Quantum Machine Learning and Grover's Algorithm for Quantum Optimization of Robotic Manipulators

Optimizing high-degree-of-freedom robotic manipulators requires searching complex, high-dimensional configuration spaces, a task that is computationally challenging for classical methods. This letter introduces a quantum-native framework that integrates Quantum Machine Learning (QML) with Grover's algorithm to solve kinematic optimization problems efficiently. A parameterized quantum circuit is trained to approximate the forward kinematics model, which then constructs an oracle to identify optimal configurations. Grover's algorithm leverages this oracle to provide a quadratic reduction in search complexity. Demonstrated on simulated 1-DoF, 2-DoF, and dual-arm manipulator tasks, the method achieves significant speedups—up to 93x over classical optimizers like Nelder-Mead—as problem dimensionality increases. This work establishes a foundational, quantum-native framework for robot kinematic optimization, effectively bridging quantum computing and robotics problems.