On the Placement of Serial Manipulators

Abstract

Abstract Criteria and implementation for the placement robot manipulators with the objective to reach specified target points are herein addressed. Placement of a serial manipulator in a working environment is characterized by defining the position and orientation of the manipulator’s base with respect to a fixed reference frame. The problem has become of importance in both the medical and manufacturing fields, where a robot arm must be appropriately placed with respect to targets that cannot be moved. A broadly applicable numerical formulation is presented. While other methods have used inverse kinematics solutions in their formulation for defining a locality for the manipulator base, this type of solution is difficult to implement because of the inherent complexities in determining al inverse kinematic solutions. The approach taken in this work is based on characterizing the placement forcing a cost function to impel the workspace envelope in terms of surface patches towards the target points and subject to functionality constraints, but that does not require the computation of inverse kinematics. The formulation and experimental code are demonstrated using a number of examples.