Obstacle Avoidance in Distributed Optimal Coordination of Multirobot Systems: A Trajectory Planning and Tracking Strategy

This article studies the problem of obstacle avoidance in the distributed optimal coordination (DOC) for a class of uncertain multirobot systems. Due to the existence of obstacle regions, the considered optimization problem is intrinsically nonconvex, which will result in the generation of some unexpected equilibriums (local minima). The existing results lack systematic obstacle-avoidance trajectory planning approaches such that the robots potentially fall in the unexpected equilibriums and cannot reach the global optimal solution. To address it, a safe reference trajectory planning approach is first designed by online projecting the unsafe part of the existing distributed optimization trajectory into the peripheral boundary of the obstacle region. On this basis, a distributed backstepping tracking control scheme is proposed based on a novel multiplicity-integral-type barrier Lyapunov function. It is proved that all the robot systems can keep away from the unexpected equilibriums and asymptotically reach the global optimal position while avoiding collisions with moving obstacles.

I. Introduction

Distributed optimal coordination (DOC), which aims to steer a group of dynamic systems to cooperatively optimize a team performance function (for example, minimize a sum of local objective functions), has drawn much attention due to its widely practical applications [1], for example, cooperative search of signal sources [2], [3], [4]; motion coordination [8], [9], [10]; multiagent persistent monitoring [11]; distributed estimation/localization [5]; and distributed optimal power flow [6], [7]. Recently, many important results on DOC have been developed for various physical dynamics, such as high-order dynamics [12], heterogeneous Euler–Lagrangian (EL) dynamics [2], and general continuous-time linear time-invariant dynamics [13], [14], [15], [16]. However, in these results, some physical safety issues such as collisions with obstacles are not considered.