Tracking the Kinematically Optimal Trajectories by Mobile Manipulators

Abstract

This paper addresses the kinematically optimal control problem of the mobile manipulators. Dynamic equations of the mobile manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the mobile manipulator when tracking the trajectory by the end-effector. A computationally simple class of the Jacobian transpose control algorithms is proposed for the end-effector trajectory tracking. Such controllers apply a new non-singular Terminal Sliding Mode (TSM) manifold defined by a non-linear integral equality of the second order with respect to the task space tracking error. Based on the Lyapunov stability theory, the proposed Jacobian transpose control schemes are proved to be finite-time stable provided that some well-founded assumptions are fulfilled during the mobile manipulator movement. The performance of the proposed control strategies is illustrated through computer simulations for a mobile manipulator that attains trajectory tracking by the end-effector in a two-dimensional task space and simultaneously minimises some objective function.

A finite‐time adaptive Taylor series tracking control of electrically‐driven wheeled mobile robots

“…As can be seen in Table 6, some refs. [43,45,48,50,52,55] have used only one Lyapunov-like positive definite function in their stability analysis because of the structure and assumptions they have made. For example, control methods designed in [43,45,48] have not contained any adaptive mechanisms or estimators.…”

“…Utilizing an output feedback design, a finite-time non-linear control scheme [49] was proposed for a non-holonomic WMR. Guaranteeing the finite-time stabilization, a torque-based robust controller [50] and a second-order sliding-mode control [51] were developed for a mobile manipulator and a WMR, respectively. A kinematic/dynamic controller equipped with an adaptive neural network control method [52] was designed for finite-time trajectory tracking of WMRs with uncertainties.…”

“…• Motivated by refs. [43,45,46,47,48,50,52] which have developed finite-time stability and refs. [36,[53][54][55][56] which have provided semi-global practical finite-time stability, the finite-time convergence of inner closed-loop system is ensured by employing a non-singular sliding surface, and two Lyapunov-like positive definite functions.…”

Normal form approach in the motion planning of space robots: a case study

“…In [17] a model predictive control algorithm has been applied to tracking control a free-floating space robot. Desirable performance qualities characterize the finite-time tracking algorithm for mobile manipulators, based on the terminal sliding mode manifold technique, described in [4]. As is well known, both the predictive control as well as the sliding mode control exhibit some robustness against model uncertainty and external disturbance.…”

Collaborative Control of Mobile Manipulator Robots Through the Hardware-in-the-Loop Technique

“…Systems generally made up of two or more mobile manipulator robots that fulfill a common objective are called collaborative robots [10] which allows for multi-tasking operations [11], allowing standard controllers to cooperate with each other, to perform complex tasks that cannot be performed by a single robot [12], The control schemes of the collaborative robots are mainly based on: i) centralized architecture in which the central computer generates the control actions to achieve the secondary projections [13]; ii) decentralized architecture, in which all components of the robotic system consist of the proprietary processing unit which develops both kinematic and dynamic control [13].…”