MIMO and SISO Self-Tuning Hybrid Position/Force Control of Robotic Manipulators

Abstract

The paper presents a new approach for the hybrid position/force control of a manipulator by using self-tuning regulators (STR). For this purpose, the discrete-time stochastic multi-input multi-output (MIMO) and single-input single-output (SISO) models are introduced. The MIMO model whose output vector has the positions and velocities of the gripper expressed in the world (xyz) coordinate system as the components. The SISO model outputs are the hybrid errors consisting of the derivatives of the position and force errors at the joints. The inputs of both models are the joint torques. The unknown parameters of those models can be calculated recursively on-line by the square-root estimation algorithm (SQR). An adaptive MIMO and SISO self-tuning type controllers are then designed by minimizing the expected value of a quadratic criterion. This performance index penalizes the deviations of the actual position and force path of the gripper from the desired values expressed in the Cartesian coordinate system. An integrating effect is also included in the performance index to remove the steady-state errors. Digital simulation results using the parameter estimation and the control algorithms are presented and the performances of those two controllers are discussed