Sailing Through Point Clouds: Safe Navigation Using Point Cloud Based Control Barrier Functions

TL;DR

The paper tackles safe local navigation for velocity-controlled robots in unstructured environments using raw point-cloud data. It introduces Vessel, a point-cloud CBF based on scaling a body-frame ellipsoid with $s_j^2 = \bm{p}_j^\top \bm{P} \bm{p}_j$ and $h = \min_j h_j$ (where $h_j = \alpha_j - \beta$, $\alpha_j = s_j^2$), and Mariner, a GPU-accelerated safe preview controller to mitigate spurious equilibria. The key contributions are (i) a general, post-processing-free CBF formulation that remains continuously differentiable, (ii) a novel preview-control mechanism that tests many fixed-path needles as higher-order ellipsoids, and (iii) extensive simulation and real-world validation on Unitree B1/Go2, demonstrating robust local planning and integration with global planners like $RRT^*$. The work enables real-time, safe navigation in dynamic obstacle environments with reduced reliance on pre-built maps, by jointly leveraging point-cloud CBFs and GPU-accelerated preview control within a global-local planning framework.

Abstract

The capability to navigate safely in an unstructured environment is crucial when deploying robotic systems in real-world scenarios. Recently, control barrier function (CBF) based approaches have been highly effective in synthesizing safety-critical controllers. In this work, we propose a novel CBF-based local planner comprised of two components: Vessel and Mariner. The Vessel is a novel scaling factor based CBF formulation that synthesizes CBFs using only point cloud data. The Mariner is a CBF-based preview control framework that is used to mitigate getting stuck in spurious equilibria during navigation. To demonstrate the efficacy of our proposed approach, we first compare the proposed point cloud based CBF formulation with other point cloud based CBF formulations. Then, we demonstrate the performance of our proposed approach and its integration with global planners using experimental studies on the Unitree B1 and Unitree Go2 quadruped robots in various environments.

Figures (7)

• Figure 1: Visualization of the proposed point cloud CBF in a 2D scenario for different versions of higher-order ellipsoids. The blue dots represent the measured point cloud. The dark orange higher-order ellipse represents the unscaled primitive defined in \ref{['eq:ellipsoid']}, and the light orange higher-order ellipse represents the primitive after it is scaled by the scaling factor. The order of the ellipse is given in the upper left corner.
• Figure 2: Visualization of the proposed preview control method in a 2D scenario with higher-order ellipsoids with order four.
• Figure 3: Illustration of the complete motion planning pipeline. The values along the orange arrows are updated at 10 Hz (LiDAR update frequency), the purple arrows are updated at 2 Hz, and the blue arrows are updated only once at the beginning of our experiments.
• Figure 4: Comparison of the proposed algorithm's computation time and GPU usage on different computers. The GPU usage is computed when running the Mariner at 2 Hz and the Vessel at 10 Hz.
• Figure 5: Examples of the environments used for the comparison studies.

Theorems & Definitions (11)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Theorem 4.1
• proof
• Remark 5
• Remark 6
• Theorem 4.2
• proof