An Extended Jacobian-Based Formulation for Operational Space Control of Kinematically Redundant Robot Manipulators With Multiple Subtask Objectives: An Adaptive Control Approach

Abstract

In this study, an extended Jacobian matrix formulation is proposed for the operational space tracking control of kinematically redundant robot manipulators with multiple subtask objectives. Furthermore, to compensate the structured uncertainties related to the robot dynamics, an adaptive operational space controller is designed, and then, the corresponding stability analysis is presented for kinematically redundant robot manipulators. Specifically, the proposed method is concerned with not only the stability of operational space objective but also the stability of multiple subtask objectives. The combined stability analysis of the operational space objective and the subtask objectives are obtained via Lyapunov based arguments. Experimental and simulation studies are presented to illustrate the performance of the proposed method.

Self-Adjusting Fuzzy Logic Based Control of Robot Manipulators in Task Space

“…The results in [14] are extended in [15] and [16] with the addition of a novel stability analysis for the subtask objectives. These results are further improved in [17], where asymptotic stability of the subtask objectives were proven. An end effector space tracking controller was designed in [18], where both kinematic and dynamic uncertainties were dealt with gradient based adaptive update laws.…”

“…However, adaptive control strategy was adopted where regressor matrices are required to be found for all robots in the network. Similarly, in [17], the dynamical uncertainties are required to satisfy the linear parametrization property. When compared with [25], our proposed approach does not require variable structure type components (i.e., signum of the error) in the design of the control input torque.…”

“…When compared with [25], our proposed approach does not require variable structure type components (i.e., signum of the error) in the design of the control input torque. When compared with relevant neural network based methods, the main advantage of the proposed AFL compensation is the self-adjusting nature of the membership value vector obtained by estimating its widths and centers via the design of dynamic adaptive update laws in (17) and (18). A possible future work may aim designing output feedback versions of the controllers designed in this article that is restricting the controller design via the unavailability of the joint velocity feedback.…”

Adaptive tracking control of robot manipulators with input saturation and time‐varying output constraints

“…In contrast with RMC in joint space, RMC in task space is more intuitive and more realistic. Some researches try to solve the RMC problems in task space, using typically the adaptive control method based on a motion regression matrix to estimate the unknown parameters in the robot systems [27–34]. Two adaptive controllers were proposed in [30] to realize the objective of task‐space trajectory tracking for robot manipulators with uncertain kinematics and dynamics.…”

“…Two adaptive controllers were proposed in [30] to realize the objective of task‐space trajectory tracking for robot manipulators with uncertain kinematics and dynamics. In [33], the control of redundant robot manipulators with multiple subtask objectives was investigated, and an adaptive operational space controller was designed to compensate the structured uncertainties related to robot dynamics. Another approach to address RMC in task space is to adopt pseudo‐inverses of the Jacobian matrix [35–37] or extended Jacobian (the configuration control) [38–40].…”