A Tandem Robotic Arm Inverse Kinematic Solution Based on an Improved Particle Swarm Algorithm
Authors: Zhao Guojun , Jiang Du , Liu Xin , Tong Xiliang , Sun Ying , Tao Bo , Kong Jianyi , Yun Juntong , Liu Ying , Fang Zifan 
Published: May 2022

The analysis of robot inverse kinematic solutions is the basis of robot control and path planning, and is of great importance for research. Due to the limitations of the analytical and geometric methods, intelligent algorithms are more advantageous because they can obtain approximate solutions directly from the robot’s positive kinematic equations, saving a large number of computational steps. Particle Swarm Algorithm (PSO), as one of the intelligent algorithms, is widely used due to its simple principle and excellent performance. In this paper, we propose an improved particle swarm algorithm for robot inverse kinematics solving. Since the setting of weights affects the global and local search ability of the algorithm, this paper proposes an adaptive weight adjustment strategy for improving the search ability. Considering the running time of the algorithm, this paper proposes a condition setting based on the limit joints, and introduces the position coefficient k in the velocity factor. Meanwhile, an exponential product form modeling method (POE) based on spinor theory is chosen. Compared with the traditional DH modeling method, the spinor approach describes the motion of a rigid body as a whole and avoids the singularities that arise when described by a local coordinate system. In order to illustrate the advantages of the algorithm in terms of accuracy, time, convergence and adaptability, three experiments were conducted with a general six-degree-of-freedom industrial robotic arm, a PUMA560 robotic arm and a seven-degree-of-freedom robotic arm as the research objects. In all three experiments, the parameters of the robot arm, the range of joint angles, and the initial attitude and position of the end-effector of the robot arm are given, and the attitude and position of the impact point of the end-effector are set to verify whether the joint angles found by the algorithm can reach the specified positions. In Experiments 2 and 3, the algorithm proposed in this paper is compared with the traditional particle swarm algorithm (PSO) and quantum particle swarm algorithm (QPSO) in terms of position and direction solving accuracy, operation time, and algorithm convergence. The results show that compared with the other two algorithms, the algorithm proposed in this paper can ensure higher position accuracy and orientation accuracy of the robotic arm end-effector. the position error of the algorithm proposed in this paper is 0 and the maximum orientation error is 1.29 × 10–8. while the minimum position error of the other two algorithms is −1.64 × 10–5 and the minimum orientation error is −4.03 × 10–6. In terms of operation time, the proposed algorithm in this paper has shorter operation time compared with the other two algorithms. In the last two experiments, the computing time of the proposed algorithm is 0.31851 and 0.30004s respectively, while the shortest computing time of the other two algorithms is 0.33359 and 0.30521s respectively. In terms of algorithm convergence, the proposed algorithm can achieve faster and more stable convergence than the other two algorithms. After changing the experimental subjects, the proposed algorithm still maintains its advantages in terms of accuracy, time and convergence, which indicates that the proposed algorithm is more applicable and has certain potential in solving the multi-arm inverse kinematics solution. This paper provides a new way of thinking for solving the multi-arm inverse kinematics solution problem.