This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE SYSTEMS JOURNAL 1 Fault-Tolerant Formation Control of Nonholonomic Robots Using Fast Adaptive Gain Nonsingular Terminal Sliding Mode Control Ranjith Ravindranathan Nair, Hamad Karki, Amit Shukla, Laxmidhar Behera, and Mo Jamshidi Abstract—This paper addresses the problem of robust relative motion control in a multirobotic system using the artificial poten- tial field (APF) method for path planning and fast adaptive gain nonsingular terminal sliding mode control (NTSMC) technique for designing a robust controller. A fast adaptive reaching law is also proposed to further improve the speed of convergence. The pro- posed sliding surface as well as the novel formation error utilizes only the relative position measurements of the follower with respect to the leader. The novel adaptive tuning algorithms are designed for tuning the controller parameters, in such a way that finite- time stability property of the NTSMC is retained. This will help to cope with uncertainties and varying operating conditions. An adap- tive fuzzy-based fast reaching law is also proposed as an alternative to reduce the chattering. In the event of any critical system fault, to isolate the faulty robots and to facilitate the formation reconfig- uration avoiding the collision between the healthy robots and the faulty ones, we have proposed a fault-tolerant APF module em- ploying the fault parameters. The fault parameters are estimated using a residual-based synchronous fault-detection scheme. The ef- ficacy of the proposed strategy has been validated through rigorous real-time experimentations. Index Terms—Artificial potential field (APF), fault-tolerant fast adaptive nonsingular terminal sliding mode control (NTSMC), leader–follower formation, nonholonomic robots. I. INTRODUCTION T HE concept of multirobotic system (MRS) has drawn re- markable attention among the research community, be- cause of its advantages over a single robotic system in diverse applications ranging from surveillance and security to collabo- rative transportation. But the success of such missions greatly depends upon the efficacy of the co-ordination and control mod- ule. The task allocation and co-ordination problems in an MRS Manuscript received June 15, 2017; revised October 14, 2017 and December 14, 2017; accepted January 10, 2018. This work was supported in part by a grant from Adnoc-GRC, Abu Dhabi, funding under Project EE/PI/2015449: a con- dition monitoring system with multi-agent mechanism for external noncontact smart inspection of buried oil and gas pipelines. The work of M. Jamshidi was supported in part by the U.S. AFRL under Grant FA8750-15-2-0116 and OSD through NCA&T State University. (Corresponding author: Laxmidhar Behera.) R. R. Nair and L. Behera are with the Department of Electrical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016, India (e-mail: ranjith@ iitk.ac.in; lbehera@iitk.ac.in). H. Karki and A. Shukla are with the Department of Mechanical Engineer- ing, The Petroleum Institute, Abu Dhabi 2533, United Arab Emirates (e-mail: hkarki@pi.ac.ae; ashukla@pi.ac.ae). M. Jamshidi is with the Department of Electrical and Computer Engineering and ACE Laboratories, University of Texas, San Antonio, TX 78249 USA (e-mail: moj@wacong.org). Digital Object Identifier 10.1109/JSYST.2018.2794418 have already been explored in the literature [1]–[6]. A robust control module is equally significant in fulfilling the mission objective successfully in an MRS. The speed of convergence, fault tolerance capability, adaptability to varying operating con- ditions, etc., are some of the major performance measures to be considered in validating the efficacy of a control module. Apart from all this, the controller should be robust enough to retain the stability of formation, even after one or more agents are isolated due to some critical system fault and the formation is reconfigured. Also, it should be able to handle the delay introduced by the fault-detection and isolation (FDI) module. In case of all such detrimental, unforeseen situations, the speed at which the system adapts to them is equally critical. Formation control problem has been solved using different control approaches in the literature, including model predictive control [7], H ∞ control [8], backstepping [9], feedback lin- earization (FL) [10], sliding mode control (SMC) [11], [12], etc. In [13], a robust, composite adaptive fuzzy controller has been proposed for underwater vehicles, in which an adaptive fuzzy law has been designed to compensate the unknown uncer- tainties and disturbances in the system. Similarly, an adaptive fuzzy-based control strategy has been presented in [14] for gen- eralized MIMO systems with input saturation, in which an H ∞ term is utilized to mitigate the effects of fuzzy approximation errors. An observer-based composite fuzzy control scheme is proposed in [15] for uncertain nonlinear systems, in which a fuzzy logic system with the feedback error function as the in- put, and a state observer are presented to estimate the system uncertainties and the unmeasured states, respectively. Considering the disturbances and model uncertainties, which are prevalent in an MRS, a sliding mode-based robust control approach [16], [17] has been considered in this paper. We try to analyze the feasibility of using adaptive sliding mode techniques to design a robust and fast, fault-tolerant formation controller for an MRS with disturbances, which can guarantee the finite-time stability of the system. The relative motion control problem in an MRS, for maintaining a time-varying formation, has been solved using the first- and second-order SMC in [18]. Similarly, a fuzzy SMC-based approach has been designed by Yeong et al. in [19] to deal with the consensus-based formation of the multirobot system. In [12], Gian et al. have adopted a supervi- sory SMC-based approach for controlling a robotic system of systems consisting of distributed, co-operative robotic manip- ulators, where a linear sliding surface has been chosen for the position/force control. For fast and finite-time convergence, fast nonsingular termi- nal sliding mode control (NTSMC) approaches are introduced 1937-9234 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.