ソボレフノルムによる衝突力の上限保証
Bounded Collision Force by the Sobolev Norm
ソボレフノルムをシステムノルムとして用い、一般的な動的システムにおける剛性要素への最大衝突力の厳密な上限を与え、制御や柔軟関節ロボットへの応用を可能にした。
著者: Kevin Haninger, Dragoljub Surdilovic
分類: cs.RO, cs.SY, eess.SY
原文アブストラクト
A robot making contact with an environment or human presents potential safety risks, including excessive collision force. While experiments on the effect of robot inertia, relative velocity, and interface stiffness on collision are in literature, analytical models for maximum collision force are limited to a simplified mass-spring robot model. This simplified model limits the analysis of control (force/torque, impedance, or admittance) or compliant robots (joint and end-effector compliance). Here, the Sobolev norm is adapted to be a system norm, giving rigorous bounds on the maximum force on a stiffness element in a general dynamic system, allowing the study of collision with more accurate models and feedback control. The Sobolev norm can be found through the $\mathcal{H}_2$ norm of a transformed system, allowing efficient computation, connection with existing control theory, and controller synthesis to minimize collision force. The Sobolev norm is validated, first experimentally with an admittance-controlled robot, then in simulation with a linear flexible-joint robot. It is then used to investigate the impact of control, joint flexibility and end-effector compliance on collision, and a trade-off between collision performance and environmental estimation uncertainty is shown.
