Inverse kinematics for the variable geometry truss manipulator via a Lagrangian dual method

Abstract

This article studies the inverse kinematics problem of the variable geometry truss manipulator. The problem is cast as an optimization process which can be divided into two steps. Firstly, according to the information about the location of the end effector and fixed base, an optimal center curve and the corresponding distribution of the intermediate platforms along this center line are generated. This procedure is implemented by solving a non-convex optimization problem that has a quadratic objective function subject to quadratic constraints. Then, in accordance with the distribution of the intermediate platforms along the optimal center curve, all lengths of the actuators are calculated via the inverse kinematics of each variable geometry truss module. Hence, the approach that we present is an optimization procedure that attempts to generate the optimal intermediate platform distribution along the optimal central curve, while the performance index and kinematic constraints are satisfied. By using the Lagrangian duality theory, a closed-form optimal solution of the original optimization is given. The numerical simulation substantiates the effectiveness of the introduced approach.