[Paper Review] Enhancing Mobile Robot Navigation Safety and Efficiency through NMPC with Relaxed CBF in Dynamic Environments

Nhat Nguyen Minh, Stephen McIlvanna+3 more|arXiv (Cornell University)|Nov 21, 2022

Advanced Control Systems Optimization4 citations

TL;DR

This paper proposes a safety-critical nonlinear model predictive control (NMPC) framework for nonholonomic mobile robots that integrates a relaxed control barrier function (CBF) to ensure obstacle avoidance in dynamic environments. By incorporating CBF constraints into a short-horizon NMPC formulation, the method guarantees safety and optimal performance while reducing computational load, outperforming NMPC with Bug-Type (BT) constraints in both point stabilization and trajectory tracking under shorter prediction horizons.

ABSTRACT

In this paper, a safety-critical control strategy for a nonholonomic robot is developed to generate control signals that result in optimal, obstacle-free paths through dynamic environments. We formulate the control synthesis problem as an Optimal Control Problem (OCP) that enforces Control Lyapunov Function (CLF) constraints for system stability as well as safety-critical constraints using Control Barrier Function (CBF) with a relaxing decay rate of the barrier function. A Nonlinear Model Predictive Control (NMPC) integrates with CLF and CBF to ensure system safety and facilitate optimal performance within a short prediction horizon, reducing the computational burden in real-time implementation. Additionally, we incorporate an obstacle avoidance constraint based on the Euclidean norm into the NMPC framework, showcasing the CBF approach's superiority in addressing mobile robotic systems' point stabilisation and trajectory tracking challenges. Through extensive simulations, the proposed controller demonstrates proficiency in static and dynamic obstacle avoidance under various scenarios. Experimental validations conducted using the Husky A200 robot align with simulation results, reinforcing the applicability of our proposed approach in real-world scenarios, notably improving the computational efficiency and safety in practical mobile robot applications.

Motivation & Objective

• To develop a safety-critical control framework for nonholonomic mobile robots that ensures obstacle avoidance in dynamic environments.
• To integrate control barrier functions (CBF) into nonlinear model predictive control (NMPC) for real-time safety guarantees.
• To reduce computational burden by enabling effective obstacle avoidance with a shorter prediction horizon.
• To compare NMPC-CBF performance against NMPC with Bug-Type (BT) constraints in point stabilization and trajectory tracking tasks.
• To validate the method in simulations with static and dynamic obstacles under varying prediction horizons.

Proposed method

• Formulates a discrete-time NMPC controller using a nonlinear kinematic model of a differential-drive robot.
• Incorporates a relaxed control barrier function (CBF) constraint into the NMPC optimization to enforce forward invariance of the safe set.
• Uses the Lyapunov stability theorem to derive stability conditions for the NMPC-CBF formulation.
• Applies Euclidean norm-based obstacle avoidance constraints to enhance CBF effectiveness in both point stabilization and trajectory tracking.
• Replaces CBF constraints in NMPC with Bug-Type (BT) constraints in a comparative controller for performance evaluation.
• Employs a short prediction horizon (N=5 or N=10) to reduce computational cost while maintaining safety and tracking performance.

Experimental results

Research questions

• RQ1 Can a relaxed CBF be effectively integrated into NMPC to ensure safety in dynamic obstacle environments?
• RQ2 How does NMPC-CBF perform in point stabilization tasks compared to NMPC with Bug-Type constraints?
• RQ3 To what extent does CBF enable effective obstacle avoidance with a shorter prediction horizon than BT-based NMPC?
• RQ4 How does the NMPC-CBF controller maintain tracking performance in the presence of static and dynamic obstacles?
• RQ5 What is the computational efficiency gain of using CBF over BT constraints in NMPC for mobile robot navigation?

Key findings

• NMPC-CBF successfully stabilizes the robot to the goal pose with a smooth, obstacle-free trajectory using a prediction horizon of N=5, while NMPC-BT fails to reach the goal due to getting stuck between obstacles.
• With N=5, NMPC-CBF achieves better trajectory tracking performance than NMPC-BT in dynamic environments with multiple static and moving obstacles.
• The use of CBF reduces the optimization problem size by 50%, decreasing average computational time from 9.3 ms to 9.1 ms per time step in obstacle-rich scenarios.
• NMPC-CBF maintains safe and stable performance even at N=5, whereas NMPC-BT shows large overshoots in the error state vector due to obstacle-induced stalling.
• The CBF-based approach enables safe navigation with a shorter prediction horizon, significantly reducing computational burden for real-time implementation.
• In trajectory tracking with obstacles, NMPC-CBF converges faster and maintains lower tracking error compared to NMPC-BT, especially under short horizons.