Dynamics And Control Of Rope Driven Snake Manipulator Considering The Rope-hole Characteristics

The rope-driven snake manipulator(RDSM)is a hyper-redundant mechanism designed based on the principle of bionics,which is composed of multiple rigid or flexible joints in series.It is also known as the elephant nose robot,bionic octopus,bionic tentacle,etc..For the operating environment with narrow space,closed structure and dense obstacles,ordinary manipulators cannot enter due to less freedom and large size of the mechanism,while RDSMs can enter with operating tools.Therefore,there are broad application prospects for the RDSM in aerospace,petrochemical,medical equipment,nuclear industry and other fields.Although the RDSM has achieved certain results at this stage,it is faced with the shortcomings of low motion accuracy and poor anti-interference ability.Incomplete control modeling and failure to consider model uncertainty are the main reasons for the above shortcomings.Aiming at the above problems,this paper conducts research on the modeling and sliding mode control of a RDSM considering the rope hole nonlinearity.This paper designed a 16 degrees of freedom(DOFs)RDSM and established a virtual prototype model and an experimental prototype.The modeling process of the RDSM based on the ideal rope hole model is as follows: First,the rope is simplified to the rope segment force,and the kinematics model of the articulated robot is established using the DH matrix.Then the rope hole position and the position are calculated through the mechanism kinematics model,from which the mapping relationship between rope velocity and joint velocity is obtained.Finally,the rope equivalent driving torque the joint is calculated based on the principle of virtual work,and the dynamic model RDSM is established by using the Lagrange equation.When considering rope hole friction,rope hole gap,rope flexibility,rope length and rope tension are greatly affected.In order to establish the rope hole nonlinear model,the rope hole friction model based on the Stribeck model are established,and then the Chebyshev polynomial is usd to fit the rope length error caused by the rope hole gap.Finally the rope segment tension based on the rope hole friction model and the rope flexibility error are calculated.The rope length error is caused by the rope hole gap error and the rope flexibility error.Through the rope length error modeling,the kinematics model of the RDSM can be corrected.The pulling force of the rope segment can be equivalent to the force spiral acting on the center of the universal joint,thus the rope force can be converted into the equivalent driving force of the joint,and the Lagrange equation is used to obtain the RDSM dynamic model with the the rope hole friction.Simulation and experimental results show that by considering the rope hole nonlinear compensation,the error between simulation and experimental results can be greatly reduced,thereby verifing the kinematic and dynamic model of the rope-driven snake-shaped manipulator.In order to perform the inverse kinematic and inverse dynamic calculation,the nullspace self-motion of the redundant robot is optimizeed necllarily when completing the main-motion in the task space.There are many DOFs for the RDSM,and multiple extreme values for the optimization objective function in the motion space.The Jacobian matrix pseudo-inverse method which is commonly used is not ideal for the optimization effect,while the intelligent optimization algorithm cannot guarantee real-time performance.To solve this problem,this paper uses shape optimization and joint angle optimization methods to optimize the kinematics of the RDSM.Firstly,The shape of the serpentine arm is identified based on the 3rd-order Bézier curve,and the curve length is calculated by the 3/8 Simpson rule.Then the optimization objective function is formulated according to the length error between the curve and the actual mechanism.Finally,the Bézier curve control point coordinates are calculated by the gradient method to obtain the shape function.The shape universal joint center is constrained on the shape curve,which can transform the hyper redundant mechanism into multiple low redundant mechanisms.Based on the Jacobian matrix pseudo-inverse method,the joint angle can be optimized.The position variation of the dynamic model is used to derive the stiffness model of the RDSM,and the rope tension that satisfies both the dynamic equation and the stiffness equation can be solved.The rope tension optimization is realized based on the linear quadratic optimization method.At the same time,the model reconstruction technology is used to adjust the rope tension which can prevent the driving force from exceeding the limit during the motion.In this paper,a trajectory tracking controller is designed based on the variable structure sliding mode control,so that the RDSM can effectively resist the uncertainty disturbance during the movement.By constructing a joint state observer and using the torque calculation method for feedback linearization,the disturbance observer and the hyperbolic tangent function are used to weaken the "chattering" phenomenon of sliding mode control.Based on the feedback linearization model of RDSM,the trajectory tracking sliding mode controllers of the joint space,the task space and the extended task space are designed respectively.The co-simulation method is used to compare the motion control effects of the three controllers with considering the rope hole compensation and without the rope hole compensation.The results show that the position tracking error and control force "chattering" of the sliding mode controller considering the rope hole compensation are smaller than those of the sliding mode controller without considering the rope hole compensation;There are higher trajectory tracking accuracy for the sliding mode controller based on the extended task space than the the joint space sliding mode controller and stronger stability than the task space sliding mode controller.Finally,an experimental prototype is used to verify the trajectory tracking effect of the sliding mode controller based on the extended task space.