Optimal Control For The Pneumatic Muscle Actuated Continuum Robot Based On The Online Jacobian Estimation

In recent decades,the higher requirements for safety,adaptiveness and flexibility were proposed for robots due to the extension of their tasks and working environment.Thereby the designs,actuations,theories and respective applications of continuum robots have been starting to draw increasing attentions.Thanks to the high compliant characteristic of mechanical structures and actuators,continuum robots can adapt to different geometric shapes and constrained environments.Due to the above advantage,continuum robots are promisingly applied to various settings with a lot uncertainty to accomplish complex tasks,such as rescues,explorations and surgeries.The complexity of the compliant mechanical structures and actuators,however,also brings some challenges to the controller design.For example,compared to the rigid industrial robots,the model of continuum robots includes a lot uncertainty and therefore it cannot be count on.Other than that,sensors are normally required to measure state variables of a robot to achieve a good control performance.But,it is not the case for continuum robots.Since complex sensors have to be mounted to measure the arc length of compliant actuators,the sensor system will become a way too complex and expensive,which is not practical and economical.To address the above issues,this paper proposed a model-free controller for a pneumatic muscle actuated continuum robot.It was able to estimate the Jacobian matrix of the continuum robot based on the adaptive Kalman filter.Without relying on an accurate model as well as complex sensors,it could drive the continuum robot to accomplish path tracking tasks.As the Kalman filter operated only a two-step algebraic calculation in every control interval,the low computational load and real-time control capability were guaranteed.By leveraging the null space projection method on the top of the estimated Jacobian,the robot configuration could be optimized and the buckling of the robot could also be avoided.Through simulation analysis and experimental validations,this control method showed accurate trajectory tracking and good robustness against the system uncertainty and external disturbance.