Real-Time Constraint-Aware Inverse Kinematics via Passivity-Based Dynamics Simulation

We propose a novel inverse kinematics (IK) solver based on an optimization–simulation duality, in which the conventional optimization-based IK problem is reformulated as a forward dynamics simulation of a virtual mechanical system. The IK solution emerges as the equilibrium of this system, corresponding to the Karush-Kuhn-Tucker (KKT) conditions of the original problem. To ensure the stability of the discrete-time forward simulation, we adopt the passive midpoint integrator (PMI) [1], which enforces a discrete-time passivity. This allows the proposed method to converge to an equilibrium without the need for line search. The resulting solver is lightweight, scalable, and suitable for real-time inverse kinematics computation in high-degree-of-freedom (DOF) systems, while satisfying joint limits, obstacle avoidance, and other task-specific constraints. The efficacy of the algorithm is validated and demonstrated through extensive simulations on various robotic platforms.