Non-singular configuration analyses of redundant manipulators for optimizing avoidance manipulability

This paper is concerned with a new concept of avoidance manipulability inspired from manipulability. The manipulability represents the ability to generate velocity at the tip of each link without any designated hand task. The avoidance manipulability represents the shape-changeability (avoidance ability) of each intermediate link when a prior hand task is given. The intermediate links represents all comprising links of robot except top link with end-effector. The avoidance matrices, ¹M _i (i = 1; ¢ ¢ ¢ ; n ¡ 1) corresponding to all i-th intermediate links, are used for analyzing avoidance manipulability, resulting in that rank( ¹M _i) declares the shape-changeable space expansion and singular values of ¹M _i indicates the avoidance ability of i-th link. In this research, what assumption can guarantee mathematically the configurations with maximum rank( ¹M _i) is our main concern for maximizing shape-changeability to prepare effectively dynamic change of environment or sudden appearance of obstacles. Then we proved that our "Non-singular Configuration Assumption" can guarantee the maximum rank of ¹M _ithrough detailed decomposition analyses of ¹M _i.