**Multi-Path Planning on a Sphere with LMI-Based Collision Avoidance** Multi-Path Planning on a Sphere with LMI-Based

DOI: 10.5772/intechopen.71216

Innocent Okoloko

Collision Avoidance

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

http://dx.doi.org/10.5772/intechopen.71216 Additional information is available at the end of the chapter

#### Abstract

The problem of path planning with collision avoidance for autonomous flying vehicles will become more critical as the density of such vehicles increase in the skies. Global aerial navigation paths can be modeled as a path-planning problem on a unit sphere. In this work, we apply consensus theory and semidefinite programming to constrained multi-path planning with collision avoidance for a team of communicating vehicles navigating on a sphere. Based on their communication graph, each vehicle individually synthesizes a time-varying Laplacian-like matrix which drives each of them from their initial positions to consensus positions on the surface of the sphere. The solution trajectories obtained on the unit sphere are transformed back to actual vehicle coordinates. Formation configurations are realized via consensus theory, while collision avoidance is realized via semidefinite programming. A Lyapunov-based stability analysis is also provided, together with simulation results to demonstrate the effectiveness of the approach.

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