Vertex Search Algorithm of Convex Polyhedron Representing Upper Limb Manipulation Ability

Abstract

In the evaluation of robot manipulator, all possible velocities, accelerations, and forces at the end-effector can be represented as a polyhedra using the concept of manipulability (Yoshikawa, 1990). This evaluation method, which is commonly used in the field of robotics, provides effective knowledge for evaluation of the manipulability of upper and lower limbs considering both the kinematics and dynamics of the system (Sasaki et al., 2008, 2010). The manipulability of the upper and lower limbs in three-dimensional task space is expressed as an invisible six-dimensional polytope. For such evaluation, a slack variable is generally introduced in order to search for the vertex of the polytope (Shim & Yoon, 1997; Chiacchio et al., 1997; Lee, 2001). However, it is extremely difficult to search for the region of a higher-dimensional polytope accurately using conventional methods because of their huge computational complexity, and it is also difficult to formulate an objective function in the case of linear programming. In this chapter, we present a manipulating force polytope reflecting an individual’s joint torque characteristics as a new evaluation method for assessing the manipulability of an upper limb. We also present a visualization algorithm and a vertex search algorithm for a higher-dimensional polytope based on the geometric characteristic of joint torque space. The effectiveness of the method proposed for quantitative evaluation of the individual’s manipulability of the upper limb is confirmed through the presented experimental result.