A constrained model predictive controller for two tripod mobile robots performing cooperative transportation of an object through a pre-defined trajectory in the presence of external disturbances has been developed and validated in this paper. The robots are designed to hold an object through their end effectors while applying controlled forces to the object and transitioning along the pre-defined reference trajectory. In this collaborative transportation task, a constrained model predictive controller to control the applied forces and a sliding-mode controller to control the motion of the systems are implemented. A load-sharing algorithm allowed for decentralizing the control system to determine the share of the force applied to the object from each end effector. The system and control algorithms are modeled and simulated in a computational environment using MATLAB software. The results showed that the cooperative system’s position tracking and the force control on the object are successfully achieved using the developed algorithms with minimum deviation from the desired trajectory. In addition, robustness to a continuously increasing external disturbance exerted on the system was achieved using the proposed force control strategy.
AiyamaYHaraMYabukiT, et al. (1999) Cooperative transportation by two four-legged robots with implicit communication. Robotics and Autonomous Systems29(1): 13–19.
2.
AlkilabiMHMNarayanATuciE (2017) Cooperative object transport with a swarm of e-puck robots: Robustness and scalability of evolved collective strategies. Swarm Intelligence11(3): 185–209.
3.
AzizzadehHMenhajMBTalebiHA (2021) Decentralized force and motion control of multiple cooperative manipulators. Automatika62(1): 98–108.
4.
BennaniMGiriF (1996) Dynamic modelling of a four-legged robot. Journal of Intelligent and Robotic Systems17: 419–428.
5.
BestMChakravartiN (1990) Stability of linearly constrained convex quadratic programs. Journal of Optimization Theory and Applications64: 43–53.
6.
BorrelliFBemporadAMorariM (2017) Predictive Control for Linear and Hybrid Systems. Cambridge: Cambridge University Press.
7.
DongbingGErfuY (2005) A suboptimal model predictive formation control. In: Proceedings of the 2005 IEEE/RSJ international conference on intelligent robots and systems, Edmonton, AB, Canada, 2–6 August, pp. 1295–1300. New York: IEEE.
8.
ElAshryAFRamadanMMElAlailyZA, et al. (2020) Development of a hybrid multi-layer control architecture for a cooperative team of N: Homogeneous robots. Transactions of the Institute of Measurement and Control42(3): 404–421.
9.
FaiglJČížekP (2019) Adaptive locomotion control of hexapod walking robot for traversing rough terrains with position feedback only. Robotics and Autonomous Systems116: 136–147.
10.
GaytánASanchez-MagosMCruz-OrtizD, et al. (2018) Adaptive proportional derivative controller of cooperative manipulators. IFAC: PapersOnline51: 232–237.
11.
GhediniCRibeiroCHCSabattiniL (2018) Toward efficient adaptive ad-hoc multi-robot network topologies. Ad Hoc Networks74: 57–70.
12.
GhoreishiSAEhyaeiAFRahmaniM (2020) Double hyperbolic sliding mode control based on unscented Kalman filter for three-legged mobile manipulator. Amirkabir Journal of Mechanical Engineering53(4): 2105–2116.
13.
GildertNMillardAGPomfretA, et al. (2018) The need for combining implicit and explicit communication in cooperative robotic systems. Frontiers in Robotics and AI5: 65.
14.
HamedKAMaWLKamidiVR, et al. (2019) Hierarchical feedback control for complex hybrid models of multiagent legged robotic systems. Mathdoc Digital Mathematics Library. Available at: http://ames.caltech.edu/akbari2019hierarchical.pdf
15.
HawleyLSuleimanW (2019) Control framework for cooperative object transportation by two humanoid robots. Robotics and Autonomous Systems115: 1–16.
16.
InglettJERodríguez-SedaEJ (2017) Object transportation by cooperative robots. In: Proceedings of the SoutheastCon, Concord, NC, 30 March–2 April, pp. 1–6. New York: IEEE.
17.
JinLLiSLuoX, et al. (2018) Neural dynamics for cooperative control of redundant robot manipulators. IEEE Transactions on Industrial Informatics14: 3812–3821.
18.
KadaBBalameshASAJuhanyKA, et al. (2020) Distributed cooperative control for nonholonomic wheeled mobile robot systems. International Journal of Systems Science51: 1528–1541.
19.
KeshmiriSPayandehS (2011) A centralized framework to multi-robots formation control: Theory and application. In: GuttmannCDignumFGeorgeffM (eds) Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Berlin, Heidelberg: Springer, pp. 85–98.
20.
KorayemMHHedayatADehkordiSF (2021) Dynamic modeling of cooperative manipulators with frictional contact at the end effectors. Applied Mathematical Modelling90: 302–326.
21.
KorodiACormanM (2012) Wheeled mobile robot model and cooperative formation control. WSEAS Transactions on Systems11: 618–627.
22.
KowalczykWKozlowskiK (2018) Leader-follower control and collision avoidance for the formation of differentially-driven mobile robots. In: Proceedings of the 2018 23rd international conference on methods & models in automation & robotics (MMAR), Miedzyzdroje, 27–30 August, pp. 132–137. New York: IEEE.
23.
LeeGChwaD (2018) Decentralized behavior-based formation control of multiple robots considering obstacle avoidance. Intelligent Service Robotics11(1): 127–138.
