Abstract
In this study, the solution to the kinematically optimal control problem of the mobile manipulators is proposed. Both dynamic equations are assumed to be uncertain, and globally unbounded disturbances are allowed to act on the mobile manipulator when tracking the trajectory by the end effector. We propose a computationally efficient class of cascaded control algorithms, which are based on an extended Jacobian transpose matrix. Our controllers involve two new non-singular terminal sliding mode manifolds defined by nonlinear integral equalities of both the second order with respect to the task space tracking error and the first order with respect to reduced mobile manipulator acceleration. Using the Lyapunov stability theory, we prove that the proposed Jacobian transpose cascaded control schemes are finite time stable provided that some practically reasonable assumptions are fulfilled during the mobile manipulator movement. The numerical examples carried out for mobile manipulators [consisting of a non-holonomic platform of type (2, 0) and holonomic manipulators of 2 and 3 revolute kinematic pairs], which operate in two-dimensional and three-dimensional work spaces, respectively, illustrate both the trajectory tracking performance of the proposed control schemes and simultaneously their minimising property for some practically useful objective function.
Highlights
Mobile manipulators are robotic systems, for which the range in the work space of the non-holonomic mobile platforms is, unbounded
Controllers to be designed should accurately track desired end effector trajectory despite possible singularities met on this trajectory, uncertain dynamic equations, unknown payload to be transferred by the end effector and external disturbances
The present study introduces a new class of controllers being finite time stable for mobile manipulators whose mobile platforms are subject to non-holonomic constraints
Summary
Mobile manipulators are robotic systems, for which the range in the work space of the non-holonomic mobile platforms is, unbounded. The task of the second sub-system, which takes into account uncertain dynamics and unknown disturbances, is a dynamic compensation of the error appearing between the actual reduced acceleration of the mobile manipulator and the reference acceleration obtained from the first sub-controller Both controllers use ( introduced in the paper) a new dynamic version of the classic (static) computed torque known from the literature [38,39]. 3. Section 4 presents numerical simulation results carried out for a mobile manipulator (consisting of a non-holonomic platform of type (2, 0) and a holonomic manipulator of two revolute kinematic pairs) operating in a two-dimensional work space whose task is to track a desired end effector trajectory and simultaneously to minimise some practically useful objective function. Throughout this paper, λmin(·), λmax(·) denote the minimal and maximal eigenvalues of the matrix (·)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
