Inverse Kinematics and Sensitivity Minimization of an nStack Stewart Platform The method of Frobenius Norm (FN) minimization of forward kinematic Jacobians is presented to minimize the sensitivity of a robotic manipulator. We demonstrate the effectiveness of this approach with a Monte Carlo simulation of an Assembler robot. The Assembler is described as a stack of Stewart Platforms designed for inspace assembly to aide NASA in deep space exploration. The translations and rotations between each Stewart Platform define the forward kinematics of the Assember, which analytically determine the end effector position and orientation. However, selecting the poses of each Stewart Platform which yield a desired end effector state, defined as the inverse kinematics, is an underconstrained nonlinear optimization problem for large Assembler stacks.

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 multibody 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.