Predictive Inverse Kinematics: optimizing Future Trajectory through Implicit Time Integration and Future Jacobian Estimation

This paper presents an inverse kinematics (IK) method which can control future velocities and accelerations for multi-body systems. The proposed IK method is formulated as a quadratic programing (QP) that optimizes future joint trajectories. The features of the proposed IK are: (1) the evaluation of accelerations at future time instances, (2) the trajectory representation that can implicitly integrate the time integral formula into QP, (3) the computation of future Jacobian matrices based on the comprehensive theory of differential kinematics proposed in our previous work. Those features enable a stable and fast IK computation while evaluating the future accelerations. We also conducted thorough numerical studies to show the efficiency of the proposed method.