Consensus based distributed motion planning on a sphere

In this paper, consensus theory and semidefinite programming techniques are applied for planning of multiple collision free trajectories, for a team of communicating vehicles whose motions are constrained to evolve on the surface of a sphere. Such algorithms have applications in planetary-scale motion control for mobile sensing networks in air and space. Based on the communication graph for each vehicle, each vehicle synthesizes a time-varying Laplacian-like matrix Lⁱ. The set of Laplacian-like matrices are used individually in a distributed manner to drive given initial positions of the vehicles to consensus positions on the sphere. Collision avoidance and formation configurations are realized via the concept of semidefinite programming. For each vehicle, the problem is coded as a set of linear matrix inequalities (LMI), augmented with a number of constraints, and solved by semidefinite programming (SDP). We also provide Lyapunov-based stability analysis, together with simulation results to demonstrate the effectiveness of the approach.