Microsoft Word - 3-V10N4(2025)-AITI#14579(358-369).docx Advances in Technology Innovation, vol. 10, no. 4, 2025, pp. 358-369 DBSCAN-Based Minimum Enclosing Ellipse Using the Control Barrier Function for Safe Navigation of Mobile Robots Ju-Feng Wu, Chia-Chun Huang, Ming-Yang Cheng* Department of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan, ROC Received 03 December 2024; received in revised form 28 February 2025; accepted 11 March 2025 DOI: https://doi.org/10.46604/aiti.2025.14579 Abstract This paper aims to reduce the redundant unsafe area in quadratic program approaches based on the Control Barrier Function (CBF) and the Control Lyapunov Function (CLF) for collision avoidance, hereafter referred to as the CBF-CLF approach. Existing CBF-CLF quadratic program approaches typically construct CBF based on Euclidean distance; however, the redundant unsafe area due to obstacles is excessively large, which may prevent finding feasible solutions. To address this issue, this study employs density-based spatial clustering of applications with noise (DBSCAN) and the Minimum Enclosing Ellipse (MEE) to reduce the unsafe area. The proposed approach is referred to as the DBSCAN-MEE-CBF. The effectiveness of the proposed method is demonstrated through both computer simulations and real-world experiments. Specifically, the proposed method reduces the size of the redundant unsafe area by up to 26.52% while maintaining robust collision avoidance. Keywords: collision avoidance, mobile robot navigation, Control Barrier Function, Control Lyapunov Function 1. Introduction Various robotic systems are commonly used in automated factories [1]. In addition to industrial robot manipulators that are typically fixed to a specific site, other robotic systems, such as automated guided vehicles (AGV) and autonomous mobile robots (AMR), are also deployed in factories to improve production efficiency. In particular, AGVs move along a pre-defined path. The AGV will stop moving when it detects obstacles that may cause a possible collision. However, the number of AGVs used in modern automated factories or logistics centers is very large. Since the predefined paths for AGVs to move along may intersect, collision events will likely occur and lead to a deterioration in production efficiency. To cope with this problem, developing a mobile robot that does not need to move along a predefined path and can avoid obstacles autonomously is crucial. In particular, commonly used collision avoidance algorithms for AMRs include the potential field method [2], vector field histogram (VFH) [3], and Rapidly-Exploring Random Tree (RRT) and its improved variant, RRT*, etc. These aforementioned methods cannot guarantee the safety of AMRs or AGVs. To cope with this problem, the ideas of Control Barrier Function (CBF) and Control Lyapunov Function (CLF) are adopted in this paper to avoid collisions with obstacles. Moreover, this paper uses density-based spatial clustering of applications with noise (DBSCAN) in combination with a Minimum Enclosing Ellipse (MEE) to define the unsafe regions around obstacles. Compared to the enclosing circle, the MEE provides more space for the robot. Both computer simulations and actual experiments are conducted to verify the effectiveness of the proposed DBSCAN-MEE-CBF approach. In particular, a TurtleBot running on Robot Operating System (ROS) is used to perform navigation while avoiding obstacles. Both the simulation and experimental results indicate that the proposed DBSCAN-MEE-CBF approach can reduce the size of the redundant unsafe area of obstacles from 1.602% to 26.52% and accomplish collision avoidance. * Corresponding author. E-mail address: mycheng@mail.ncku.edu.tw Advances in Technology Innovation, vol. 10, no. 4, 2025, pp. 358-369 359 The remainder of this paper is organized as follows. Section 2 provides a brief review of previous works related to obstacle avoidance algorithms, CBF-CLF-based approaches, and DBSCAN clustering. Section 3 gives a brief introduction to the CBF, which serves as the foundation for the proposed method. Section 4 introduces the proposed DBSCAN and MEE method, explaining how it improves obstacle avoidance by reducing the size of the redundant unsafe areas. Section 5 presents simulation and experimental results to validate the effectiveness of the proposed approach. Finally, Section 6 concludes the paper and discusses potential future research directions. 