Trajectory-based sequential learning for efficient and stable inverse kinematics of robotic manipulators

Inverse kinematics (IK) for robotic manipulators is nonlinear and multi-solution: multiple joint configurations can realize the same end-effector pose, and small perturbations can trigger discontinuous switching between kinematic branches during execution. This makes learning from real robot trajectories difficult because recorded data provides only the executed configuration rather than the full set of valid solutions. In this paper, we address this mismatch by reframing inverse kinematics as a sequential, state-conditioned learning problem and predicting joint updates relative to the previously executed configuration instead of regressing absolute joint angles. The model uses geometry-aware inputs that combine the current pose, short-horizon pose change, and the previous joint state, while handling rotational continuity and joint periodicity through continuous orientation features, trigonometric joint embeddings, and a wrap-aware training loss. Trained on real-robot trajectories, the proposed approach is evaluated by autoregressive rollout on unseen test trajectories and achieves sub-degree joint errors together with millimeter-level end-effector position errors verified by forward kinematics. Ablation and loss-component studies confirm that delta learning and explicit state conditioning are critical for stable long-horizon rollout. Comparisons with learning-based IK baselines and damped least-squares numerical IK baselines show that the proposed method provides a favorable speed–accuracy trade-off, with feedforward inference suitable for real-time trajectory-level deployment.