Implan: Scalable Incremental Motion Planning for Multi-Robot Systems

Abstract

Abstract-We consider the collision-free motion planning problem for a group of robots using a library of motion primitives. To cope with the complexity of the problem, we introduce an incremental algorithm based on an SMT solver, where we divide the robots into small groups based on a priority assignment algorithm. The priority assignment algorithm assigns priorities to the robots in such a way that the robots do not block the cost-optimal trajectories of the other robots. While the priority assignment algorithm attempts to assign distinct priorities to the robots, the algorithm ends up with assigning the same priority to some robots due to the dependencies among themselves. The algorithm includes the robots with the same priority in the same group. Our incremental algorithm then considers the robot groups one by one based on their priority and synthesizes the trajectories for the group of robots together. While synthesizing the trajectories for the robots in one group, the algorithm considers the higher priority robots as dynamic obstacles, and introduces a minimal delay in executing the cost-optimal trajectories to avoid collision with the higher priority robots. We apply our method to synthesize trajectories for a group of quadrotors in our lab space. Experimental results show that we can synthesize trajectories for tens of robots with complex dynamics in a reasonable time.

Multi-Robot Coordination Analysis, Taxonomy, Challenges and Future Scope

“…Some other works use LTL are [163,164]. In [165] motion planning incremental algorithm is presented based on satisfiability modulo theories [166], robots are assigned priorities and divided into groups. The scalability of the algorithm is tested using an experiment, and it can perform motion planning of twenty-five, fifty quadrotors in compact and obstacle-free environment, respectively.…”

Multirobot Coordination With Counting Temporal Logics

“…Traditional algorithms for multirobot coordination tend to focus on relatively simple tasks such as reaching a goal state while avoiding unsafe regions and collisions [32], [41], [38], or reaching a consensus [14], [22]. Temporal logics, such as Linear Temporal Logic (LTL), provide a powerful framework for defining more complex specifications, for example: Always avoid collision with obstacles, do not cross into region A before visiting region B, and eventually visit regions A and C repeatedly.…”

On the timed temporal logic planning of coupled multi-agent systems

“…The qualitative specification language that has primarily been used to express the high-level tasks is Linear Temporal Logic (LTL) (see, e.g., [1]). There is a rich body of literature containing algorithms for verification and synthesis of multi-agent systems under high level specifications ( [2][3][4]). Controller synthesis under timed specifications has been considered in [5][6][7][8].…”