Quantum annealing for inverse kinematics in robotics
Hadi Salloum, S. I. Savin, Yaroslav Aleksandrovich Kholodov, Gleb Vladimirovich Ryzhakov, Mirko Farina, Ivan Valer'evich Oseledets · Scientific Reports · 2025
We study a proof-of-concept workflow that reformulates planar inverse kinematics (IK) for robotic manipulators as a Quadratic Unconstrained Binary Optimization (QUBO) using a linear binary discretization of joint angles and one-hot (big-M) constraints, and then solves the QUBO with quantum annealing on D-Wave hardware. We (i) define and report time-to-solution (TTS) rigorously, (ii) evaluate solution accuracy back in the original IK space via end-effector error and feasibility of one-hot constraints, and (iii) analyze embedding choices on Pegasus/Zephyr. On the tested two-link planar IK instances, Global Embedding on Zephyr uses fewer physical qubits and yields shorter access times than alternatives (see Tables 1,2), and a hybrid quantum-classical solver achieves lower TTS than classical QUBO baselines at larger Q sizes (see Figure 6). These results do not claim superiority over state-of-the-art continuous IK solvers; rather, they demonstrate that an IK-to-QUBO mapping can be executed on current quantum annealing systems with quantified accuracy and runtime, clarifying where such an approach may be useful as hardware improves.