We address the problem of tracking control of multiple mobile robots advancing in formation along straight-line paths. We use a leader-follower approach, and hence, we assume that only one swarm leader robot has the information of the reference trajectory. Then, each robot receives information from one intermediary leader only. Therefore, the communications graph forms a simple spanning directed tree. As the existence of a spanning tree is necessary to achieve consensus, it is the minimal configuration possible to achieve the formation-tracking objective. From a technological viewpoint, this has a direct impact on the simplicity of its implementation; e.g., less sensors are needed. Our controllers are partially linear time-varying with a simple added nonlinearity satisfying a property of persistency of excitation, tailored for nonlinear systems. Structurally speaking, the controllers are designed with the aim of separating the tasks of position-tracking and orientation. Our main results ensure the uniform global asymptotic stabilization of the closed-loop system, and hence, they imply robustness with respect to perturbations. All these aspects make our approach highly attractive in diverse application domains of vehicles' formations such as factory settings.
We solve the formation tracking control problem for mobile robots via linear control, under the assumption that each agent communicates only with one 'leader' robot and with one follower, hence forming a spanning-tree topology. We assume that the communication may be interrupted on intervals of time. As in the classical tracking control problem for non-holonomic systems, the swarm is driven by a fictitious robot which moves about freely and which is a leader to one robot only. Our control approach is decentralised and the control laws are linear with time-varying gains; in particular, this accounts for the case when position measurements may be lost over intervals of time. For both velocity-controlled and force-controlled systems, we establish uniform global exponential stability, hence consensus formation tracking, for the error system under a condition of persistency of excitation on the reference angular velocity of the virtual leader and on the control gains.
In this paper, the position synchronization problem of robotic manipulators, in master–slave form, under a coordinated control scheme is addressed in both joint and task/operation space. The manipulators are considered fully actuated, with all system states measurable. The desired trajectory is only accessible to the master robot and information flow is only from master to slaves as opposed to the usual but restrictive assumption of cooperative synchronization scheme. Despite the parametric uncertainty in the system dynamics the proposed adaptive controllers yield asymptotic synchronization of the network in both joint and task space. Lyapunov-based arguments are applied in the stability proofs and controller design. Simulation studies performed on a two-robot manipulator network are presented to demonstrate the viability and performance of the proposed control methods.
In this study, we present a new robust continuous controller mechanism for the tracking problem of uncertain nonlinear systems. The proposed strategy is based on a Lyapunov-type stability argument and only requires the uncertainties of the dynamical system to be the first-order differentiable to achieve asymptotic practical tracking. For the ease of presentation, the controller formulation is presented on a general, second-order dynamical system, extension to higher order versions are also possible with a considerably small effort. Simulation studies comparing the performance of the proposed method with the classical Sliding mode and robust integral of the sign of the error controller are presented to illustrate the performance and the feasibility of the proposed strategy. Experimental validation on a two link direct drive robot manipulator are also included to illustrate the implementability of the proposed method.
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