Induced Norm-Based Analysis for Computed Torque Control of Robot Systems

摘要

This paper is concerned with providing a new quantitative analysis method of computed torque control of robot systems by using three types of induced norm. This paper first considers design of a computed torque controller to achieve a trajectory tracking performance of a robot manipulator. Taking into account of the effects of unknown elements on the tracking performance, this paper next divides the unknown elements into model uncertainty and disturbance, and introduces various closed-loop representations of robot systems consisting of robot manipulators together with computed torque controllers and unknown elements. This paper further derives a readily applicable robust stability condition for the model uncertainty by using two types of induced norm from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> and from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_\infty $ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_\infty $ </tex-math></inline-formula> . Regarding a performance analysis for the disturbance, this paper also proposes to take the induced norm from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_\infty $ </tex-math></inline-formula> , by which the relation between the maximum tracking errors caused by the disturbance and the corresponding parameters of the computed torque controllers are dealt with. Finally, this paper gives some experiments to validate the effectiveness of the performance analysis methods based on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_\infty /L_{2}$ </tex-math></inline-formula> -induced norm.