Received September 3, 2020, accepted September 12, 2020, date of publication September 18, 2020, date of current version October 1, 2020. Digital Object Identifier 10.1109/ACCESS.2020.3024685 Scalable Decentralized Multi-Robot Trajectory Optimization in Continuous-Time SIVANATHAN KANDHASAMY 1 , (Member, IEEE), VINAYAGAM BABU KUPPUSAMY 2 , AND SHRAVAN KRISHNAN 1 1 Autonomous Systems Laboratory, Department of Mechatronics Engineering, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kanchipuram 603203, India 2 Department of Mechatronics Engineering, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kanchipuram 603203, India Corresponding author: Sivanathan Kandhasamy (sivanatk@srmist.edu.in) This work was supported in part by the SRM Institute of Science and Technology through Internal Seed Funding. ABSTRACT This article presents a decentralized algorithm that generates continuous-time trajectory online for a swarm of robots based upon model predictive control. To generate collision-free trajectory, temporally distinct safe regions are formed such that the robots are confined to move within these safe regions to avoid collisions with one another. The distinct safe regions are temporally linked by generating a B-spline. Additionally, to ensure that collisions are avoided, collision-regions that the robots have to stay outside are also generated distinctly. A non linear program (NLP) with an objective to make the robots stay outside the collision-regions and stay within the safe regions is formulated. The algorithm was tested in simulations on Gazebo with aerial robots. The simulated results suggest that the proposed algorithm is computationally efficient and can be used for online planning in moderate sized multi-robot systems. INDEX TERMS Multi-robot system, trajectory optimization, obstacle avoidance, model predictive control. I. INTRODUCTION Multi-Robot, warehouse management [4], entertainment [5], search and rescue missions, defense and so forth. Essen- tially, there are certain attractive characteristics of MRS which make it an ideal solution in the afore-mentioned appli- cations and some of those characteristics are highlighted in Section II. The success of such applications primarily depends on autonomous navigation of robots- the ability of robots to move from their current positions to their desired goal positions while avoiding collisions with one another and obstacles in the environment. To provide robots with this ability, four interlaced processes are programmed in to them, viz. state estimation, mapping, trajectory planning and con- trol. This work specifically focuses on the trajectory planning for MRS. Many methods have been proposed for multi-robot trajec- tory planning thus far. They can be categorised as central- ized, decentralized and distributed. Centralized techniques can generate smooth and optimal trajectories, but they fail in several scenarios. Particularly, centralized techniques are not suitable for applications where scalability and robustness are The associate editor coordinating the review of this manuscript and approving it for publication was Xiwang Dong. desired. For example, time-critical applications like search and rescue mission and war-field operations need typically high speed navigation of robots that can adapt to unforeseen environmental changes quickly enough in terms of their size and motions. For such applications, decentralized methods are highly suitable, because they are scalable and robust unlike centralized methods. Nevertheless, the generated tra- jectories by decentralized methods are usually sub-optimal and non-smooth. The existing decentralized trajectory planning methods work based on two approaches. One approach assumes that the robots share their trajectories with one another and re-plan them to account for changes in the environment. While, the second approach exploits the constant acceleration or velocity assumptions. The former one poses serious privacy concern and communication bottleneck; and the later one tends be very conservative. To address these challenges, we propose a decentralised algorithm that generates locally optimal minimum-time tra- jectories while attempting to mitigate inter-robot collisions in the environment. Basically, it is an online decentralized trajectory optimization algorithm for the labelled multi-robot motion planning problem. 173308 This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/ VOLUME 8, 2020