Solving the analytical inverse kinematics (IK) of redundant manipulators in real time is a difficult problem in robotics since its solution for a given target pose is not unique. Moreover, choosing the optimal IK solution with respect to application-specific demands helps to improve the robustness and to increase the success rate when driving the manipulator from its current configuration towards a desired pose. This is necessary, especially in high-dynamic tasks like catching objects in mid-flights. To compute a suitable target configuration in the joint space for a given target pose in the trajectory planning context, various factors such as travel time or manipulability must be considered. However, these factors increase the complexity of the overall problem which impedes real-time implementation. In this paper, a real-time framework to compute the analytical inverse kinematics of a redundant robot is presented. To this end, the analytical IK of the redundant manipulator is parameterized by so-called redundancy parameters, which are combined with a target pose to yield a unique IK solution. Most existing works in the literature either try to approximate the direct mapping from the desired pose of the manipulator to the solution of the IK or cluster the entire workspace to find IK solutions. In contrast, the proposed framework directly learns these redundancy parameters by using a neural network (NN) that provides the optimal IK solution with respect to the manipulability and the closeness to the current robot configuration. Monte Carlo simulations show the effectiveness of the proposed approach which is accurate and real-time capable ($\approx$ \SI{32}{\micro\second}) on the KUKA LBR iiwa 14 R820.

翻译：实时求解冗余机械臂的解析逆运动学（IK）是机器人学中的一个难题，因为针对给定目标位姿的解并不唯一。此外，根据具体应用需求选择最优的IK解，有助于提升机械臂从当前构型运动至目标位姿时的鲁棒性与成功率。这在高速动态任务（如空中抓取物体）中尤为关键。在轨迹规划中，为给定目标位姿计算关节空间的合适目标构型时，需考虑行程时间、可操作性等多种因素。然而，这些因素增加了整体问题的复杂度，阻碍了实时实现。本文提出了一种实时框架，用于计算冗余机器人的解析逆运动学。为此，将冗余机械臂的解析IK通过所谓的冗余参数进行参数化，这些参数与目标位姿相结合，从而得到唯一的IK解。现有文献中的大多数工作要么尝试近似机械臂目标位姿到IK解的直接映射，要么对整个工作空间进行聚类以寻找IK解。相比之下，所提框架直接利用神经网络（NN）学习这些冗余参数，该网络能够提供关于可操作性与当前机器人构型接近程度的最优IK解。蒙特卡洛仿真验证了所提方法的有效性，其在KUKA LBR iiwa 14 R820上精度高且具备实时能力（约\SI{32}{\micro\second}）。