An extended stiffness model for 7 Dofs collaborative robots using the virtual joint method In order to improve the stiffness modeling accuracy, an extended stiffness modeling and identification method of a 7 degrees of freedom(Dofs) collaborative robot is introduced in this paper. Unlike the traditional stiffness model which is assumed that each actuated joint is presented by a single onedimensional virtual spring, the compliance of links, bearings and other structural components are considered and equivalent to two virtual joints in this method. These two additional virtual joints are orthogonal to the rotation axis of actuated joints. Including the equivalent virtual joint of joint torsional stiffness, each actuated joint of the robot has three virtual joints eventually. The method extends the traditional virtual joint method(VJM) and opens new prospects in terms of the stiffness optimal synthesis. Meanwhile, the accuracy of stiffness modeling is improved. Based on a 7 Dofs collaborative robot SHIR5, the static compliance simulations are performed to identify the elastic parameters of the robot, and the results show that more precise Cartesian stiffness characteristics are obtained from the extended stiffness model. Finally, the influence of compliance of links, bearings and other structural components on the stiffness model of the robot are analyzed.

Impedance Control Strategy and Experimental Analysis of Collaborative Robots Based on Torque Feedback In this paper, through the modeling and analysis of flexible joints, an impedance controller based on torque feedback is proposed, which is used to realize the active compliance of collaborative robots. The controller includes two parts: torque controller and impedance controller. The torque controller is used to compensate the robot dynamics, and the impedance controller is used to adjust the joint stiffness and damping. The theoretical analysis of the control strategy shows that the significance of torque feedback is that it can reshape the inertia of the motor, reduce friction torque and suppress unknown disturbances. In order to ensure tracking accuracy, a task errorbased disturbance observer is designed. Experiments with a 7DOF collaborative robot show that the proposed controller in this paper can realize the body compliance and obtain better compliance performance than the traditional compliance control method.