Spline-based Distributed Motion Planning for Mobile Robots

The demand for scalable and flexible systems in the field of intralogistics motivates the use of mobile robot fleets. The robots should complete their tasks as quickly as possible to increase the throughput in logistics processes. This work considers time-optimal motion planning problems, which are parameterized using B-splines. It is shown that B-splines are a suitable choice for continuous trajectory optimization since B-spline relaxation provides continuous constraint satisfaction. This ensures the most important requirement of collision-freeness among the trajectories. The trajectory optimization using B-splines is compared to a classical multiple shooting approach. It shows that optimization using multiple shooting requires a post-analysis of the trajectories in contrast to the B-spline approach. The time-optimal motion planning problem is formulated in a centralized fashion. However, a limitation of the time-optimal approach is that all trajectories must have the same time range to define collision avoidance constraints. The centralized solution is compared to the closed-loop trajectories solved in a decentralized fashion using Alternating Direction Method of Multipliers (ADMM). The results are discussed and it is found that ADMM converges only for a small fleet size since more non-convex collision avoidance constraints are added as the fleet size increases. Therefore, future work should address simplifying the problem formulation by, for example, segmenting the workspace so that each robot only considers obstacles in a local area.