A Grover-Operator-Based Quantum Variant of Particle Swarm Optimization for Robot Manipulators’ Inverse Kinematics: Theory and Simulation

Particle Swarm Optimization (PSO) is a widely used solver for the Inverse Kinematics (IK) problem, offering competitive convergence rates compared to methods like Damped Least Squares and Forward and Backward Reaching Inverse Kinematics. However, PSO’s high computational cost per iteration remains a challenge. While many PSO variants focus on reducing the number of iterations, this work introduces a novel approach to decrease the computational cost per iteration by minimizing direct kinematics calculations. Leveraging quantum computing algorithms, specifically Quantum Amplitude Amplification (QAA), we developed Quantum-Grover PSO (QG-PSO), which identifies a suboptimal particle to guide the swarm. This approach capitalizes on QAA’s quadratic speedup for unstructured search problems. Simulated experiments demonstrate that QG-PSO significantly reduces computational costs compared to classical PSO when solving the IK problem for robotic manipulators with 7 and 15 joints, highlighting the potential of quantum computing in robotics. In addition to position correction, we considered orientation correction while respecting joint limits and avoiding obstacles.