Chaos-Steered Exploration with Safety-Constrained Kinematics in Redundant Systems

Safety critical human–robot collaboration requires inverse kinematics schemes that simultaneously maintain tracking accuracy in task space, exploit redundancy, and guarantee collision avoidance in human proximal workspaces. This paper proposes a Chaos-Aware Inverse Kinematics (CAIK) framework in which a low-dimensional deterministic chaotic map generates a structured and repeatable exploration signal injected into the Jacobian null space, while a safety critical quadratic program with higher-order control barrier function constraints enforces admissible motion. Simulation studies on a seven degree-of-freedom collaborative manipulator using a synthetic VR taught trajectory dataset show that CAIK preserves millimeter-scale Cartesian tracking accuracy, achieving [Formula: see text] of [Formula: see text], [Formula: see text], and [Formula: see text][Formula: see text]mm on circular, line, and figure eight tasks, respectively, while the corresponding minimum norm IK baseline yields [Formula: see text], [Formula: see text], and [Formula: see text][Formula: see text]mm. When the HoCBF constraints are enabled, collision violations are eliminated, and joint space dispersion increases markedly, reaching [Formula: see text] rad on the circular task compared to [Formula: see text] rad and [Formula: see text] rad on line and figure eight. These results indicate that deterministic chaos can provide posture diversity without degrading task tracking when coupled with barrier certified optimization, offering a computationally tractable pathway to safer and more versatile redundancy utilization in collaborative robotics.