Robotics and Autonomous Systems 105 (2018) 69–84 Contents lists available at ScienceDirect Robotics and Autonomous Systems journal homepage: www.elsevier.com/locate/robot Globally rigid formation of n-link doubly nonholonomic mobile manipulators Bibhya Sharma b, *, Shonal Singh a , Jito Vanualailai b , Avinesh Prasad b a University of Sydney, Australia b The University of the South Pacific, Suva, Fiji article info Article history: Received 21 September 2017 Received in revised form 27 December 2017 Accepted 9 February 2018 Available online 6 March 2018 Keywords: Lyapunov-based control scheme Doubly nonholonomic manipulators Kinodynamic constraints Globally rigid formation Leader–follower Ghost target abstract This paper provides a new framework for the collective motion control of a team of n-link doubly nonholonomic mobile manipulators in a constrained environment. A continuous decentralized motion planner is proposed. It guarantees the establishment and strict maintenance of a team formation using the Lyapunov-based control scheme (LbCS), which takes into account all the practical limitations, and the constraints due to fixed obstacles, nonholonomy and globally rigid formation requirements. The control scheme inherently utilizes artificial potential fields within an overarching leader–follower framework to mobilize the prescribed globally rigid formation. The designated leader of the team is modeled as a moving reference point, referred to as the virtual leader. With its protective polygonal region, it directs the motion of the team and manipulate the geometry of the formation. It is the authors’ belief that this navigation and globally rigid formation control problem of n-link doubly nonholonomic mobile manipulators is treated for the first time with the use of continuous time-invariant control laws within the framework of LbCS and a variant of the leader–follower scheme. The effectiveness of the motion planner and the resulting acceleration-based control laws are demonstrated via computer simulations. © 2018 Elsevier B.V. All rights reserved. 1. Introduction In recent years, the concept of formation control of multi- robot systems has received an unprecedented uptake and attention from researchers all over, in both theoretical research and real- world applications. Formation control is an integrated branch of motion planning and control of robots, which is the coordinated and collision free movement of multiple robots, and completion of tasks [1–3]. While copious methodologies appear in literature that address control of multi-robot systems, formation control of such systems operating in difficult, dull, dirty and constrained environments is been favored because of its relevancy to various real-life applica- tions [4–9]. As emphasized in the literature the primary objective of formation control is to control the posture of a team of robots while normally maintaining constant their relative locations or the prescribed geometrical structure and allowing them to travel to their desired destinations [10,8]. Its applications include surveil- lance, transportation, health-care, reconnaissance, save and res- cue, pursuit-evasion, tunnel passing, surveying, troop hunting, and explorations, in various environments [9,11,6]. * Corresponding author. E-mail address: sharma_b@usp.ac.fj (B. Sharma). The idea of formation by design is inspired by collective be- haviors seen in nature [12], such as ant swarming, bird flocking, fish schooling and animal herding. Accordingly, to mimic these group behaviors, formation control can be divided into four layers: formation shape, formation type, formation tracking, and robot roles [6,7]. In general, the literature harbors numerous approaches to address the problem of formation control in robotic applications. These approaches can be roughly categorized into five generic approaches [13], namely, leader–follower, virtual structure, gen- eralized coordinates, behavior-based, and social potential fields. A brief review of these approaches is presented in [14,13,7,15,3] and the references therein. Nonetheless, incorporating leader–follower schemes via an artificial potential fields (APFs) method is gaining popularity for formation control due to their seamless formulation and scalability [16–18,9]. One of the adaptive challenges of formation control is the maintenance of a degree of rigidity of the pattern formed by the multi-agents. Using the nomenclature from [19,20]; while one end of the formation spectrum allows for ungoverned changes to the formation, essentially known as the split/rejoin or minimally rigid formation, the other end requires a strict maintenance of the forma- tion which is classified as the globally rigid formation. Finally, there is the locally rigid formation which allows for temporary distortions to the formation upon encountering obstacles and restrictions. https://doi.org/10.1016/j.robot.2018.02.006 0921-8890/© 2018 Elsevier B.V. All rights reserved.