Global optimisation analysis for a planar redundant serial manipulator

Abstract

A planar serial manipulator with three rotational joints (planar 3R) can be seen to be a kinematically redundant system if only the position of the end-effector is taken into account. A symbolic computation analysis reveals that kinematic singularities for such manipulators appear at the position of the end-effector where the number of real connected components changes. In addition, apart from the singularities at the boundaries of the workspace, all inner singularities have a symmetric characteristics such that one rotational angle equals to 180 degrees, which often corresponds to an excess of a joint limit with real industrial robots systems. A global optimisation with a cost function regarding the joint limits depended on configurations of planar serial 3R manipulators will be considered in this work in detail. We analyse and show the variation behaviour of the global minimisation among its workspace with a fixed end-effector or when the end-effector follows algebraic motions (for instance, algebraic curves in the special Euclidean group). This gives us new insights. First, the global minimum is not unique. Second, the global minimum could have a jump in the configuration set due to ambiguous minima.