2. Literature Review In recent years, environmental modeling and risk-aware navigation have become crucial in public health surveillance [4] and mobile robot navigation [5]. In particular, the role of fluid dynamics in airborne disease transmission is investigated in Koley [4], demonstrating that precise environmental modeling is essential for optimizing ventilation strategies and infection risk assessment. Similarly, mobile robots operating in complex environments also require an accurate perception of obstacle distributions and risk areas to navigate safely and efficiently. In the existing obstacle avoidance approaches, the potential field [6] approach can be applied to obstacle avoidance problems for different types of robotic systems, such as mobile robots [7-9] and industrial robot manipulators [10-12]. To increase computation speed and enhance the stability of error detection, the moving direction of a mobile robot is represented by a histogram in the VFH method [13]. The moving direction with a higher histogram has a higher cost and is thus less desirable. The VFH* approach [14], an enhanced version of the VFH method, integrates the VFH method with the A-star pathfinding (A*) algorithm to handle the dead-end problem. However, the common drawback of the approaches mentioned above is that the mobile robot may be trapped at a local minimum, so it may fail to reach its destination. In contrast, the RRT approach [15] adopts a different strategy. In the RRT approach, the environment model is constructed in advance. The tree and nodes between the starting and destination points are also built. If there are obstacles between the starting point and the destination point, these obstacles can be avoided during the tree construction process. After completing the tree and nodes, the mobile robot can move along the planned path to prevent it from being trapped in a local minimum. However, one of the biggest problems for the RRT approach is that if an object accidentally appears on the planned path when the mobile robot is moving along the path, the mobile robot must stop to replan the path to avoid the obstacle. This may significantly slow down the moving task, and the production efficiency will be affected as well. To remedy the aforementioned drawback, a motion planning approach that combines the CBF and CLF was proposed [16-17]. In particular, the CLF is employed as the control scheme to control the mobile robot moving from the starting point to the destination point. At the same time, the CBF is used as a safety filter to ensure the safety of the mobile robot when avoiding obstacles. Moreover, through some mathematical manipulations, CBF and CLF are unified as a quadratic program, referred to as the CBF-CLF quadratic program. Nevertheless, when using the CBF-CLF quadratic program to perform motion planning, it may not be possible to find feasible solutions since the redundant unsafe area due to obstacles is excessively large. To tackle this problem, this paper proposes an approach that exploits the idea of DBSCAN clustering [18] to find the MEE for the CBF-CLF quadratic program, which is called the DBSCAN-MEE-CBF in this paper. The proposed DBSCAN- MEE-CBF approach can reduce the size of the redundant unsafe area of obstacles while ensuring that the mobile robot can successfully avoid obstacles. Compared with the original CBF-CLF quadratic program, the moving space of the mobile robot, as well as the chance of finding feasible solutions, becomes larger for the proposed DBSCAN-MEE-CBF approach. In addition, the trajectory planned by the proposed DBSCAN-MEE-CBF is shorter. The relationship and comparison of the existing literature are shown in Table 