Analytical inverse kinematics solution and global arm angle optimization method for 7-DOF redundant robotic arms...

In this paper, a novel analytical inverse kinematics solution method is proposed for seven-degree-of-freedom (7-DOF) redundant robotic arms without offset. Building upon the inverse kinematics solution, an arm angle optimization strategy is introduced to determine the optimal configuration among multiple feasible solutions. Based on spherical geometry, an arm angle is constructed, and the mapping relationships between joint angles and the arm angle are derived. The feasible interval of the arm angle is identified by analyzing joint limits and singularity conditions. A mechanism is introduced to prevent joint angles from approaching their limit positions, incorporating constraints on joint velocity and acceleration. Furthermore, a dynamic risk assessment and smooth update strategy is proposed, which integrates the boundary repulsion effect and the central attractive guidance mechanism for the global optimization of the arm angle parameters. Simulation results indicate that, relative to state-of-the-art optimization methods, the proposed algorithm exhibits notable advantages in terms of trajectory tracking error, average arm angle change rate, joint angle variation, maximum joint velocity, maximum joint acceleration, and computational time.