Optimal placement of serial manipulators

This dissertation presents mathematical methods for the placement of serial robot manipulators with respect to predefined target points. A number of evaluation measures used to optimize such placement are implemented in terms of cost functions. 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 medical, manufacturing, and ergonomic fields where a kinematic chain must be appropriately placed with respect to targets that cannot be moved. A broadly applicable numerical formulation based on optimization techniques is proposed. Other methods have used inverse kinematic 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 inverse kinematics solutions. Methods given in the dissertation do not rely upon inverse kinematics but present an effective optimization-based method for placement. The approach proposed in this research is of twofold: (1) Characterizing the placement by forcing a cost function to impel the workspace envelope in terms of surface patches towards the target points and, (2) Positioning and orienting the workspace with respect to the target points, thus defining the new placement. Implementation of the methods in other fields pertaining to human modeling and simulation are addressed with implications to ergonomics. The formulations and methods presented in this dissertation are demonstrated using a number of planar and spatial examples, including redundant models.