A Safe Hybrid Control Framework for Car-like Robot with Guaranteed Global Path-Invariance using a Control Barrier Function

TL;DR

This work tackles the problem of safe, globally invariant path-following for a car-like robot in obstacle-laden environments. It introduces a two-stage strategy: a local path-invariant controller augmented with a Control Barrier Function to avoid singularities, and a global-tracking controller integrated via a hysteresis-based hybrid framework to guarantee global convergence to the path. The key contributions are a path-invariant local controller with a singularity filter, a hybrid uniting framework that ensures robust, global path invariance, and simulation-based validation demonstrating obstacle avoidance and invariance properties. The approach offers a practical, robust solution for safe operation in real-world settings and is extensible to other nonholonomic systems.

Abstract

This work proposes a hybrid framework for car-like robots with obstacle avoidance, global convergence, and safety, where safety is interpreted as path invariance, namely, once the robot converges to the path, it never leaves the path. Given a priori obstacle-free feasible path where obstacles can be around the path, the task is to avoid obstacles while reaching the path and then staying on the path without leaving it. The problem is solved in two stages. Firstly, we define a ``tight'' obstacle-free neighborhood along the path and design a local controller to ensure convergence to the path and path invariance. The control barrier function technology is involved in the control design to steer the system away from its singularity points, where the local path invariant controller is not defined. Secondly, we design a hybrid control framework that integrates this local path-invariant controller with any global tracking controller from the existing literature without path invariance guarantee, ensuring convergence from any position to the desired path, namely, global convergence. This framework guarantees path invariance and robustness to sensor noise. Detailed simulation results affirm the effectiveness of the proposed scheme.

Figures (5)

• Figure 1: Our proposed solution, shown in bold green and blue, guarantees global path invariance and robustness to sensor noise. In contrast, other solutions, shown in red and blue, fail to achieve both. LP-I stands for locally path invariant.
• Figure 2: The hybrid control diagram of the globally path-invariant control framework.
• Figure 3: The desired path $\Gamma$ is shown as a red solid line. The flow sets $C_{0}$ and $C_{1}$ are depicted in green and yellow, respectively, with their overlap also shown in green. Green dotted lines mark the boundaries of $C_{1}$, blue dotted lines indicate the boundaries of $C_{0}$, and red dotted lines represent the boundaries of $\mathcal{N}_{\Gamma}^{\delta_{y}}$.
• Figure 4: CBF-based singularity filter prevents singularity point.
• Figure 5: Simulation results of the proposed hybrid controller.

Theorems & Definitions (17)

• Definition II.1: Finite-time stability
• Lemma IV.1
• proof
• Proposition IV.2
• proof
• Corollary IV.3
• proof
• Remark IV.4
• Proposition IV.5
• proof