Research On Optimal Control Of 4RRR Redundantly Actuated Flexible Parallel Mechanism

Parallel robot is a closed chain mechanism composed of multiple branch chains.The structural characteristic of the closed chain constraint limits the size of robot’s motion workspace and the kinematics operability and force operability are complex in the workspace.There are often maneuverability singularities which bring certain challenges to robot’s global motion planning and control.Redundant actuation technology is not only expected to overcome the singularity of force maneuverability of parallel mechanism,but also to eliminate clearance of the mechanism,dynamically adjust the operating stiffness and achieve energy optimization operation,etc.Redundant actuation,as its name implies,refers to a kind of mechanism whose number of original motion parts is more than the number of kinematics degrees of freedom.The extra redundant actuation inputs can realize the internal force adjustment of the mechanism,thus eliminating the structure clearance and the mechanical transmission backlash,achieving real-time adjustment of the mechanism operating stiffness and reducing the system energy consumption in complex operation tasks.Therefore,redundantly actuated mechanism has important application value in the high-speed and high-precision operation robot system.In this paper,the kinematics analysis,dynamics analysis,optimization control,and compliance control strategy of 4RRR redundantly actuated parallel robot are studied.Based on the geometrical structure of 4RRR redundantly actuated parallel robot,the forward and inverse kinematics models were established by using geometric method to solve the position,velocity,and acceleration of the end effector.The correctness of the kinematics model was verified by MATLAB.The dynamics models of joint space and operation space were built by Lagrange function,and the generation and application of internal forces were analyzed.The relationship among internal forces,driving forces and stiffness were established,therefore,the operation stiffness can be adjusted by controlling internal forces.In order to improve the situation of infinitely solutions of driving forces,4RRR redundantly actuated parallel robot was optimized with the minimum driving forces and energy consumption as optimization targets.Using MATLAB simulated the two optimization methods,the results show that the four driving forces are relatively balanced in driving forces as the optimization goal.The errors and driving forces are incorporated into a target system,and the optimal controller is designed according to the LQR principle.The effectiveness of the controller is verified by MATLAB,which can be applied to the high speed and high precision operation tasks of the robot.In order to make 4RRR redundantly actuated parallel robot complete the more complex tasks of surface polishing,assembly,and grinding,variable impedance control is proposed,and MATLAB is applied to verify the response characteristics.However,time variable impedance control can not suppress external interference.For further improving anti-interference ability of the system,sliding mode variable impedance control was put forward.The stability conditions of the system are analyzed using the Lyapunov stability theory,and the relationship between control parameters is derived.The results of simulation by MATLAB verified the control system performance.