Optimal path placement for kinematically redundant manipulators

The problem of path placement for redundant manipulators is discussed. This includes the problem of where to place the art and other components (such as other robots, tables, or machining stations) relative to each other and how to resolve the redundancies of the system and process in an optimal fashion. The method developed involves assigning a variable to each degree of freedom of the transforms which define the system (i.e. to the system redundancies). These variables are then used to incorporate the path constraints of the robot into the cost function to be minimized. The resulting unconstrained minimization problem is numerically solved. This method is applied to a system of three cooperating robots, and results are presented