In this thesis, we develop a set of inverse kinematics algorithms suitable for an anthropometric arm or leg. We use a combination of analytic and numerical methods to solve generalized inverse kinematics problems including position, orientation, and aiming constraints. Our combination of analytic and numerical methods result in faster and more reliable algorithms than conventional inverse jacobian and optimization based techniques. Additionally, unlike conventional numerical algorithms, our methods allow the user to interactively explore all possible solutions using an intuitive set of parameters that define the redundancy of the system.
In addition to computational speed and ease of interaction, we also address the problem of obtaining a realistic model of the workspace of the arm. In a conventional robotics-based approach the joints of the shoulder complex are modeled as independent degrees of freedom subject to simple linear inequality constraints. We use triangular Bezier surfaces to model the workspace of the arm and to encode the coupling between the clavicle and shoulder joints. Our approach can be used to fit empirical data thereby permitting accurate kinematic behavior to be incorporated into the model.
