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Recently, robots with high degree-of-freedom (DOF) have been used widely in various fields. These robots are able to conduct multiple purposes such as obstacle avoidance, postural control, trajectory tracking, etc. simultaneously using their redundancy. Hence, various motion generation methods are proposed for such robots. However, many conventional methods use the pseudo-inverse and null-space of the Jacobian matrix. Then the dedicated evaluation indexes are needed to solve the redundancy. These processes generally require the advanced expertise. Meanwhile, methods using configuration space have been utilized for a long time. However, these methods require enormous computation since the methods use iterative calculation. Recently, “virtual spring-damper hypothesis” was proposed as the motion generation method without using the expertise and iterative calculation for high redundant systems. In this method, the end-effector of the robot arm and reference point is connected by the virtual spring and damper in simulation space. The dynamic motion simulation is performed, then, from the simulation result, reference motion of the real robot arm is obtained. In this paper, a method that extends the virtual spring-damper hypothesis is proposed. In the proposed method, the virtual external force and torque are used to satisfy multiple constrains. Then, the effectiveness of the method is confirmed through several numerical simulations. 1. 緒 言 近年のロボットは多自由度化が進み,冗長性の高いものが利用されるようになってきている.高い自由度を 持つロボットは,その冗長性を利用することで,障害物の回避や重心位置の制御といった,複数の要求を満た した動作が可能になる.しかしその一方で,動作の生成そのものが課題となっている.冗長性を持つロボット は,動作目標を与えられたとき,目標を達成できる動作が無数に存在する.そのため,一般的に逆運動学の解 が一意に定まらない.これは逆運動学の不良設定問題として知られ,動作生成を難しくする一因となっている. 高冗長性を持つ多関節ロボットに対する動作の生成手法としてこれまでに数多くの手法が提案されている (Whitney, 1969)(Liegeois, 1977)(Yoshikawa, 1985)(Nakamura, 1991)(Hollerbach and Suh, 1987)(Khatib, 1987).これらの 手法は,大まかに運動学的アプローチと動力学アプローチに分類できる.どちらのアプローチでもヤコビ行列 の疑似逆行列(Whitney, 1969)を導入し,その零空間を特定の評価指標によって最適になるように決定することで, 冗長性を解決する(Liegeois, 1977).運動学的アプローチでは,可操作性(Yoshikawa, 1985)や,障害物回避(Nakamura, 1991),等が評価指標として利用され,ロボットの動作は関節角速度レベルで最適化される.また,動力学的ア プローチでは,トルクの二乗和(Hollerbach and Suh, 1987)や,運度エネルギー(Khatib, 1987)などが評価指標となり, 和地 天平*1,田川 泰敬*2

Motion planning of multi body robots using feedback control simulation (In the case of multiple physical constrains)