Nonlinear PDE control of flexible robotic arms for state tracking and link-deflection mitigation

Abstract

This work presents a novel nonlinear control scheme for simultaneous state tracking and mitigation of undesired deflection effects in flexible robotic manipulators. The presented method directly incorporates the partial differential equations (PDEs) used for describing dynamics of the mechanism into the corresponding control calculations and assumes no form of reduction in PDEs (which in this work have been derived according to extended Hamilton principle for a rigid-flexible manipular when considering the flexible arm as an Euler-Bernoulli beam). Hence, the presented methodology should be considered as considerably more feasible for a wide range of applications in comparison with the conventional strategies which use assumed modes to analyze link flexibility dynamics or vibration effects. Furthermore, the proposed controller ensures state tracking and link-deflection boundedness only using standard control inputs to the mechanism without incorporating additional boundary inputs (which essentially represents satisfaction of more control objectives than the limited number of inputs would allow in conventional controllers), which would render it a viable choice for robotic applications where additional inputs cannot be easily exerted to end effector or cases where this strategy would require significant modifications in existing devices. Numerical simulations indicate the effectiveness of the presented control scheme.