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Dynamic Log-Gaussian Process Control Barrier Function for Safe Robotic Navigation in Dynamic Environments

Xin Yin, Chenyang Liang, Yanning Guo, Jie Mei

TL;DR

The paper tackles safe autonomous navigation in unknown dynamic environments by developing a Dynamic Log Gaussian Process Control Barrier Function (DLGP-CBF). It combines a logarithmic GP-based barrier with obstacle-position (and velocity) data to create an informative, motion-aware safety constraint and solves a QP to ensure safety while following a goal-directed nominal controller. Key contributions include (1) a log-transformed GP CBF that maintains informative gradients even with sparse data, (2) explicit inclusion of predicted obstacle velocities through time derivatives, and (3) a perception-to-control pipeline validated in dynamic Gazebo simulations showing improved safety margins, smoother trajectories, and faster task completion compared with baselines.

Abstract

Control Barrier Functions (CBFs) have emerged as efficient tools to address the safe navigation problem for robot applications. However, synthesizing informative and obstacle motion-aware CBFs online using real-time sensor data remains challenging, particularly in unknown and dynamic scenarios. Motived by this challenge, this paper aims to propose a novel Gaussian Process-based formulation of CBF, termed the Dynamic Log Gaussian Process Control Barrier Function (DLGP-CBF), to enable real-time construction of CBF which are both spatially informative and responsive to obstacle motion. Firstly, the DLGP-CBF leverages a logarithmic transformation of GP regression to generate smooth and informative barrier values and gradients, even in sparse-data regions. Secondly, by explicitly modeling the DLGP-CBF as a function of obstacle positions, the derived safety constraint integrates predicted obstacle velocities, allowing the controller to proactively respond to dynamic obstacles' motion. Simulation results demonstrate significant improvements in obstacle avoidance performance, including increased safety margins, smoother trajectories, and enhanced responsiveness compared to baseline methods.

Dynamic Log-Gaussian Process Control Barrier Function for Safe Robotic Navigation in Dynamic Environments

TL;DR

The paper tackles safe autonomous navigation in unknown dynamic environments by developing a Dynamic Log Gaussian Process Control Barrier Function (DLGP-CBF). It combines a logarithmic GP-based barrier with obstacle-position (and velocity) data to create an informative, motion-aware safety constraint and solves a QP to ensure safety while following a goal-directed nominal controller. Key contributions include (1) a log-transformed GP CBF that maintains informative gradients even with sparse data, (2) explicit inclusion of predicted obstacle velocities through time derivatives, and (3) a perception-to-control pipeline validated in dynamic Gazebo simulations showing improved safety margins, smoother trajectories, and faster task completion compared with baselines.

Abstract

Control Barrier Functions (CBFs) have emerged as efficient tools to address the safe navigation problem for robot applications. However, synthesizing informative and obstacle motion-aware CBFs online using real-time sensor data remains challenging, particularly in unknown and dynamic scenarios. Motived by this challenge, this paper aims to propose a novel Gaussian Process-based formulation of CBF, termed the Dynamic Log Gaussian Process Control Barrier Function (DLGP-CBF), to enable real-time construction of CBF which are both spatially informative and responsive to obstacle motion. Firstly, the DLGP-CBF leverages a logarithmic transformation of GP regression to generate smooth and informative barrier values and gradients, even in sparse-data regions. Secondly, by explicitly modeling the DLGP-CBF as a function of obstacle positions, the derived safety constraint integrates predicted obstacle velocities, allowing the controller to proactively respond to dynamic obstacles' motion. Simulation results demonstrate significant improvements in obstacle avoidance performance, including increased safety margins, smoother trajectories, and enhanced responsiveness compared to baseline methods.

Paper Structure

This paper contains 16 sections, 1 theorem, 21 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Description
  3. Preliminaries
  4. Dynamic Control Barrier Function
  5. Gaussian Process Regression
  6. Problem Description
  7. Methodology
  8. Local Perception
  9. Dynamic Log-GP CBF Synthesis
  10. Safe Control via DLGP-CBF
  11. Simulations
  12. Experiment Setup
  13. Simulations
  14. Performance of DLGP-CBF
  15. Comparison with Baseline Methods
  16. ...and 1 more sections

Key Result

Theorem 1

Consider the input dataset $\mathcal{D}$ defined in eq:input_dataset consisting of obstacle positions, and the corresponding label dataset $Y=\mathbf{1}_N$, where $\mathbf{1}_N$ is the vector of ones. The DLGP-CBF $h(x,\mathcal{D})$ defined in eq:dlgp_cbf maps the robot's state to the range $[-d_{\t

Figures (4)

  • Figure 1: Visualization of the DLGP-CBF function with $c_s = 1$, $d_{\text{shift}} = 0.1$, and the SE kernel length scale $l = 0.9$.
  • Figure 2: Trajectory generated by the DLGP-CBF method. Dynamic and static obstacles are shown as colored and black circles, respectively. Dotted rectangles indicate the positions of the robot and dynamic obstacles at selected timestamps.
  • Figure 3: Evolution of the minimum distance to obstacles and the time derivative $\frac{\partial h}{\partial t}$ over time. Green vertical lines correspond to the snapshot timestamps in Fig. \ref{['fig::trajactory']}.
  • Figure 4: Comparison of trajectories generated by different methods. The colored circles represent dynamic obstacles with different velocities and the black circles represent static obstacles.

Theorems & Definitions (5)

  • Definition 1: jian2023dynamic
  • Theorem 1
  • proof
  • Remark 1
  • Remark 2