Multi-Solution Inverse Kinematics for Robotic Manipulators via Permutation-Invariant Set Prediction

Inverse kinematics (IK) for 6-DoF manipulators is inherently set-valued, since multiple distinct joint configurations can realize the same end-effector pose. Nevertheless, learning-based IK is frequently posed as single-output regression, which can induce mode collapse and unstable predictions near branch boundaries. In this work, IK is cast as a deterministic set-prediction problem, in which an unordered set of feasible joint candidates is produced in a single forward pass. A multi-head network is trained with permutation-invariant supervision via optimal bipartite matching, eliminating the need for a fixed global ordering of IK branches. High-fidelity multi-solution supervision on a UR3 platform is obtained through a hybrid analytic–numerical procedure, in which branch seeds are enumerated and refined using Levenberg–Marquardt optimization, followed by feasibility filtering. At deployment, the predicted set is mapped to an executable joint-command sequence through a continuity-aware selection rule, thereby promoting temporally consistent branch choices. On real UR3 trajectories, improved set fidelity and branch coverage are observed relative to single-solution and fixed-assignment baselines, while accurate joint-space and task-space tracking is maintained on held-out motions. Runtime benchmarks further indicate that multi-branch inference is faster than repeated numerical IK when multiple solutions are required.