Inverse kinematics and redundancy resolution in manipulators: Methods, optimization objectives, and future trends

Redundant manipulators possess additional degrees of freedom that enable superior dexterity, adaptability, and fault tolerance in complex environments. However, this redundancy also introduces challenges in inverse kinematics (IK) and redundancy resolution, as multiple feasible joint configurations may exist for a given end-effector task. This review systematically summarizes the state of the art in IK methods and optimization objectives for redundant manipulators. It first classifies IK approaches into analytical, numerical, optimization-based, and artificial intelligence-driven categories, highlighting their mathematical foundations, computational efficiency, and real-time feasibility. Next, various optimization objectives are analyzed from three perspectives: manipulability and dexterity indices, joint-level criteria such as torque or energy minimization, and task-level performance metrics including accuracy, smoothness, and collision avoidance. The integration of IK and redundancy resolution within hierarchical control, task-priority, and multi-objective frameworks is discussed, along with representative applications in industrial, medical, service, and space robotics. Finally, emerging research directions are identified, including hybrid learning-optimization paradigms, system-level fusion, collaborative redundancy resolution in multi-agent systems, and digital twin-enabled evaluation for trustworthy deployment. This survey provides both theoretical and practical insights for developing adaptive, explainable, and deployable redundancy-resolution systems for next-generation intelligent robots.