Inverse kinematics of asymmetric octahedral variable geometry truss manipulator with obstacle avoidance through inexact interior point optimization

Abstract

This article studies the inverse kinematics for asymmetric octahedral variable geometry truss manipulator with obstacle avoidance. The inverse kinematics problem is cast as a nonconvex optimization that having quadratic objective function subject to quadratic constraints. This article uses an inexact interior point optimization to solve it, which is developed on the basis of the imprecise algorithm Ipopt. According to the particularity of our actual optimization problem, each iteration undergoes specific modifications so as to minimize the memory consumption as well as computation time. Utilizing the sparse and binary characteristics of the coefficient matrix, respectively, the algorithm allocates the computation to the finite sparse matrix vector multiplication and changes the storage form, which greatly reduces the memory space. Based on the unique rules of inverse kinematics, the iteration direction of the algorithm becomes more clear. With the aid of mechanical constraints inherent in the manipulator, the algorithm omits the feasibility recovery part that embedded in the solver Ipopt. All these make us save the operation time greatly while utilizing Ipopt algorithm. To demonstrate the effectiveness of the proposed approach, the scheme was applied to obstacle avoidance inverse kinematics of variable geometry truss manipulator with three modules.