###### Abstract
As for the treatment of singularities in robotic arms, the mentioned methods do not explicitly identify or avoid singular points. Instead, they handle the singular regions by applying certain treatments to the Jacobian matrix to ensure smooth passage through the singular points. Processing the Jacobian matrix in a certain way can allow the robotic arm to work in the singular region, such as through methods like damping least squares. However, these methods have issues with error accumulation and multiple solutions [14]. Therefore, when it is not necessary to pass through the singular region, it is better to select a reasonable trajectory that avoids singular points. [PERSON] et al. decomposed the Jacobian matrix and eliminated singular points by determining whether the determinant of the Jacobian matrix is zero, ensuring that the trajectory solutions obtained through genetic algorithms were feasible [15]. [PERSON] et al. used the condition number index as an optimization indicator and proposed a high-order joint smooth trajectory planning method for singularity avoidance [16]. [PERSON] et al. proposed an artificial potential field method based on known singular configurations, incorporating manipulability indicators as optimization criteria for singularity avoidance [17]. [PERSON] et al. proposed a robotic arm control method that maximizes manipulability indicators [18]. [PERSON] et al. presented a robotic arm control strategy that autonomously learns task constraints and plans trajectories by maximizing manipulability indicators [19]. [PERSON] analyzed the singular configuration of robot trajectories using dexterity indicators and applied them to robotic arm path planning [20]. [PERSON] et al. constructed the workspace of a robotic arm using flexibility indicators and applied it to grasping tasks [21]. To better utilize the geometric shape of the manipulability ellipsoid, [PERSON] et al. used Riemann distance to measure the proximity between a given configuration and a singular configuration, proposing geometry-aware singularity avoidance costs [22; 23]. These methods primarily utilize optimization-based trajectory planning approaches for singularity avoidance without combining their optimization objectives with sample-based path planning methods. Moreover, these methods focus on improving the motion performance of the robotic arm and rarely discuss the issues of obstacle avoidance and singularity avoidance simultaneously. Table 1 shows the methods used and problems addressed by all the scholars mentioned above. In response to the aforementioned issues, this paper integrates the geometry-aware singularity avoidance cost with the FMT\({}^{\star}\) algorithm to generate a path plan for obstacle and singularity avoidance in the Cartesian space of the robotic arm. To ensure a more suitable quantity and distribution of sampling points in space, a two-stage sampling point generation strategy is proposed. To avoid interference between obstacles and the robotic arm's joints, a geometric envelope method is used for collision detection. To achieve smoother generated paths, a quasi-uniform cubic \(B\)-spline curve is employed for path optimization. These improvements enable the proposed algorithm to simultaneously achieve good performance and acceptable computational complexity. Through simulation experiments and real-world robotic arm verification, the proposed algorithm demonstrates shorter path lengths and stable obstacle avoidance capabilities compared to other methods. These experimental results showcase the superiority and potential of the proposed algorithm in robotic arm obstacle avoidance planning.