Kinematic Synthesis of Multi-fingered Robotic Hands for Finite and Infinitesimal Tasks

In this paper we present a novel method of designing multi-fingered robotic hands using tasks composed of both finite and infinitesimal motion. The method is based on representing the robotic hands as a kinematic chain with a tree topology. We represent finite motion using Clifford algebra and infinitesimal motion using Lie algebra to perform finite dimensional kinematic synthesis of the multifingered mechanism. This allows tasks to be defined not only by displacements, but also by the velocity and acceleration at different positions for the design of robotic hands. The additional information enables an increased local approximation of the task at critical positions, as well as contact and curvature specifications. An example task is provided using an experimental motion capture system and we present the design of a robotic hand for the task using a hybrid Genetic Algorithm/LevenbergMarquadt solver.