsafe controller. An approach to apply the CBF inside a safety filter without the need for a consistent map or position estimate is developed. Subsequently, the resulting reactive safety filter is deployed on a multirotor platform integrating a LiDAR sensor both in simulation and real-world experiments.

Neural Control Barrier Functions for Safe Navigation

TL;DR

The paper tackles map-less safe navigation in unknown environments by learning neural Control Barrier Functions (CBFs) and corresponding safe controllers using an SDRE-inspired framework. It introduces a neural CBF formulation that depends on instantaneous LiDAR observations and current state, plus a switching mechanism to handle unknown observation dynamics, enabling a reactive safety filter that does not require a global map. The authors jointly train a safety controller and a CBF via a matrix-valued SDRE-based objective, with a multi-objective loss that promotes obstacle avoidance, safe-set expansion, and consistency with the CBF condition. They implement and evaluate the approach on a quadrotor using simulated data and real-world experiments, demonstrating reliable collision avoidance and safe behavior in cluttered, unknown environments. The results indicate practical significance for safe autonomous navigation in GPS-denied or feature-sparse settings using only local range observations.

Abstract

Autonomous robot navigation can be particularly demanding, especially when the surrounding environment is not known and safety of the robot is crucial. This work relates to the synthesis of Control Barrier Functions (CBFs) through data for safe navigation in unknown environments. A novel methodology to jointly learn CBFs and corresponding safe controllers, in simulation, inspired by the State Dependent Riccati Equation (SDRE) is proposed. The CBF is used to obtain admissible commands from any nominal, possibly unsafe controller. An approach to apply the CBF inside a safety filter without the need for a consistent map or position estimate is developed. Subsequently, the resulting reactive safety filter is deployed on a multirotor platform integrating a LiDAR sensor both in simulation and real-world experiments.
Paper Structure (20 sections, 1 theorem, 26 equations, 7 figures, 2 tables)

This paper contains 20 sections, 1 theorem, 26 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Symbols and Abbreviations
  5. System Definition
  6. Control Barrier Functions
  7. Neural Navigation CBFs
  8. Constructive Safety from Observation CBFs
  9. Learning Observation CBFs
  10. Joint Learning of Controller and CBF
  11. Training the Networks
  12. Implementation for Quadrotor Navigation
  13. Dataset
  14. Training
  15. Recursive Filtering
  16. ...and 5 more sections

Key Result

Theorem 1

Under assumption assumption1, the switching update switching_update applied at discrete time steps $t_i \in \{t_1, t_2, ..., t_e\}, e \in \mathbb{N}$ with $t_i \leq t_{i+1}$ together with any control law satisfying: $\forall t \neq t_i$ with $\mathbf{o}_\text{safe}, \xi_\text{safe}$ from switching_update guarantees forward invariance of the switching safe set $\mathcal{X}_\text{safe}=\{\mathbf{x}

Figures (7)

  • Figure 1: Instance of the presented experiments for safe navigation through direct learning of neural control barrier functions commanding accelerations. Video: https://www.youtube.com/watch?v=1id0C6jiFEg
  • Figure 2: Fig. A (left): $\mathbf{x}_{i}$ is in the new safe set an the new certificate (using new latest observation) can be applied. Fig. B (right): $\mathbf{x}_{i}$ is not in the new safe set and invariance of a previous safe set is enforced.
  • Figure 3: Proposed network architecture for jointly training a safety controller and CBF. The observations $\mathbf{o}$ and states $\mathbf{x}$ are first passed through a latent network to generate a latent representation $\mathbf{z}(\mathbf{o},\mathbf{x})$, which is then passed through a controller network and a CBF network to generate the control input $\mathbf{u}(\mathbf{o},\mathbf{x})$ and CBF value $h(\mathbf{o},\mathbf{x})$, respectively. The CBF value $h(\mathbf{o},\mathbf{x})$ is then passed through a (static) class $\mathcal{K}_{\infty}$ function $\alpha$. The method relies only on instantaneous observations $\mathbf{o}$ and not a map.
  • Figure 4: Network structure and dimensions for quadrotor navigation on $xy$. The output of the CBF and controller network consist of the sum of 32 "feature matrices" each to allow superposition of features in the final output.
  • Figure 5: Experimental evaluation of the proposed safety filter in a corridor. The safety filter receives a constant acceleration input of $2m\per s^2$ in the vehicle frame (black arrow) and produces a safe reference output (green arrow). The safety filter passes through safe reference inputs (a), deflects the multirotor when passing obstacles (b&c) and brings the robot to a full stop in front of the final panel (d). The observation (range image) at each instance is shown. CBF level sets are drawn for all instances (a-d) at the current velocity in the vehicle frame where purple denotes $h\geq0$ and red denotes the obstacle boundary. The position of points $\mathbf{x}_j$ is shown as blue crosses.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Definition 1: Control Invariant Set
  • Definition 2: Control Barrier Function ames2019control
  • Theorem 1
  • proof