Distributed Coordination Theory for Ground and Aerial Robot Teams

This thesis investigates distributed coordination problems for two important classes of robots. One class corresponds to ground-based mobile robots, each modelled as a kinematic unicycle. The second corresponds to flying robots, each propelled by a thrust vector and endowed with an actuation mechanism producing torques about three orthogonal body axes. The following coordination problems are studied in this thesis: rendezvous, formation control, linear and circular formation flocking and formation path following. For rendezvous of kinematic unicycles, a smooth, time-independent control law is presented that drives the unicycles to a common position from arbitrary initial conditions, under the assumption that the sensing digraph is time-invariant and contains a globally reachable node. The proposed feedback is very simple and is local and distributed. For rendezvous of flying robots, a control strategy is presented that makes the centres of mass of the vehicles converge to an arbitrarily small neighborhood of one another. The convergence is global, and each vehicle can compute its own control input using local and distributed feedback. For formation control, the objective is to make an ensemble of kinematic unicycles achieve pre-defined inter-agent spacings with parallel heading angles. We consider scenarios where the formation either stops or moves with a final collective motion. In the latter case, problems of linear and circular formation flocking and formation path following are studied. A control law is presented in each case that solves the problem for almost all initial conditions. For stopping and flocking formations, the proposed control laws are local and distributed while for formation path following, the control laws additionally require each agent to measure its displacement from the path. The idea used to solve the formation control problems is to rigidly attach an offset vector to the body frame of each unicycle. It is shown that stabilizing the desired formation amounts to achieving consensus of the endpoints of the offset vectors, and simultaneously synchronizing the unicycles' heading angles. Extension of formation control to flying robots using strictly local and distributed feedback is not addressed in this work and remains a challenging open problem.Ph.D