## 1 Introduction  
Matrix multiplication dominates over 90% of the control calculations in robotic arms, especially the reconfigurable robotic arm. Therefore, the forward and inverse solution calculation process becomes key to the real-time autonomous planning of the robotic arm [1]. With the development of intelligent robots, sophisticated and complex operations place an increasing demand on real-time kinematics calculations [2], and traditional matrix calculations alone cannot achieve such high performance [3]. The degrees of freedom of the robotic arms are generally less than seven, which also leads to the application of some acceleration algorithms with high degrees of freedom [4]. At the same time, unlike image processing, classification, and other calculations that can reduce matrix multiplication by cutting and approximation [5], the control of robotic arms requires higher precision and more precise matrix multiplication calculations. In some fine operation application scenarios where the end moves at a close distance and with low speed, sometimes a double precision floating point base is inevitable to meet the application requirements. Thus, it is necessary to consider the impact on the accuracy of the calculation results in the algorithm design process [6], and directly applying the control training method based on neural networks in the high-precision control process is inappropriate [7]. In addition, for the calculation process of matrix multiplication with sparse features, parallel computing based on digital logic or dedicated processor chips can improve the calculation rate [8; 9], and the cycle of accessing the cache can also be reduced after processing zero data [10]. Currently, there are three main methods for matrix computing acceleration. The first is to use high-performance processors such as GPUs to achieve real-time computing [11]. However, its heat rate is usually high and difficult to be applied in miniaturized or long-term work scenarios [12]. The second is to design digital logic to implement a special matrix computing architecture [13], which takes up substantial hardware resources, making it challenging to implement a flexible matrix computing mode [14]. Especially for specific calculation scenarios, such as the calculation of a homogeneous matrix in the process of computing the forward solution of a manipulator, it is hard to reduce the amount of calculation by using the sparse nature of the matrix itself [15]. Another immediate improvement of fast matrix multiplication [16], such as Strassen and Cannon's fast matrix multiplication, is combined with multi-core parallel computing to improve the system efficiency. There is an upper limit in improving fast matrix multiplication, and the implementation of parallel multi-core computing mainly focuses on the block parallelism of matrix data, not considering the optimization of matrix chain multiply-add operations [17]. In reference [15], the forward and inverse kinematics solution module based on FPGA was designed to realize the millisecond-level control rate of the medical robot. The analytical solution was adopted without considering the factor of shape reconstruction. Based on searching for optimal matrix chain multiplication in dynamic programming and adding the interaction cost between multiple processors, the optimal calculation method closer to the real-world application is designed in the literature [16]. In the literature [18], a single matrix multiplication module completed the chain multiplication of forward and inverse solutions, and the calculation time reached 87.25 milliseconds. Reference [19] realized the parallel distribution of the dot product in the matrix chain process based on GPU design and parallel C++ calculation, which reduced the computation time by 97.27%. Previous design methods in the literature mainly focused on improving the efficiency of matrix cascade multiplication through fixed digital logic acceleration or process optimization of multi-core parallel processors.