1. Advances in Technology Innovation, vol. 10, no. 4, 2025, pp. 358-369 360 Table 1 The relationship and comparison of the literature Method Key Concept Advantages Disadvantages References Potential field Uses attractive and repulsive forces to navigate obstacles Easy to implement; real- time responsiveness May get stuck in a local minimum [2, 6] Vector field histogram (VFH) A bar chart can represent the traveling cost in different directions. The higher the bar, the greater the cost of moving in that direction, indicating a lower likelihood of passage. Efficient obstacle detection; fast computation The performance is not good when the robot encounters a dead end and needs a sharp turn. [13] VFH* Combines VFH with A* algorithm to address dead- end issues Improved pathfinding in complex environments Still susceptible to local minima [14] Rapidly-Exploring Random Tree (RRT) Constructs a tree to find feasible paths from start to goal Can handle complex environments Requires re-planning if new obstacles appear [15] Traditional CBF-CLF quadratic program Uses Control Barrier Function (CBF) for safety and Control Lyapunov Function (CLF) for control Ensures safety constraints; robust control It needs to define unsafe regions. If the unsafe region is too large, the space available for the robot to move will be limited. [16-17, 19- 20] DBSCAN-MEE-CBF Uses DBSCAN clustering to refine CBF-CLF safety constraints Reduces the size of redundant, unsafe areas; improves feasible solutions Requires additional computation for clustering This study 3. Brief Review of CBF and CBF-CLF Quadratic Programming In safety-critical systems, the system states must remain within the set defined by the safety constraint. One effective means for dealing with the abovementioned problem is to ensure that the system possesses the property of set invariance using CBF. CBF has been widely applied in safety-critical control tasks, which ensure the trajectories of an AGV remain within the safe regions. In addition, CLF provides a framework to let AGV move from the initial position to the final destination. The combination of CBFs and CLFs has been effectively used in quadratic programming [16-17, 19-20], allowing the system to stay in safe regions while moving from the initial position to the final destination. Consider a nonlinear control-affine system, where the system dynamics are a linear combination of the system state and control input. The system dynamics can be expressed as: ( ) ( )= +ɺx f x g x u (1) where ��∙�: ℝ� → ℝ� and �∙�: ℝ� → ℝ�. 3.1. Control Barrier Function (CBF) The concept of the CBF is similar to that of the CLF. The goal of CBF is to ensure that the system states remain within the set defined by the safety constraints. Namely, the system possesses the property of set invariance. Consider a dynamical system described by Eq. (1), where ��∙�, �∙� are local Lipschitz continuous. According to the definition given in Xu [15], given a set � defined by a continuously differentiable function ℎ���: ℝ� → ℝ as described by: { } { } { } : ( ) 0 : ( ) 0 ( ) : ( ) 0 = ∈ ≥ ∂ = ∈ = = ∈ > ℝ ℝ ℝ n n n C x h x C x h x Int C x h x (2) where ��, ������ represents the set boundary and the interior of the set, respectively. Advances in Technology Innovation, vol. 10, no. 4, 2025, pp. 358-369 361 If there exists an extended class K function ��∙� such that the system satisfies a certain inequality, ( )( ) ( ) ( ) 0α+ + ≥gfL h x L h x u h x (3) then, this ℎ��� is called the zeroing CBF. Based on this definition, a control law can be derived to ensure that the set � possesses the property of set invariance. The control law is expressed as: ( ){ }: ( ) ( ) ( ) 0α= ∈ + + ≥ ZCBF gfK u U L h x L h x u h x (4) 3.2. CBF-CLF quadratic program If the control system of a mobile robot only contains a CLF, then it can control the mobile robot moving toward the destination. However, the mobile robot cannot avoid obstacles. In contrast, if the control system of a mobile robot only contains a CBF, then the mobile robot can avoid obstacles but cannot control the mobile