Placement of robot manipulators to maximize dexterity

Placement of robotics manipulators involves the specification of the position and orientation of the base with respect to a predefined work environment. This work presents a general approach to the placement of manipulators based on the kinematic dexterity of mechanisms. In many robotic implementations, it is necessary to carefully plan the layout of the workplace, whether on the manufacturing floor or in robot-assisted surgical interventions, whereby the robot base must be located in a way that maximizes dexterity at or around given targets. In this article we pose the problem in an optimization form without the utilization of an inverse kinematics algorithm, but rather by employing a dexterity measure. A new dexterous performance measure is developed and used to characterize a formulation for moving the workspace envelope (and hence the robot base) to a new position and orientation. Using this dexterous measure, numerical techniques for placement of the robot based on a method for determining the exact boundary to the workspace are presented and implemented in computer code. Examples are given to illustrate the techniques developed using planar and spatial serial manipulators.