Finite-Time Convergence of Multi-robot Segregation using MPC with Aperiodic Motion Smoothing

Many applications of multi-robot systems require them to achieve a segregated formation in a finite amount of time and then perform subsequent tasks without colliding with each other. This paper proposes a finite-time Model Predictive Control (MPC) based framework for such systems. This includes a cost function to ensure finite-time convergence to segregated formation and a constraint for collision avoidance. An upper bound on the time steps required by the robots to converge to the segregated formation is also derived. Moreover, such systems often suffer from perturbations in the states of the robots, which may produce jitters in their motion profiles. A bound-based Aperiodic Motion Smoothing method is also integrated to ensure a smooth motion profile for the robots, even in the presence of perturbations in their states. By appropriate selection of bound on perturbations, the communication between the sensor and controller can be minimized by reducing the number of triggers. The performance of the proposed framework is verified via simulations and hardware implementation by performing the segregation of five robots.