Optimal Virtual Tube Planning and Control for Swarm Robotics

This paper presents a novel method for efficiently solving a trajectory planning problem for swarm robotics in cluttered environments. Recent research has demonstrated high success rates in real-time local trajectory planning for swarm robotics in cluttered environments, but optimizing trajectories for each robot is still computationally expensive, with a computational complexity from Oleft(kleft(nt,varepsilon right)nt2right) to Oleft(kleft(nt,varepsilon right)nt3right) where nt is the number of parameters in the parameterized trajectory, varepsilon is precision and kleft(nt,varepsilon right) is the number of iterations with respect to nt and varepsilon. Furthermore, the swarm is difficult to move as a group. To address this issue, we define and then construct the optimal virtual tube, which includes infinite optimal trajectories. Under certain conditions, any optimal trajectory in the optimal virtual tube can be expressed as a convex combination of a finite number of optimal trajectories, with a computational complexity of Oleft(ntright). Afterward, a hierarchical approach including a planning method of the optimal virtual tube with minimizing energy and distributed model predictive control is proposed. In simulations and experiments, the proposed approach is validated and its effectiveness over other methods is demonstrated through comparison.