A Passivity-Based Regressor-Free Adaptive Controller for Robot Manipulators With Combined Regressor/Parameter Estimation

Abstract

This paper develops a new function approximation technique (FAT)-based adaptive controller for the control of rigid robots called the adaptive passivity function approximation technique (APFAT) controller. This controller utilizes the passivity-based approach and simplifies the FAT controller design by eliminating the need for simultaneous estimation of the robot’s inertia matrix, Coriolis matrix, and gravity vector. The controller achieves its simplicity by treating the product of the regressor matrix and parameter vector as an unknown time-varying function to be approximated. The controller can be implemented in robots where the dynamic equations of motion are unknown. The stability of the controller is verified with Lyapunov functions by taking advantage of the passivity property of the robot dynamics. Simulation results on a three degree-of-freedom (DOF) PUMA500 robot demonstrate the ability to track reference trajectories using reasonable control signals when the inertia matrix, Coriolis matrix, and gravity vector are unavailable.

Robust tracking control of a robot manipulator using a passivity‐based extended‐state observer approach

“…Simulations were conducted for the proposed controller using the PUMA 500 robot at the Cleveland State University Controls, Robotics, and Mechatronics Laboratory. The reference trajectories, PUMA robot parameters, and controller gains were from [14], while b , the dc gain had a value of 1 for the three links. The reference trajectories are , , and .…”

“…The reference trajectories are , , and . The controller gains are K = diag([10 30 10]) and λ = diag([6 35 6]).The input constants were used to convert the manipulator's control signals from N‐m to V as in [14]. The input constants represent the combined effect of gear ratios, amplifier gains, and motor torque constants.…”

“…Passivity-based control was first introduced in [13], so that the closed-loop system becomes passive. Many control methods take advantage of this property in their control design [14][15][16][17]. In [14], the passivity-based properties were used to develop a new function approximation technique adaptive controller for the tracking performance of a robot manipulator.…”

“…Many control methods take advantage of this property in their control design [14][15][16][17]. In [14], the passivity-based properties were used to develop a new function approximation technique adaptive controller for the tracking performance of a robot manipulator. In [15], a passivity-based control scheme was designed for a certain class of non-holonomic mechanical systems by passive configuration decomposition.…”