robot to reach its destination. One way to overcome this difficulty is by using the CLF as the control scheme while the CBF is used as a safety filter to ensure the safety of the mobile robot. To combine CLF and CBF, the CLF and CBF constraints can be reformulated as a quadratic program. The quadratic program is expressed as: ( ) 2 , 1 min 2 . ( ) ( ) ( ) ( ) ( ) ( ) 0 δ δ δ α ∈ + + + + ≤ + + ≥ T Uu gf gf u Hu Fu p s t L V x L V x u cV x L h x L h x u h x (5) where � ∈ ℝ��� is a positive definite matrix, � ∈ ℝ� and � � 0. To prevent a situation wherein the constraints are too strict for feasible solutions, a relaxed term δ is added to the inequality for the CLF to relax the constraint. 4. Proposed Methodology–DBSCAN and MEE In this paper, the mobile robot is equipped with a LiDAR. The depth detected by the LiDAR for each angle ����� is denoted as !���� . Each pair of depth and angle (polar) coordinates can be converted into its corresponding Cartesian coordinates. The conversion is expressed as: ( ) ( ) [ ] ,LiDAR ,LiDAR ,LiDAR ,LiDAR cos , for 0, 2 sin θ π θ  = ∈ = i i i i i i x d i y d (6) Note that these coordinates do not contain the information about the obstacles. This paper utilizes the DBSCAN approach [14] to perform clustering for the data points detected by the LiDAR. In particular, the DBSCAN approach performs clustering based on the density of the detected data points. In the DBSCAN approach, the data points are categorized into three classes— kernel points, boundary points, and noise points. Two parameters ∈ and ��"�_$%"�&' are used to categorize a given data point. If ( ) *, ��"�+,-./0 ) 4, then point A is a kernel point, point B is a boundary point, and point C is a noise point (Fig. 1). Fig. 1 Illustration of kernel points, boundary points, and noise points Advances in Technology Innovation, vol. 10, no. 4, 2025, pp. 358-369 362 For any given data point, define a circle with a radius, and its center is at this given data point. If the number of data points inside the defined circle is larger than ��"�_$%"�&', then this given data point belongs to the class of kernel points. Any data points that are not kernel points but are located inside a circle defined by any kernel points are called boundary points. For any data points that are neither kernel points nor boundary points, they are called noise points. For a kernel point P, all the data points that are located within the distance (radius) ∈ of P are called P reachability. For a kernel point P, if both data points 23, 24 are P reachability, then data points 23, 24 possess connectedness. As a result, one can define that any two data points inside the same cluster possess connectedness. Namely, if data point Q and data point P possess connectedness, they must be in the same cluster. Through the above clustering process, one can obtain the clustering results after several iterations. Based on the clustering results of DBSCAN, the environment can be divided into several smaller regions containing obstacles. In the proposed obstacle avoidance algorithm, for each obstacle, an ellipse is used to enclose the obstacle and will be used to define the safety set of CBF. Firstly, find the minimum convex hull that encloses all the data points belonging to the obstacle, and the average ��56� ) 7��56� , 9�56�: of the data points enclosed by the convex hull is chosen as the center of the ellipse. Then, compute the covariance matrix Σ ∈ ℝ4. Since this covariance matrix is symmetric, its eigenvectors are orthogonal to each other. Based on the eigenvalue <�6= with the largest modulus and its corresponding eigenvector >�6=, one can compute the length a and the orientation >�6?%@ for the long axis of the ellipse. Similarly, according to the eigenvalue <�"� with the smallest modulus and its corresponding eigenvector >�"� , one can compute length b and orientation >�"�%@ for the short axis of the ellipse. As a result, one can find the MEE as described by: ( ) ( ) 2 2 2 2 'cos( ) 'sin( ) 'cos( ) 'sin( ) 1 0 φ φ φ φ+ − + − = x y y x a b (7) where �A ) � B ��56� , 9A ) 9 B 9�56� , C ) D1.5<�6= , H ) D1.5<�"� , I ) �C�J3KL�6?