# Formal Specification of Continuum Deformation Coordination

## TL;DR

This paper formally defines continuum deformation coordination for multi-agent systems in obstacle-rich environments using linear temporal logic, ensuring safety and liveness through precise conditions.

## Contribution

It introduces a formal specification framework for continuum deformation coordination incorporating safety and liveness in complex environments.

## Key findings

- Safety conditions for collision avoidance and containment are established.
- Liveness ensures the system reaches the desired formation.
- Formal LTL specifications enable rigorous verification of multi-agent coordination.

## Abstract

Continuum deformation is a leader-follower multiagent cooperative control approach. Previous work showed a desired continuum deformation can be uniquely defined based on trajectories of d +1 leaders in a d-dimensional motion space and acquired by followers through local inter-agent communication. This paper formally specifies continuum deformation coordination in an obstacle-laden environment. Using linear temporal logic (LTL), continuum deformation liveness and safety requirements are defined. Safety is prescribed by providing conditions on (i) agent deviation bound, (ii) inter-agent collision avoidance, (iii) agent containment, (iv) motion space containment, and (v) obstacle collision avoidance. Liveness specifies a reachability condition on the desired final formation.