Impedance Controller Design and Dynamic Solution of The Manipulandum

Abstract

This article explains the dynamic solution of the manipulandum that interact with the human upper arm, controller design, model simulation and simulation results. Manipulandum design in this field are used in human-machine interaction experiments to understand human motor learning skills. While the subject of experiments is handled in the field of medicine, appropriate manipulandum design is the subject of the engineering field. In this article, the engineering qualities of the device were evaluated, its mathematical model obtained, dynamic model simulation made and control elements were examined, but the experimental use of this device, which is serve medical science were not discussed in this context. In the literature review; The manipulandum have a 2-dof, 5-link closed chain structure that moves in the horizontal plane, their movement is provided by 2 actuators, their interaction with the human upper arm is made with a fixed joystick (end-effector) on the 2nd link, their dimensions are smooth and compatible with the human upper arm. It is understood that the manipulandum must be of a size that can safely interact with the human arm. A conceptual design was made for the manipulandum and the movement parameters of the manipulandum were obtained by creating a kinematic model accordingly. While creating the dynamic model of the system; It is accepted that the manipulandum moves in the horizontal plane, therefore there is no effect of gravity, there is no spring, damper or similar potential energy source in the system, and there is heat loss due to friction. The dynamic model obtained with the Euler Lagrange Method (ELM) was compared with the system model obtained with the Simulink Simscape Multibody (SSM) tool in the Simulink environment; The consistency of model parameters (friction coefficients, moment of inertia, etc.) was mutually checked. Since human-manipulandum interaction requires force control, an impedance controller has been designed for the system dynamics, instead of classical controllers. The success of the controller on both the ELM dynamic model and the model created in SSM was examined and the results were evaluated. As a result of the simulations; It is understood that in order to achieve meaningful position and force control, there must be a proportional magnitude relationship between the torques applied to the model by the actuators and the force applied to the end-effector.