Compressed Orientation Reachability Maps for Sub-Second Robotic Needle Entry Point Planning

In the context of multi-stage trajectory planning for robotic percutaneous liver interventions, identifying a kinematically feasible entry point remains a critical computational bottleneck. Existing methods rely on exhaustive inverse kinematics or randomized searches, incurring delays of 13 to 27 seconds per target and limiting real-time intraoperative adaptation. This paper introduces an Orientation-Based Reachability Map (ORM) that precomputes the kinematic feasibility of a 6 Degrees of Freedom (DoF) serial manipulator across 188,873 workspace positions and encodes orientation feasibility into a compact, indexed 83 MB map. A Just-In-Time (JIT) compiled runtime pipeline replaces live optimization with near-instantaneous array lookups. Experimental evaluation demonstrates a reduction in planning latency from 13.5-26.9 s to 0.289-0.349 s per target while maintaining high geometric fidelity, achieving a mean convex hull volume overlap ratio of 0.933 and a mean alpha-shape volume ratio of 0.976 relative to the baseline reachable point cloud. The proposed ORM framework enables sub-second entry point planning and provides an efficient computational framework for robotic needle insertion in percutaneous liver ablation.