Sensor-Based Distributionally Robust Control for Safe Robot Navigation in Dynamic Environments

TL;DR

This work tackles safe, real-time mobile robot navigation in unknown dynamic environments under sensing and estimation uncertainty. It introduces a distributionally robust control barrier function (DR-CBF) that uses on-board sensor samples and a Wasserstein-based ambiguity set to enforce probabilistic safety, paired with a CLF-based path-following strategy in a convex QP. The key contributions include a tractable convex reformulation for the DR-CBF constraint via CVaR, a CLF-DR-CBF QP for general control-affine systems, and a practical sample-based strategy that avoids full environmental reconstruction. Extensive simulations and real-world tests with differential-drive robots demonstrate improved safety, robustness to noise, and competitive computation times compared with map-based or GP-driven approaches. The approach offers a practical pathway to robust, sensor-driven safety guarantees in dynamic, unknown settings with direct applicability to a range of robotic platforms.

Abstract

We introduce a novel method for mobile robot navigation in dynamic, unknown environments, leveraging onboard sensing and distributionally robust optimization to impose probabilistic safety constraints. Our method introduces a distributionally robust control barrier function (DR-CBF) that directly integrates noisy sensor measurements and state estimates to define safety constraints. This approach is applicable to a wide range of control-affine dynamics, generalizable to robots with complex geometries, and capable of operating at real-time control frequencies. Coupled with a control Lyapunov function (CLF) for path following, the proposed CLF-DR-CBF control synthesis method achieves safe, robust, and efficient navigation in challenging environments. We demonstrate the effectiveness and robustness of our approach for safe autonomous navigation under uncertainty in simulations and real-world experiments with differential-drive robots.

Figures (11)

• Figure 1: ClearPath Jackal robot equipped with a LiDAR sensor navigating in unknown environments.
• Figure 2: Overview of our approach for safe robot navigation in unknown dynamic environments. The system consists of three main components: (1) localization and mapping, (2) path planning, and (3) control. The contribution of this work lies in the control component, where a novel distributionally robust control barrier function is used to ensure safety in real-time, directly utilizing sensor data, and a control Lyapunov function is used to navigate cluttered and dynamic environments.
• Figure 3: Wasserstein ambiguity set illustration. The figure shows the relationship between the samples, empirical distribution, true distribution, and the Wasserstein ambiguity set. The blue squares represent the available samples from the true distribution (yellow dot), which form the empirical distribution (red dot). The Wasserstein ambiguity set (green region) is constructed as a ball of distributions centered at the empirical distribution, with a radius $r$ that depends on the sample size and the desired confidence level. The ambiguity set aims to contain the true distribution with high probability.
• Figure 4: (a) A robot is depicted following a path generated by a motion planning algorithm, and a dynamic local reference goal is highlighted in yellow. (b) The robot senses the environment with a $360$-degree LiDAR sensor mounted at $\tilde{\mathbf{x}}$. The CBF samples $\{h_{i}(\mathbf{x})\}_{i=1}^N$ are the rays with boundary points highlighted as red triangles, and are selected based on the distance from the LiDAR detections to the robot body.
• Figure 5: Simulated environments in Gazebo.

Theorems & Definitions (19)

• Definition 2.1
• Definition 2.2
• Definition 2.3
• Remark 5.2
• Lemma 5.4
• Proposition 5.5
• Remark 5.6
• Lemma 6.3
• Lemma 6.4
• Theorem 6.5