24.
LiDGeSSHeW, et al. (2019) Multilayer formation control of multi-agent systems. Automatica109: 108558.
25.
LiZDengSSuC-YY, et al. (2014) Decentralised adaptive control of cooperating robotic manipulators with disturbance observers. IET Control Theory & Applications8: 515–521.
26.
LiuJTanMZhaoX (2007) Legged robots: An overview. Transactions of the Institute of Measurement and Control29: 185–202.
27.
LiuY-HArimotoS (1998) Decentralized adaptive and nonadaptive position/force controllers for redundant manipulators in cooperations. The International Journal of Robotics Research17: 232–247.
28.
MachadoJATSilvaMF (2006) An overview of legged robots. In: Proceedings of the MME 2006: International symposium on mathematical methods in engineering, Ankara, 27–29 April.
29.
MaithaniHRamonJACMezouarY (2019) Predicting human intent for cooperative physical human-robot interaction tasks. In: Proceedings of the 2019 IEEE 15th international conference on control and automation (ICCA), Edinburgh, 16–19 July, pp. 1523–1528. New York: IEEE.
30.
MikulášO (2013) Quadratic Programming Algorithms for Fast Model-Based Predictive Control. Prague: Czech Technical University in Prague.
31.
MoosavianSAAKhorramMZamaniA, et al. (2011) PD regulated sliding mode control of a quadruped robot. In: Proceedings of the 2011 IEEE international conference on mechatronics and automation (ICMA 2011), Beijing, China, 7–10 August, pp. 2061–2066. New York: IEEE.
32.
MorishitaMMaeyamaSNogamiY, et al. (2018) Development of an omnidirectional cooperative transportation system using two mobile robots with two independently driven wheels. In: Proceedings of the 2018 IEEE international conference on systems, man, and cybernetics (SMC), Miyazaki, Japan, 7–10 October, pp. 1711–1715. New York: IEEE.
33.
Muñoz-VázquezA-JParra-VegaVSánchez-OrtaA, et al. (2018) A novel force-velocity field for object manipulation with a model-free cooperative controller. Transactions of the Institute of Measurement and Control41(2): 573–581.
34.
NascimentoTPMoreiraAPScolari ConceiçãoAG (2013) Multi-robot nonlinear model predictive formation control: Moving target and target absence. Robotics and Autonomous Systems61: 1502–1515.
35.
NikkhahMAshrafiuonHFahimiF (2007) Robust control of underactuated bipeds using sliding modes. Robotica25: 367–374.
36.
NoguchiNWillJReidJ, et al. (2004) Development of a master–slave robot system for farm operations. Computers and Electronics in Agriculture44(1): 1–19.
37.
ÖgrenPFiorelliENaomiEL (2004) Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment. IEEE Transactions on Automatic Control49: 1292–1302.
38.
RenYChenZLiuY, et al. (2017) Adaptive hybrid position/force control of dual-arm cooperative manipulators with uncertain dynamics and closed-chain kinematics. Journal of the Franklin Institute354(17): 7767–7793.
39.
RezaeeA (2017) Model predictive for mobile robot control. Transactions on Environment and Electrical Engineering2(2): 17–22.
40.
RezaeeHAbdollahiF (2014) A decentralized cooperative control scheme with obstacle avoidance for a team of mobile robots. IEEE Transactions on Industrial Electronics61: 347–354.
41.
SayedASAmmarHHShalabyR (2020) Centralized multi-agent mobile robots SLAM and navigation for COVID-19 field hospitals. In: Proceedings of the 2020 2nd novel intelligent and leading emerging sciences conference (NILES), Giza, 24–26 October, pp. 444–449. New York: IEEE.
42.
SunHYangJAnH, et al. (2021) Improved online adjustment of step timing and location for legged locomotion. Journal of Intelligent & Robotic Systems102(2): 37.
43.
TzafestasSRaibertMTzafestasC (1996) Robust sliding-mode control applied to a 5-link biped robot. Journal of Intelligent and Robotic Systems: Theory and Applications15: 67–133.
44.
WangJDoddsSJBailyWN (1997) Co-ordinated control of multiple robotic manipulators handling a common object: Theory and experiments. IEEE Proceedings144: 73–86.
45.
WuMHMaHZhangX (2018) Decentralized cooperative localization with fault detection and isolation in robot teams. Sensors18(10): 3360.
46.
WuMHOgawaSKonnoA (2016) Symmetry position/force hybrid control for cooperative object transportation using multiple humanoid robots. Advanced Robotics30: 131–149.
47.
XiaYSattarJ (2019) Visual diver recognition for underwater human-robot collaboration. In: Proceedings of the 2019 international conference on robotics and automation (ICRA), Montreal, QC, Canada, 20–24 May, pp. 6839–6845. New York: IEEE.
48.
YangJTsujitaTKomizunaiS, et al. (2019) Cooperative massive object transportation by two humanoid robots. In: Proceedings of the 2019 12th Asian control conference (ASCC), Kitakyushu, Japan, 9–12 June, pp. 498–503. New York: IEEE.
49.
ZhangZSongYZhaoK (2019) Neuroadaptive cooperative control without velocity measurement for multiple humanoid robots under full-state constraints. IEEE Transactions on Industrial Electronics66(4): 2956–2964.