%@,M L�6?%@,=⁄ O; L�6?%@,=, L�6?%@,M represent the x components and the y components of L�6?%@ , respectively, and the flowchart of the proposed approach is shown in Fig. 2. Fig. 2 Flowchart of the proposed approach 5. Simulation and Experimental Results To validate the effectiveness of the proposed DBSCAN-MEE-CBF approach, both simulation and real-world experiments were conducted. The results from both evaluations demonstrate that the proposed approach successfully reduces the redundant unsafe area and improves the feasibility of motion planning. The details of these evaluations are presented in the following sections. Advances in Technology Innovation, vol. 10, no. 4, 2025, pp. 358-369 363 5.1. Simulation TurtleBot3 Burger is used as the experimental platform in this paper. The state vector is denoted as � ) 7P, Q, �:R ∈ ℝS, where X and Y are the Cartesian coordinates of the TurtleBot3 Burger and � is its orientation. The state equation is given as: ( ) ( ) cos 0 sin 0 0 1 θ θ ω θ            = = +               ɺ ɺɺ ɺ X v x Y v (8) In the simulation, the translation velocity command v is a constant, while the angular velocity command T is time-varying. 5.1.1. The original CBF-CLF obstacle avoidance method In the simulation, the initial state �U ) 7PU, QU, �U:R ) 70.0,0.0,0.0:R , the goal state (i.e., destination) is � %6V ) WP %6V , Q %6V , � %6VX R ) 7B1.2,1.2,0.0:R, where the units of X and Y are meters (m), and the unit for � is radian (rad). To verify the effectiveness of the CBF obstacle avoidance method, the continuously differentiable function ℎ��� is constructed to include the square of the distance, the derivative of the square of the distance, and the square of the safety distance. ( ) ( ) ( ) ( ) 2 2 2( ) 2 cos( ) 2 sin( )θ θ= − + − − + − + −obs obs safe obs obsh x X X Y Y d v X X v Y Y (9) where X, Y, and � are system states; P%Z', Q%Z' are the coordinates of the center of the obstacle; and !'6[5 is the pre-defined safety distance. In addition, one can use the CLF to ensure that the system state converges to the goal state. The CLF is defined as: ( ) ( ) 2 2 ( ) = − + −goal goalV x X X Y Y (10) Reformulating the above CBF and CLF yields a quadratic program. ( ) ( ) 2 1 2 , 1 min 2 . ( ) ( ) ( ) ( ) ( ) ( ) 0 δ δ δ − − + + + ≤ + + ≥ T ref ref u gf gf u u H u u p s t L V x L V x u c V x L h x L h x u c h x (11) The environment used in the simulation is illustrated in Fig. 3. Three rectangular obstacles consist of many detected data points. In the original CBF-CLF quadratic program, circles are used to construct the model for obstacles. Fig. 4 shows the simulation results for the original CBF-CLF quadratic program. Clearly, the new trajectory generated by the original CBF- CLF quadratic program can avoid obstacles and reach the goal state safely. In addition, the values of CBF for three obstacles shown in Fig. 5(a) are all positive, indicating that all the system states are in the safety set. In addition, the value of CLF shown in Fig. 5(b) converges exponentially. Fig. 6(a) shows the clustering results of the detected data points using the DBSCAN method. The MEE for these three obstacles obtained using Eq. (7) is shown in Fig. 6(b). Based on the obtained MEE, one can define the CBF with a new ℎ���. It is given by: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 cos( ) sin( ) sin( ) cos( ) ( ) 2 cos( ) sin( ) cos( ) cos( ) sin( ) sin( ) 2 sin( ) cos( ) cos( ) sin( ) sin φ φ φ φ φ φ θ φ θ φ φ φ θ φ    − + − − − + −   = + + +  − + − + + +  − − + − − + + obs obs obs obs safe safe obs obs safe obs obs X X Y Y X X Y Y h x a d b d X X Y Y v v a d X X Y Y v v( ) ( ) 2 ( ) cos( ) 1 θ φ − + safeb d (12) Advances in Technology Innovation, vol. 10, no. 4, 2025, pp. 358-369 364 Fig. 3 Three rectangular obstacles were used in the simulation Fig. 4 Simulation results of the original CBF-CLF quadratic program (a) Value of CBF (b) Value of CLF Fig. 5 Simulation results of the original CBF-CLF quadratic program (a) Results of data point clustering using DBSCAN (b) MEE Obtained from Eq. (7) Fig. 6 Results of DBSCAN clustering and MEE 5.1.2. The proposed DBSCAN-MEE-CBF obstacle avoidance method Fig. 7 shows the simulation results for the proposed DBSCAN-MEE-CBF obstacle avoidance method. The new trajectory can avoid obstacles and reach the goal state safely. Moreover, compared with the circles used to model the obstacles in the original CBF-CLF quadratic program, the ellipses used to model the obstacles in the proposed method fit more closely with the shape of the obstacle. In addition, the values of CBF for the three obstacles shown in Fig. 8(a) are all positive, indicating that all the system states are within the safety set. In addition, the value of CLF shown in Fig. 8(b) converges exponentially. Advances in Technology Innovation, vol. 10, no. 4, 2025, pp. 358-369 365 Fig. 7 Obstacle avoidance in the X-Y plane using DBSCAN-MEE-CBF (a) Value of CBF (b) Value of CLF Fig. 8 DBSCAN-MEE-CBF obstacle avoidance 5.2. Experimental results In the experiment, Python is used to solve the quadratic program, and ROS is used to broadcast the translation velocity command and rotational velocity command to the TurtleBot3 Burger. In addition, for safety concerns, an additional 1.5- centimeter distance will be added to the obstacle models for all methods tested in the experiment. 5.2.1. The original CBF-CLF quadratic program obstacle avoidance method In this experiment, the original CBF-CLF quadratic program is used to avoid obstacles. Fig. 9 shows the image sequences of the TurtleBot moving from the starting point (Fig. 9(a)) to the destination point (Fig. 9(b)). Fig. 10 shows the new trajectory generated by the original CBF-CLF quadratic program obstacle avoidance method. The new trajectory can successfully avoid obstacles and reach the goal state safely. The values of CBF for three obstacles shown in Fig. 11(a) are all positive, indicating that all the system states are in the safety set. In addition, the value of CLF shown in Fig. 11(b) converges exponentially. (a) Starting point of the TurtleBot (b) Destination point of the TurtleBot Fig. 9 Comparison of TurtleBot trajectories: original CBF-CLF vs. proposed DBSCAN-MEE-CBF Advances in Technology Innovation, vol. 10, no. 4, 2025, pp. 358-369 366 Fig. 10 X-Y plane trajectory using the original CBF-CLF quadratic program (a) Value of CBF (b) Value of CLF Fig. 11 Experimental results of the original CBF-CLF quadratic program 5.2.2. The proposed DBSCAN-MEE-CBF obstacle avoidance method In this experiment, the proposed DBSCAN-MEE-CBF obstacle avoidance method is used to avoid obstacles. Fig. 12 shows the new trajectory generated by the proposed DBSCAN-MEE-CBF obstacle avoidance method. Unlike enclosing circles, which are used in Fig. 10, enclosing ellipses are adopted in Fig. 12. As a result, the size of the unsafe area is reduced, and the new trajectory can successfully avoid obstacles and reach the goal state safely. The values of CBF for three obstacles shown in Fig. 13(a) are all positive, indicating that all the system states are within the safety set. In addition, the value of CLF shown in Fig. 13(b) converges exponentially. Fig. 12 X-Y plane trajectory using the proposed DBSCAN-MEE-CBF approach Advances in Technology Innovation, vol. 10, no. 4, 2025, pp. 358-369 367 (a) Value of CBF (b) Value of CLF Fig. 13 Experimental results of the proposed DBSCAN-MEE-CBF obstacle avoidance method 5.2.3. Comparison of experimental results As indicated by Table 2, the actual curve length for the original CBF-CLF quadratic program is longer than the actual curve length for the proposed DBSCAN-MEE-CBF obstacle avoidance method. Table 3 shows a comparison of the area of the enclosing circle used in the original CBF-CLF quadratic program and the area of the enclosing ellipse used in the proposed DBSCAN-MEE-CBF obstacle avoidance method without considering the extra safety distance. Table 4 shows a comparison of the area of the enclosing circle used in the original CBF-CLF quadratic program and the area of the enclosing ellipse used in the proposed