###### Abstract  
The quest for efficient and safe trajectory planning in robotic manipulation poses significant challenges, particularly in complex obstacle environments where the risk of encountering singularities and obstacles is high. Addressing this critical issue, our study presents a novel enhancement of the Fast Marching Tree (FMT) algorithm, ingeniously designed to navigate the complex terrain of Cartesian space with an unprecedented level of finesse. At the heart of our approach lies a sophisticated two-stage path point sampling strategy, ingeniously coupled with a singularity avoidance mechanism that leverages geometric perception to assess and mitigate the risk of encountering problematic configurations. This innovative method not only facilitates seamless obstacle navigation but also adeptly circumvents the perilous zones of singularity, ensuring a smooth and uninterrupted path for the robotic arm. To further refine the trajectory, we incorporate a quasi-uniform cubic \(B\)-spline curve, optimizing the path for both efficiency and smoothness. Our comprehensive simulation experiments underscore the superiority of our algorithm, showcasing its ability to consistently achieve shorter, more efficient paths while steadfastly avoiding obstacles and singularities. The practical applicability of our method is further corroborated through successful implementation in real-world robotic arm trajectory planning scenarios, highlighting its potential to revolutionize the field with its robustness and adaptability. robotic arm trajectory planning; singularity avoidance; FMT path searching algorithm; singularity metric +
Footnote †: journal: Medical  
for planning Cartesian trajectories of robotic arms [6]. [PERSON] et al. proposed BI-FMT* and applied it to trajectory planning for spatial robotic arms [7]. Optimization-based methods have also been utilized for trajectory planning. For example, [PERSON] et al. used Chaos Particle Swarm Optimization (CPSO) combined with damping least squares (DLS) and feedback compensation to avoid singularity [8]. [PERSON] et al. proposed a dynamic damping least squares method based on the minimum singular value to adjust Cartesian space trajectories in singular regions [9]. [PERSON] et al. used the least squares method and optimized the trajectory using \(B\)-splines [10]. [PERSON] et al. introduced a model-based approach for robotic arm trajectory planning. They developed a predictive obstacle avoidance model that takes into account the geometric configuration of the arm. By considering motion state cost, frontal collision cost, and approach time cost, they formulated a cost function. This method also accounts for the deformation of the model when approaching singular points [11]. Learning-based approaches have also been explored. [PERSON] et al. used a novel neural network for gap inference to accelerate the generation of robotic arm motion trajectories [12]. [PERSON] et al. proposed a model-free supervisor executor deep reinforcement learning method for path planning of UR5 robotic arms [13]. In the above discussion, several methods for obstacle avoidance planning of robotic arms in Cartesian space were discussed. Among them, the sampling-based method is simple, intuitive, and easy to understand and implement. Due to the randomness of the sampling, it also performs well in complex spaces. With a moderate number of sampling points, the computational complexity is not high. The optimization-based method requires setting appropriate optimization objectives. It consumes a lot of computation in complex spaces and is prone to becoming trapped in local optima. The model-based method relies on mathematical models established based on prior knowledge, and the accuracy of the modeling has an impact on the results. The learning-based method requires a large amount of data for training and has poor interpretability. Therefore, the sampling-based method has the advantages of speed, robustness, and wide applicability.