Design and Implementation of Non-Uniform Sampling Cooperative Control on A Group of Two-Wheeled Mobile Robots
This paper investigates the consensus prob- lem for a group of two-wheeled mobile robots (2WMRs) using non-uniform sampling. The directed and switching communication topologies are considered. The control pro- tocols for the first-order/second-order system dynamics are designed with bounded control gains. The Rotate&Run Scheme is proposed to update the vehicles’ states: 1) The vehicle calculates its goal orientation and the input of each wheel at the sampling time instants by using the states of itself and the neighbors; 2) the vehicle rotates in place until it aims at the calculated direction; 3) the vehicle moves for- ward/backward with the calculated wheel velocities until the next sampling time instant. It is shown that consensus in a group of 2WMRs can be achieved when the switching di- rected graphs satisfy certain conditions. The convergence analysis of consensus is conducted based on algebraic graph theory and stochastic matrix analysis. Experiments demonstrate the effectiveness of the proposed methods.
In the literature, most of the existing work for the MASs have the theoretical analysis and the effectiveness of the proposed control protocols are only verified by simulations. The application-oriented research on MASs is still at the early stage. In recent years, the control of a 2WMR attracts much attention , . For instance, the Qbot developed by Quanser Consulting Inc. is an innovative 2WMR . This mobile robot consists of two wheels in parallel, and is equipped with wireless embedded computer Gumstix and built-in sensors. With the accurate indoor global positioning systems, OptiTrackTM cameras from NaturalPoint Inc., the group of Qbots is ideally suited for the experimental study of the MASs. Motived by the aforementioned discussion, our objective is to design and implement the consensus protocol for the practical industrial systems of a group of 2WMRs. In this work, both the first-order and second-order system dynamics are considered in the consensus problem with non-uniform sampling. The communication topologies in this work are assumed to be directed and switching. Since the two wheels of a 2WMR are mounted on a common axis, it is impossible for a 2WMR to accelerate in the direction along the axis. Such a system that has a lower numbers of actuators than the degrees of freedom (DOF) is the underactuated system. We develop the Rotate&Run Scheme for the cooperative control of a group of 2WMRs and prove that consensus can be reached with non-uniform sampling if the directed graphs satisfy certain conditions.
The major contributions of the paper are as follows: (1) The new Rotate&Run Scheme is developed to solve the consensus problem for a group of underactuated 2WMRs with non- uniform sampling. The physical constraints of the wheel ve- locities are considered in the design. The results on stochastic matrices are applied to study the stability of the MAS. (2) Compared with the existing work, our paper provides a more general methodological framework by studying the synchro- nized but non-periodical sampling control to solve a consensus problem. The traditional synchronized and periodical sampling can be considered as a special case under our proposed framework. Moreover, the communication topology for the non-uniform sampling consensus protocol investigated in  is fixed and directed. However, the interaction topologies are always complicated and may change dynamically in reality. In this work we consider the scenario of the cooperative control of the MASs under switching topologies. (3) The designed al- gorithms are efficiently implemented on the practical industrial systems for solving the consensus problem.
In this paper, we investigated the consensus problem for a group of 2WMRs with non-uniform sampling and switch- ing directed communication topologies. We developed the consensus algorithms for the first-order and second-order underactuated systems, respectively. The control gains are properly chosen and the sufficient conditions are established in terms of the graph connectivity to ensure consensus. The effectiveness is validated by experimental results. Future re- search will be focused on the convergence speed analysis for the proposed algorithms and the study of the consensus algorithms with asynchronous and non-uniform sampling.
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