This paper considers a multi-robot formation control scheme for high-order bipartite consensus under time-varying delays. First, a third-order bipartite consensus protocol under time-varying delays is presented, and then a high-order bipartite consensus protocol is extended from it. Then, necessary and sufficient conditions for third-order and high-order multi-agent systems without time-delays are given to attain bipartite consensus following the protocols. Communication time-delays are added to the protocols, and the theory of Lyapunov asymptotic stability is used to obtain sufficient conditions for the multi-agent systems with communication delays to ultimately attain a bipartite consensus. Furthermore, the given protocol is employed for the formation control of multi-robot systems, and a formation control scheme for multi-robot systems with time-varying delays is proposed. Finally, a few simulations are implemented to demonstrate the rationality and availability of the method.
AbdessameudATayebiA (2018) Distributed consensus algorithms for a class of high-order multi-agent systems on directed graphs. IEEE Transactions on Automatic Control63(10): 3464–3470.
2.
Alonso-MoraJMontijanoENägeliT, et al. (2019) Distributed multi-robot formation control in dynamic environments. Autonomous Robots43(5): 1079–1100.
3.
AltafiniC (2013) Consensus problems on networks with antagonistic interactions. IEEE Transactions on Automatic Control58(4): 935–946.
4.
ChenJLiJYuanX (2019) Global fuzzy adaptive consensus control of unknown nonlinear multi-agent systems. IEEE Transactions on Fuzzy Systems28(3): 510–522.
5.
ChenJSunDYangJ, et al. (2010) Leader-follower formation control of multiple non-holonomic mobile robots incorporating a receding-horizon scheme. The International Journal of Robotics Research29(6): 727–747.
6.
DouLWangLWangX (2015) Leader-following bipartite consensus of high-order multi-agent systems on signed networks. In: Proceedings of the 2015 10th Asian control conference (ASCC), Kota Kinabalu, Malaysia, 31 May–3 June, pp. 1–5. New York: IEEE.
7.
FidanBGaziVZhaiS, et al. (2013) Single-view distance-estimation-based formation control of robotic swarms. IEEE Transactions on Industrial Electronics60(12): 5781–5791.
8.
FuJWenGYuW, et al. (2018) Consensus of second-order multi-agent systems with both velocity and input constraints. IEEE Transactions on Industrial Electronics66(10): 7946–7955.
9.
GaoZZhangHDuanJ, et al. (2020) Consensus conditions for higher-order descriptor multi-agent systems with communication time-delays. Transactions of the Institute of Measurement and Control42(11): 2127–2136.
10.
GuilletALenainRThuilotB, et al. (2014) Adaptable robot formation control: Adaptive and predictive formation control of autonomous vehicles. IEEE Robotics & Automation Magazine21(1): 28–39.
11.
GuoXLuJAlsaediA, et al. (2018) Bipartite consensus for multi-agent systems with antagonistic interactions and communication delays. Physica A: Statistical Mechanics and Its Applications495: 488–497.
12.
HanZGuoKXieL, et al. (2018) Integrated relative localization and leader-follower formation control. IEEE Transactions on Automatic Control64(1): 20–34.
13.
HuJWuYLiuL, et al. (2018) Adaptive bipartite consensus control of high-order multiagent systems on coopetition networks. International Journal of Robust and Nonlinear Control28(7): 2868–2886.
14.
HuaCCYouXGuanXP (2016) Leader-following consensus for a class of high-order nonlinear multi-agent systems. Automatica: 73138–73144.
15.
HuangJSongYDWangW, et al. (2017) Smooth control design for adaptive leader-following consensus control of a class of high-order nonlinear systems with time-varying reference. Automatica83: 361–367.
16.
LeeSMKimHMyungH, et al. (2014) Cooperative coevolutionary algorithm-based model predictive control guaranteeing stability of multirobot formation. IEEE Transactions on Control Systems Technology23(1): 37–51.
17.
LiuKXieGWangL (2014) Containment control for second-order multi-agent systems with time-varying delays. Systems & Control Letters: 6724–6731.
18.
PengZWenGYangS, et al. (2016) Distributed consensus-based formation control for nonholonomic wheeled mobile robots using adaptive neural network. Nonlinear Dynamics86(1): 605–622.
19.
QinJGaoHZhengWX (2011) Second-order consensus for multi-agent systems with switching topology and communication delay. Systems & Control Letters60(6): 390–397.
20.
RenJSongQGaoY, et al. (2020) Leader-following bipartite consensus of second-order time-delay nonlinear multi-agent systems with event-triggered pinning control under signed digraph. Neurocomputing385: 186–196.
21.
ShiLXieD (2020) Leader-following consensus of second-order multi-agent systems with time-varying delays and arbitrary weights. Transactions of the Institute of Measurement and Control42(16): 3156–3167.
22.
SunYWangLXieG (2008) Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays. Systems & Control Letters57(2): 175–183.
23.
TianLJiZHouT, et al. (2018) Bipartite consensus on coopetition networks with time-varying delays. IEEE Access6: 10169–10178.
24.
TianYPZhangY (2012) High-order consensus of heterogeneous multi-agent systems with unknown communication delays. Automatica48(6): 1205–1212.
25.
ValcherMEMisraP (2014) On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions. Systems & Control Letters: 6694–6103.
26.
WangCHePLiH, et al. (2020) Noise-tolerance consensus formation control for multi-robotic networks. Transactions of the Institute of Measurement and Control42(8): 1569–1581.
27.
WangYShanMYueY, et al. (2019) Vision-based flexible leader-follower formation tracking of multiple nonholonomic mobile robots in unknown obstacle environments. IEEE Transactions on Control Systems Technology28(3): 1025–1033.
28.
WangYSongYKrsticM, et al. (2016) Adaptive finite time coordinated consensus for high-order multi-agent systems: Adjustable fraction power feedback approach. Information Sciences37: 2392–2406.
29.
WenGWangHYuX, et al. (2017) Bipartite tracking consensus of linear multi-agent systems with a dynamic leader. IEEE Transactions on Circuits and Systems II: Express Briefs65(9): 1204–1208.
30.
XiaoHChenCLP (2018) Incremental updating multirobot formation using nonlinear model predictive control method with general projection neural network. IEEE Transactions on Industrial Electronic66(6): 4502–4512.
31.
YouXHuaCCYuHN, et al. (2019) Leader-following consensus for high-order stochastic multi-agent systems via dynamic output feedback control. Automatica10: 7418–7424.
32.
ZhangHChenJ (2017) Bipartite consensus of multi-agent systems over signed graphs: State feedback and output feedback control approaches. International Journal of Robust & Nonlinear Control27(1): 3–14.
33.
ZhangXLiuKJiZ (2019) Bipartite consensus for multi-agent systems with time-varying delays based on method of delay partitioning. IEEE Access7: 29285–29294.
34.
ZhengYWangL (2012) Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies. International Journal of Control85(12): 1967–1976.
35.
ZhouBLinZ (2014) Consensus of high-order multi-agent systems with large input and communication delays. Automatica50(2): 452–464.
36.
ZhuWChengD (2010) Leader-following consensus of second-order agents with multiple time-varying delays. Automatica46(12): 1994–1999.
37.
ZongCJiZTianL, et al. (2019) Distributed multi-robot formation control based on bipartite consensus with time-varying delays. IEEE Access7: 144790–144798.
