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

TL;DR

This work addresses safe robot planning in dynamic environments where obstacle motion can render hard CBF-based MPC infeasible. It introduces a soft-constrained MPC framework (SCMPC-CBF) with an exact-penalty term for slack variables and adds a one-step dynamic generalized CBF (D-GCBF) to bolster safety. The approach is validated through simulations using double-integrator and unicycle models and demonstrated on a real MR1000 robot, showing improved safety, feasibility, and navigation efficiency over baseline methods. The results indicate a practical path toward robust, safety-critical planning in crowded, dynamic environments.

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.

Figures (5)

• Figure 1: Feasibility of optimization problem (\ref{['eq:mpcdcbf']}). The reachable set propagates along the prediction horizon, starting from the initial state $\mathbf{x}_{t|t}$. The definition of the safety set $\mathcal{C}$ is derived from equation (\ref{['eq:ss']}). $\mathcal{S}$ represents the state space set that satisfies constraints (\ref{['mpcdcbf:c']}) and (\ref{['mpcdcbf:f']}). The red arc represents the boundary of $\mathcal{S}$, and its interior is depicted by a red arrow. The optimization problem is feasible only if the intersection of the reachable set and $\mathcal{S}$ is not empty.
• Figure 2: 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.
• Figure 3: 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 \ref{['tab:table1']}.
• Figure 4: 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 \ref{['tab:table2']}.
• Figure 5: 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.

Theorems & Definitions (10)

• Definition 1: Discrete-time CBFzeng2021safety
• Theorem 1
• proof : Proof
• Remark 1
• Definition 2: Relative-degree sun2003initial
• Definition 3: D-GCBF
• Theorem 2
• proof : Proof
• Remark 2
• Remark 3