**Consensus-Based Multipath Planning with Collision Avoidance Using Linear Matrix Inequalities** Consensus-Based Multipath Planning with Collision

DOI: 10.5772/intechopen.71288

Avoidance Using Linear Matrix Inequalities

Innocent Okoloko

Additional information is available at the end of the chapter Innocent Okoloko

http://dx.doi.org/10.5772/intechopen.71288 Additional information is available at the end of the chapter

#### Abstract

Consensus theory has been widely applied to collective motion planning related to coordinated motion. However, when the collective motion is highly irregular and adversarial, the basic consensus theory does not guarantee collision avoidance by default. As collision avoidance is a central problem of path planning, the incorporation of avoidance into the consensus algorithm is a subject of research. This work presents a new method of incorporating collision avoidance into the consensus algorithm, by applying the concept of constrained orientation control, where orientation constraints are represented as a set of linear matrix inequalities (LMI) and solved by semidefinite programming (SDP). The developed algorithm is used to simulate consensus-based multipath planning with collision avoidance for a team of communicating soccer robots.

Keywords: consensus, path planning, avoidance, optimization, LMI
