SA-IK: A Pathwise Inverse Kinematics Solving Algorithm Guided by a Semi-Analytical Framework

This paper proposes a pathwise inverse kinematics algorithm (SA-IK) guided by a semi-analytical framework, aiming to solve the pathwise inverse kinematics problem of an eight-degree-of-freedom redundant tunnel shotcrete manipulator. Firstly, the tunnel shotcrete machine is modeled, and the forward kinematics is derived. Subsequently, referring to the semi-analytical method TIK, the redundant joints are parameterized, and a specific interval is set for searching. Meanwhile, the analytical method is used to solve the non-parameterized joints to obtain initial accurate pose solutions. On this basis, SA-IK takes these solutions as a guide, incorporates the individuals generated by searching the intervals of all joints centered on the current joint configuration, forms a new initial population, and uses the NSGAII algorithm to carry out evolutionary operations with the optimization objectives of target trajectory point pose, joint continuity maintenance, joint limit avoidance, and obstacle avoidance, thus completing the solution process. Finally, by comparing SA-IK with the semi-analytical method TIK and the multi-objective optimization algorithm NSGAII, the significant advantages of this algorithm in multi-objective balance, solution success rate, and solution efficiency are fully demonstrated.