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Dynamic Control Barrier Function-based Model Predictive Control to Safety-Critical Obstacle-Avoidance of Mobile Robot
Zhuozhu Jian, Zihong Yan, Xuanang Lei, Zihong Lu, Bin Lan, Xueqian Wang, Bin Liang
TL;DR
Dynamic, unstructured environments make reliable obstacle detection, prediction, uncertainty representation, and real-time planning difficult. The paper combines LiDAR-based MBE perception, uncertainty-aware Kalman prediction, and D-CBF-constrained MPC; experiments report robust and safe avoidance in real and simulated scenarios.
Problem
Dynamic, unstructured navigation requires reliable obstacle detection and prediction, uncertainty representation, and real-time planning.
Method
The method detects and parameterizes obstacles as MBEs, predicts their motion with uncertainty-aware Kalman filtering, and combines D-CBF with MPC for collision-free navigation.
Results
Real-world experiments and simulations show robust, safe dynamic-obstacle avoidance, including smooth advance avoidance against dynamic obstacles.
Takeaways & Limitations
The framework supports onboard LiDAR-only navigation while balancing safe dynamic-obstacle avoidance with smooth movement toward the target.
Abstract
from arXiv · showhide
This paper presents an efficient and safe method to avoid static and dynamic obstacles based on LiDAR. First, point cloud is used to generate a real-time local grid map for obstacle detection. Then, obstacles are clustered by DBSCAN algorithm and enclosed with minimum bounding ellipses (MBEs). In addition, data association is conducted to match each MBE with the obstacle in the current frame. Considering MBE as an observation, Kalman filter (KF) is used to estimate and predict the motion state of the obstacle. In this way, the trajectory of each obstacle in the forward time domain can be parameterized as a set of ellipses. Due to the uncertainty of the MBE, the semi-major and semi-minor axes of the parameterized ellipse are extended to ensure safety. We extend the traditional Control Barrier Function (CBF) and propose Dynamic Control Barrier Function (D-CBF). We combine D-CBF with Model Predictive Control (MPC) to implement safety-critical dynamic obstacle avoidance. Experiments in simulated and real scenarios are conducted to verify the effectiveness of our algorithm. The source code is released for the reference of the community.
I. INTRODUCTION
The paper targets safe autonomous navigation amid dynamic, unstructured obstacles, where detection, prediction, uncertainty representation, and real-time planning remain difficult. It proposes LiDAR-based obstacle parameterization, uncertainty-aware prediction, and D-CBF-based MPC, with simulation and real-world experiments evaluating the approach.
- Dynamic, unstructured environments remain challenging because obstacle detection, prediction, uncertainty analysis, and real-time trajectory planning are difficult.
- The approach uses onboard LiDAR point clouds to detect and cluster obstacles, represent them as minimum bounding ellipses, and track them consistently.
- Kalman filtering estimates obstacle motion, while uncertainty extends obstacle representations to improve safety during prediction and planning.
- Dynamic Control Barrier Function-based Model Predictive Control generates safe collision-free trajectories for dynamic environments.
- Experiments in Gazebo and real scenarios evaluate the algorithm’s real-time performance, effectiveness, and stability across obstacle-avoidance tasks.
II. OVERVIEW OF THE FRAMEWORK
The framework combines LiDAR-based local perception, obstacle prediction, and D-CBF-constrained MPC for dynamic obstacle avoidance. D-CBF incorporates obstacle motion and shape changes into safety constraints so the robot maintains a safe trajectory around predicted elliptical obstacles.
- The local perception module builds a point-cloud local map, parameterizes obstacles as MBEs, predicts their trajectories with KF, and supplies them to local planning.
- Dynamic Control Barrier Function: D-CBF extends CBF to a state containing the robot, obstacle positions, and obstacle shapes, treating obstacles as movable.
- Dynamic Control Barrier Function: The safe set is defined through a differentiable barrier function whose superlevel set represents states satisfying the safety condition.
- Dynamic Control Barrier Function: The D-CBF theorem implies forward invariance and asymptotic stability of the safe set, making the robot-position component safe.
- Dynamic Control Barrier Function: For each predicted elliptical obstacle, the method computes robot-to-obstacle-periphery distances and constrains their evolution through D-CBF bounds.
- Dynamic Control Barrier Function: D-CBF accounts for the influence of obstacle position and shape changes on the control input and can impose stricter constraints than CBF.
2) Model Predictive Control:
The MPC formulates robot motion over a receding horizon using discrete-time dynamics, admissible-state and input constraints, initial conditions, terminal conditions, and reference-path tracking.
- 2) Model Predictive Control:: The robot dynamics are represented by a discrete-time equation relating the state at step t+1 to the state and control input at step t.The state belongs to X, the input belongs to U, and f is locally Lipschitz.
- 2) Model Predictive Control:: The optimization uses admissible state, input, and terminal-state sets while tracking a reference path supplied by the global planner.The reference is defined over the horizon t:t+N.
- 2) Model Predictive Control:: The objective includes terminal tracking cost, control effort, and changes between successive controls, weighted by P, Q, R, and S.The corresponding weight matrices are P, Q, R, and S.
B. Local Perception
The local perception module estimates the safety space and obstacle regions while predicting obstacle trajectories under observation uncertainty.
- B. Local Perception: Local perception estimates safety space and obstacle regions and predicts obstacle trajectories while considering observation uncertainty.Its overall organization is shown in Fig. 4.
1) Local map:
The local map converts cropped LiDAR point clouds into a real-time 2.5D elevation representation and identifies obstacles from terrain-gradient and step-height limits.