DBSCAN-MEE-CBF obstacle avoidance method by considering the extra safety distance. Table 2 Actual curve length Method Length (m) Original CBF-CLF quadratic program 1.95962927 Proposed DBSCAN-MEE-CBF obstacle avoidance method 1.923764028 Table 3 Enclosing area analysis: original CBF-CLF vs. proposed DBSCAN-MEE-CBF Enclosing circle Enclosing ellipse Comparison between the enclosing circle and the enclosing ellipse Area (m2) Area (m2) Area difference (m2) Percentage of area difference (%) Obstacle 1 0.024550164 0.018855005 0.005695159 23.2 Obstacle 2 0.129461892 0.125658986 0.003802906 2.937 Obstacle 3 0.023942989 0.017592874 0.006350115 26.52 Table 4 Area comparison between enclosing circle and enclosing ellipse in obstacle avoidance methods Enclosing circle Enclosing ellipse Comparison between the enclosing circle and the enclosing ellipse Area (m2) Area (m2) Area difference (m2) Percentage of area difference (%) Obstacle 1 0.117506749 0.108311789 0.00919496 7.825 Obstacle 2 0.298024045 0.293247445 0.0047766 1.602 Obstacle 3 0.116173866 0.105878397 0.010295469 8.86 Both Table 3 and Table 4 indicate that the proposed DBSCAN-MEE-CBF obstacle avoidance method yields a smaller area for enclosing obstacles. Namely, the size of the redundant unsafe area of obstacles can be reduced. Therefore, the mobile robot can have a larger safe space to move in, so the likelihood of finding a feasible solution will increase. The purpose of the proposed DBSCAN-MEE-CBF method is to provide a safer space for the robot during navigation compared with that obtained Advances in Technology Innovation, vol. 10, no. 4, 2025, pp. 358-369 368 from the conventional enclosing circle approach. Additionally, compared with traditional methods [N3], the use of CBF in this paper enables the robot to successfully avoid obstacles while ensuring that it does not enter restricted areas. This makes the approach not only applicable to TurtleBot3 but also extendable to other robots. 6. Conclusion and Future Work This paper presented the DBSCAN-MEE-CBF approach, which integrates DBSCAN clustering with the CBF-CLF quadratic program to determine the MEE for obstacle representation. This method aimed to reduce the redundant unsafe area in obstacle avoidance. A TurtleBot running on ROS was used as the simulation and experimental platform to validate the effectiveness of the proposed approach. Both simulation and experimental results confirmed that, compared with the original CBF-CLF quadratic program, the proposed DBSCAN-MEE-CBF approach can effectively reduce the redundant unsafe area of obstacles, thereby achieving safer and more feasible navigation. The main findings are summarized as follows: (1) The DBSCAN-MEE-CBF approach reduces the redundant unsafe area around obstacles, providing a larger feasible space for navigation. (2) Compared with the traditional CBF-CLF method, the proposed approach alleviates unnecessary safety constraints and improves path feasibility. (3) Both simulation and experimental results validated the effectiveness and practicality of the proposed method for obstacle avoidance. In addition to these conclusions, several directions for future research are highlighted. The method could be extended to handle dynamic obstacles with real-time updates to obstacle boundaries for applications in complex environments. Furthermore, integrating reinforcement learning or other AI-driven decision-making techniques with DBSCAN-MEE-CBF could enhance its adaptability, enabling autonomous robots to learn optimal navigation strategies under varying environmental conditions. Conflicts of Interest The authors declare no conflict of interest. References [1] S. Sotnik and V. Lyashenko, “Modern Industrial Robotics Industry,” International Journal of Academic Engineering Research, vol. 6, no. 1, pp. 37-46, 2022. [2] Y. K. Hwang and N. Ahuja, “A Potential Field Approach to Path Planning,” IEEE Transactions on Robotics and Automation, vol. 8, no. 1, pp. 23-32, 1992. [3] C. Zong, Q. Du, J. Chen, Y. Shan, Y. 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