Symmetric Consensus Tracking in Nonholonomic Mobile Multirobot Systems

Abstract

This paper investigates the symmetric consensus tracking problem of nonholonomic mobile multirobot systems (NMMRSs). The proposed control scheme is developed in cooperative-competitive network. A novel auxiliary reference vector which describes the local communication interaction among NMMRSs is introduced into the protocol design. Combining a kinematic and torque controller, symmetric consensus tracking can be achieved asymptotically in the network topology with parameter uncertainties. In the stability convergence analysis of the networked closed-loop system, coordinate transformation technique plays an important role. Finally, the effectiveness of the desired symmetric consensus tracking problem is verified by numerical simulations. INDEX TERMS Nonholonomic mobile multirobot systems (NMMRSs), Structural balance, Symmetric consensus tracking, The torque controller.

Group-symmetric consensus for nonholonomic mobile multirobot systems in coopetition networks

“…(1) Group-symmetric consensus effectively colligates the collective behaviors of group/cluster consensus and symmetric consensus. 23,27 This scenario extends the application scope of complete consensus in coopetition networks for NMMRSs, 16–18 which is more accorded with actual situations. (2) To accomplish multiple symmetric tasks, a novel auxiliary reference vector is introduced to eliminate the impacts between different groups and ensure the realization of group-symmetric consensus in NMMRSs.…”

“…The auxiliary vector q ri therein has two key parts u ð1Þ i ðtÞ ¼ R t 0 ððsgnða ij Þq i ðrÞ À q j ðrÞÞ À ðsgnða ij Þq ic ðrÞÀ q jc ðrÞÞÞdr and u ð2Þ ðtÞ ¼ R t 0 ðf i q i ðrÞ À q j ðrÞÞ À ðf i q ic ðrÞ Àq jc ðrÞÞdr. The structure of the control component u ð1Þ i ðtÞ is borrowed from the existing literature, 27 which is given as a control component to guarantee symmetric consensus of each group G b i . The representation of the second control component u ð2Þ i ðtÞ is designed to eliminate the influence of the agents from different groups, so as to ensure that the symmetric consensus realized in G b i under u ð1Þ i ðtÞ is not destroyed.…”

“…Therefore, the results in the existing literature are the special cases of our work. 23,27 Remark 4. Our framework is different from holonomic system group consensus that can be realized by constructing pure smooth time-invariant feedback laws.…”

“…Nevertheless, for NMMRSs, since three-coordinate symmetry cannot be realized simultaneously in the 2-D plane, bipartite consensus is not applicable to NMRRSs except for a particular steering configuration. Liu et al 27 proposed the concept of symmetric consensus for NMMRSs, realizing a two-coordinate symmetric control objective in the plane. However, when the task is composite multi-target, the scope of the symmetric consensus problem involved is very limited.…”