Solve inverse kinematics through a new quadratic minimization technique

A new technique was developed to solve inverse kinematics based on quadratic minimization. Firstly the inverse kinematic problem was formulated as a quadratic minimization problem through the constitution of a quadratic objective function derived from quaternion based kinematic description, then a new technique is developed to solve the quadratic minimization problem. The iteration procedures of the new technique are organized in two main phases: compute the search direction based on dynamic system synthesis; seek for acceptable step along the search direction. Numerical examples showed that inverse kinematic solutions can be delivered in a robust and time-efficient way, to meet the requirements coming across in the application field of every daily living support.