Robot Safe Planning In Dynamic Environments Based On Model Predictive Control Using Control Barrier Function

Abstract: Implementing obstacle avoidance in dynamic environments is a challenging problem for robots. Model predictive control (MPC) is a popular strategy for dealing with this type of problem, and recent work mainly uses control barrier function (CBF) as hard constraints to ensure that the system state remains in the safe set. However, in crowded scenarios, effective solutions may not be obtained due to infeasibility problems, resulting in degraded controller performance. We propose a new MPC framework that integrates CBF to tackle the issue of obstacle avoidance in dynamic environments, in which the infeasibility problem induced by hard constraints operating over the whole prediction horizon is solved by softening the constraints and introducing exact penalty, prompting the robot to actively seek out new paths. At the same time, generalized CBF is extended as a single-step safety constraint of the controller to enhance the safety of the robot during navigation. The efficacy of the proposed method is first shown through simulation experiments, in which a double-integrator system and a unicycle system are employed, and the proposed method outperforms other controllers in terms of safety, feasibility, and navigation efficiency. Furthermore, real-world experiment on an MR1000 robot is implemented to demonstrate the effectiveness of the proposed method.

• The paper proposes a novel MPC framework that integrates soft constraints with Control Barrier Functions and introduces a dynamic generalized CBF for improved navigation feasibility.
• It converts hard CBF constraints into soft ones using slack variables and penalty functions, enhancing robot collision avoidance in dynamic environments.
• Simulation and real-world experiments demonstrate up to 99.6% success rate in obstacle avoidance for double-integrator and unicycle robotic systems.

Safe Planning for Robot Navigation in Dynamic Environments

Introduction

The paper "Robot Safe Planning In Dynamic Environments Based On Model Predictive Control Using Control Barrier Function" (2404.05952) addresses the challenge of robot navigation in dynamic environments, focusing on the implementation of obstacle avoidance using Model Predictive Control (MPC) integrated with Control Barrier Functions (CBF). This approach aims to ensure the robot's safety and efficiency in navigating complex scenarios with moving obstacles, while resolving the infeasibility issues that may arise from hard constraints.

Problem Statement

Obstacle avoidance in dynamic environments is a critical problem for autonomous robots, which is often approached using MPC. However, the conventional use of CBF as hard constraints across the prediction horizon can lead to feasibility issues, resulting in degraded performance, particularly in crowded settings. The paper proposes a novel MPC framework that combines the strengths of CBF while introducing soft constraints and penalty functions to navigate dynamic environments more effectively.

Methodology

Soft Constrained MPC with CBF

The proposed approach converts CBF hard constraints into soft constraints within the MPC framework. By incorporating slack variables and an exact penalty function, the optimization problem remains feasible even in complex scenarios. This adjustment allows robots to dynamically seek alternative paths by strategically 'softening' constraints, preserving the safety and feasibility balance.

Dynamic Generalized CBF

Building on the existing D-CBF methodology, the paper introduces a dynamic generalized control barrier function (D-GCBF), applied as a single-step hard constraint to enhance safety. This innovative use of D-GCBF reduces computational complexity and improves the feasibility of encountering an optimal control solution, ensuring that robots maintain robust navigation safety even under constrained actuator dynamics.

Figure 1: Comparison between our obstacle avoidance constraints and those previously used. (a) shows that the CBF is imposed as hard constraints across the entire prediction horizon, and (b) represents that the CBF soft constraints functioning over this whole prediction horizon. Based on the formulation for (b), (c) introduces an additional D-GCBF constraint, which is hard and can enhance feasibility of the robot.

Experimental Results

The paper validates its approach through comprehensive simulation experiments using both double-integrator and unicycle dynamics systems. The quantitative evaluation involves comparing the success rate, collision rate, navigation time, solution failures, and computational efficiency against baseline methods such as ORCA and standard MPC approaches.

Double-Integrator System

Simulation results demonstrate significant improvements in success rates and reduced collision occurrences with the proposed method, achieving up to 99.6% success in reaching destinations without collision under crowded conditions in the double-integrator model.

Figure 2: Trajectories of different controllers with double-integrator kinematics system. The circles in the picture are the locations of the agents at the labeled time. In the 330th test case, our method can make the robot successfully reach the destination. More test results are shown in Table.

Unicycle System

Similarly, tests using the unicycle system showed enhanced safety and efficient trajectory planning, while maintaining low computational overhead, illustrating the applicability to real-world systems with non-holonomic constraints.

Figure 3: Trajectories of different controllers with unicycle system. The circles in the picture are the locations of the agents at the labeled time. In the 116th test case, our method can make the robot successfully reach the destination. More test results are shown in Table.

Real-World Experiments

The methodology was deployed on an MR1000 robot, seamlessly transitioning from simulation to real-world application. The robot's collision avoidance mechanism was validated in dynamic pedestrian environments, achieving efficient obstacle navigation and demonstrating the potential for application in practical autonomous systems.

Figure 4: Real-world experiments have confirmed the effectiveness of the proposed collision avoidance method. The robot's navigation sequence is illustrated by these six sub-images. When pedestrians enter the sensing range of the lidar, the robot detects them. As depicted on the right side of the sub-image, perceived pedestrians are depicted by red boxes.

Conclusion

This paper presents a robust and adaptable method for robot navigation in dynamic environments through the integration of soft constraints and generalized CBFs into MPC. The approach ensures feasible and safe robot trajectories without compromising computational efficiency or navigation performance. Future developments may explore extending this framework to more diverse robotic systems and real-time applications, expanding the theoretical foundation of CBF in autonomous navigation.