Real-Time Sensor-Based Feedback Control for Obstacle Avoidance in Unknown Environments (2403.08614v1)

Abstract: We revisit the Safety Velocity Cones (SVCs) obstacle avoidance approach for real-time autonomous navigation in an unknown $n$-dimensional environment. We propose a locally Lipschitz continuous implementation of the SVC controller using the distance-to-the-obstacle function and its gradient. We then show that the proposed implementation guarantees safe navigation in generic environments and almost globally asymptotic stability (AGAS) of the desired destination when the workspace contains strongly convex obstacles. The proposed computationally efficient control algorithm can be implemented onboard vehicles equipped with limited range sensors (e.g., LiDAR, depth camera), allowing the controller to be locally evaluated without requiring prior knowledge of the environment.

• The paper proposes a smooth sensor-based controller that guarantees almost globally asymptotic stability (AGAS) for navigation in n-dimensional spaces with convex obstacles.
• It leverages a locally Lipschitz continuous implementation of Safety Velocity Cones for computationally efficient, real-time responses using limited-range onboard sensors.
• Extensive 2D and 3D simulations validate the controller’s safety and convergence, demonstrating its practical potential for dynamic autonomous systems.

Summary of Real-Time Sensor-Based Feedback Control for Obstacle Avoidance in Unknown Environments

The paper authored by Lyes Smaili and Soulaimane Berkane proposes an enhanced version of the Safety Velocity Cones (SVCs) approach for real-time autonomous navigation within unknown n-dimensional environments. An extension of previous work in autonomous navigation, this research distinguishes itself through a focus on convergence guarantees in n-dimensional environments with strongly convex obstacles. The authors introduce a locally Lipschitz continuous implementation of the SVC controller, which is designed to utilize the distance-to-obstacle function and its gradient. Their findings imply broad applicability due to the method's ability to ensure safe navigation even in generic environments.

Key contributions of the paper include a smooth version of the previous discontinuous SVC controller, which is proven to admit a unique solution that ensures almost globally asymptotic stability (AGAS) towards the target destination. This is made feasible by considering the practical use case of limited-range onboard sensors such as LiDAR and depth cameras, which allow for local, real-time evaluations without prior environmental knowledge.

Key Findings:

1. Safety and Stability: The introduced controller guarantees safety and progress towards the target in generic environments by relying on a smooth implementation that leverages distance-based metrics and a projection onto tangent cones. This ensures compliance with Nagumo's invariance theorem, thereby maintaining safety within the environment.
2. Algorithmic Efficiency: The proposed method is computationally efficient and suitable for real-time application. This is significant for robotics applications requiring quick response times in dynamic and unknown surroundings.
3. Theoretical Implications: The authors present a robust theoretical framework that supports strong claims about the controller's performance with respect to AGAS in environments populated by strongly convex obstacles. It is shown that the novel smooth approach maintains the asymptotic convergence to desired destinations while inherently minimizing the influence of potential local minima.
4. Practical Validation: Extensive numerical simulations in both 2D and 3D environments depict the practical applicability of the controller. The simulations illustrate safe navigation through dynamic environments via sensor data, reinforcing the claims regarding real-time functionality without pre-existing environmental data.

In terms of practical and theoretical implications, this work not only contributes to advancements in autonomous navigation systems but also offers insights that could inspire further exploration into high-dimensional navigation problems, particularly concerning optimization in unknown and complex terrains. Moving forward, this approach could be expanded to incorporate the dynamics of more sophisticated robotic systems or even address scenarios involving dynamic obstacles and environments with varying topological features.

Overall, this research provides a significant step in developing more versatile and reliable autonomous systems that can navigate complex and uncharted environments, contributing to the overall field of robotics and autonomous systems.