End-trajectory Optimization And Control Of Rigid-flexible Coupled Manipulators

With the advancement of industrial automation technology,the structure of the manipulators has been developing from the initial bulky and huge to miniaturized and lightweight.The manipulators composed of lightweight flexible components requires less material,lighter weight,higher operating speed,lower energy consumption,etc.Therefore,under the requirement of stability and strength,flexible manipulators are more and more widely used in engineering.However,the dynamic model of the flexible arm is highly coupled,time-varying,nonlinear,and underactuated,it is a multi-input and multi-output system.During the movement of the flexible manipulator,elastic vibration is generated due to the exchange of elastic potential energy and kinetic energy.The vibration deformation not only affects the position control accuracy of the manipulator,but also reduces the tracking accuracy of the movement process.If the staff makes mistakes,it will cause the movement of the end effector of the flexible manipulator to collide,causing accidents or damage to the manipulator.Therefore,there are more uncertainties when designing the controller of the system.The research of flexible manipulator has been paid more and more attention.This paper takes the rigid-flexible coupled manipulator as the research object,and the research work is carried out from the following aspects:(1)The dynamic model of the rigid-flexible manipulator is established based on the Lagrange equation method,and the Coulomb viscous friction model is further introduced to improve the accuracy of the model.The infinite-dimensional dynamic model of the system is discretized by the hypothetical mode method,and then the discretized model is truncated in combination with the Galerkin truncation theory,and a fifth-order model is obtained to approximate the original infinite-dimensional system.Finally,The truncated first three-order modal vibration energy accounts for 99.5%of the total vibration energy of the flexible arm through the simulation solution,which proves the rationality of the dimension reduction model.(2)The relationship between the joint trajectory and the elastic deformation of the flexible arm is obtained according to the dimensionality-reduced dynamic model,and the influence of the joint trajectory on the vibration of the flexible arm end is studied.The trajectory planning effects of quintic polynomial interpolation,cycloid motion interpolation and cosine function interpolation are compared and analyzed,and then the superposition of cosine functions is selected as the joint angle planning function.The minimum residual vibration displacement at the end of the flexible arm is regarded as the objective function,and the joint trajectory parameters with the minimum elastic deformation are found based on multi-swarm genetic algorithm optimization.The simulation results show that the elastic vibration of the flexible arm end is reduced by30.3%,The residual vibration amplitude at the target point is reduced by60.6%.(3)We design a sliding mode predictive controller combined with a low-dimensional approximate fifth-order model to realize the trajectory tracking control of the end of the flexible arm.The internal dynamic subsystem that affects the vibration of the flexible arm is approximately transformed into a zero-dynamic subsystem to suppress the vibration of the end of the flexible arm;The future output of the system is predicted by the prediction model,and the motion control accuracy of the system is improved.Compared with the traditional sliding mode controller,it is concluded that the control strategy has better trajectory tracking performance,and the elastic vibration displacement amplitude at the end of the flexible arm is reduced by 70.6%.(4)We carried out trajectory tracking and residual vibration suppression experiments on the rigid-flexible coupled manipulator experimental bench.The experimental results show that the proposed trajectory optimization method significantly reduces the residual vibration at the end of the flexible arm,Compared with the traditional sliding mode controller,the sliding mode predictive controller we designed can significantly reduce the elastic vibration of the end of the flexible arm,and the trajectory tracking performance is better.