- 1) Local map:: LiDAR point clouds are cropped and transformed into a 2.5D elevation map centered on the robot to support real-time processing.The local map represents the environment around the robot.
- 1) Local map:: The local-perception overview includes cropped point-cloud generation, local-map processing, obstacle processing, and trajectory prediction with observation uncertainty.These stages are summarized in Fig. 4.
- 1) Local map:: Obstacle determination uses the robot’s maximum gradient and step-height operating conditions.These surface conditions are emphasized because UGV navigation depends on the terrain over which the robot travels.
- 1) Local map:: The local map applies 3 × 3 Sobel operators and a 3 × 3 Laplace operator to neighborhood elevations.For grid (a, b), M denotes the elevation of its 3 × 3 neighborhood.
- 1) Local map:: The map thresholds gradient, Laplacian, and step-height measures against maximum operating limits to represent local obstacles.Cells exceeding any limit are classified as obstacles; other cells are not.
2) Obstacle parameterization:
Obstacle regions are clustered, enclosed by minimum bounding ellipses, associated across frames, and tracked with consistent labels for trajectory prediction.
- 2) Obstacle parameterization:: Minimum bounding ellipses represent obstacles while preserving feasible motion after obstacle simplification.The method also tracks obstacles using consistent labels from historical data for trajectory prediction.
- 2) Obstacle parameterization:: Obstacle regions are clustered with DBSCAN and each cluster is simplified to a minimum bounding ellipse.The ellipse is parameterized by center coordinates, semi-major and semi-minor axes, and rotation angle.
- 2) Obstacle parameterization:: Data association matches ellipses between consecutive frames using center-distance affinities and the Kuhn–Munkres algorithm.Matches exceeding d_max are rejected, and unmatched new-frame ellipses receive new labels.
3) Uncertainty analysis:
The paper analyzes how changing MBE shape and point-cloud noise create position uncertainty, then estimates position confidence from shape changes when true obstacle positions are unavailable.
- MBE shape changes caused by point-cloud noise and changing detection angles can make estimated obstacle positions deviate from their real values.
- The indicator Ξp assesses confidence in the MBE position, while Ξη measures the degree of MBE shape change.
- Because obstacle shape is generally assumed stable within a limited local-map area, Ξη can estimate Ξp when the true position is unavailable.
- When [κ, γ] = [5.5, 1.3], the estimate performs well for obstacles moving below 1.5m/s with radius below 0.9m.
4) Trajectory prediction:
The method uses Kalman filtering to update and predict obstacle states from MBE observations, adapts covariance to shape-induced position deviations, and expands future obstacle ellipses with uncertainty for safer planning.
- Kalman filtering updates obstacle states using the MBE as an observation to reduce point-cloud noise.
- The modified position covariance increases when MBE shape changes rapidly, reducing vibration in the estimated MBE position.
- Future obstacle states are predicted with x_k = A x_{k−1} and P_k = A P_{k−1} A^T + Q, where Q is system-noise covariance.
- Position and shape covariance are combined to define ellipse uncertainty, which extends the obstacle ellipse for safety.
- As the prediction step increases from 0 to N, obstacle uncertainty grows and the corresponding predicted ellipse expands.
IV. EXPERIMENTS
Experiments were conducted in real and simulated environments under ROS Melodic, with local perception running at 10–20 Hz and local planning at 10 Hz.
- The experiments evaluate the method in real scenarios and a simulation environment under ROS Melodic.
- The local perception module runs at 10–20 Hz, while the local planning module runs at 10 Hz.
A. Real-world scenarios
Real-world and simulation scenarios evaluate MPC-D-CBF against four baselines using safety, travel-time, reaction-time, and speed-variance indicators. The proposed method predicts dynamic obstacles and avoids them smoothly while maintaining a safer distance than MPC-KF.
- A. Real-world scenarios: The real-world scenario uses two pedestrians and an electromobile, with a 20m route and obstacle speeds of about 1.2m/s and 1.8m/s.
- A. Real-world scenarios: The controller predicts a pedestrian moving toward the robot’s right and consequently chooses a left-side avoidance trajectory.
- B. Simulation scenario: The comparison includes MPC, MPC-CBF, MPC-KF, and MPC-CBF-curvefit, evaluated by minimum distance, travel time, reaction time, and speed variance.
- B. Simulation scenario: MPC collides with the first dynamic obstacle, while MPC-CBF and MPC-CBF-curvefit cannot avoid dynamic obstacles in advance.
- B. Simulation scenario: MPC-KF and the proposed method avoid dynamic obstacles smoothly and robustly in advance, exceeding other methods in reaction time and speed variance.
- B. Simulation scenario: Compared with MPC-KF, the proposed method maintains a safer minimum distance while navigating safely and smoothly to the target.
V. CONCLUSIONS
The paper presents a LiDAR-based safety-critical method for avoiding static and dynamic obstacles. Real-world and simulation experiments indicate robust, safe, onboard operation and improved safety and efficiency over four baselines.
- The method combines robust local perception, obstacle trajectory prediction with uncertainty, Dynamic Control Barrier Functions, and Model Predictive Control.Obstacles are parameterized as minimum bounding ellipses and predicted using a Kalman filter.
- Real-world experiments avoiding different obstacle types validate robust, safe, and onboard execution of all algorithms.
- Simulation comparisons against MPC, MPC-CBF, MPC-KF, and MPC-CBF-curvefit show greater safety and efficiency during obstacle avoidance.