Geometric Cooperative Control of Particle Formations

We present a geometric approach for formation control that explicitly decouples translation dynamics from the orientation and shape dynamics. The formation dynamics are modeled as controlled Lagrangian systems on Jacobi shape space, and measurements of shape variables are used as feedback to control the entire formation. This geometric approach allows each member of the formation, modeled as a Newtonian particle, freedom to choose different coordinate frame and shape variables to describe observed orientation and shape of the formation. We derive a class of cooperative control laws and shape consensus algorithms with provable convergence. They can be implemented in a distributed fashion thanks to gauge covariance and coordinate independence associated with the geometric approach.