chapter  9
18 Pages

## Abstractions for Planning and Control of Robotic Swarms

WithCALIN BELTA

Contents 9.1 Speciﬁcation-Induced Hierarchical Abstractions . . . . . . . . . . . . . . . . . . . . . . . . . 226 9.2 Continuous Abstractions: Extracting the Essential Features

of a Swarm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 9.2.1 Examples of Continuous Abstractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

9.3 Discrete Abstractions: Accommodating Rich Speciﬁcations . . . . . . . . . . . . . . 234 9.4 Hierarchical Abstractions: Automatic Deployment of Swarms from

Human-Like Speciﬁcations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 9.5 Limitations of the Approach and Directions for Future Work . . . . . . . . . . . 238 9.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

In this chapter, we outline a hierarchical framework for planning and control of arbitrarily large groups (swarms) of robots. At the ﬁrst level of hierarchy, we aggregate the high dimensional control system of the swarm into a small dimensional

control system capturing its essential features, such as position of the center, shape, orientation, and size. At the second level, we reduce the problem of controlling the essential features of the swarm to a model checking problem. In the obtained hierarchical framework, high-level speciﬁcations given in natural language such as linear temporal logic formulas over linear predicates in the essential features are automatically mapped to provably correct robot control laws. We present simulation results for the particular case of a continuous abstraction based on centroid and variance of a planar swarm made of fully actuated robots with polyhedral control constraints.