Input Efficiency for Influencing Swarm

Many cooperative control problems ranging from formation following, to rendezvous to flocking can be expressed as consensus problems. The ability of an operator to influence the development of consensus within a swarm therefore provides a basic test of the quality of human-swarm interaction (HSI). Two plausible approaches are : Direct- dictate a desired value to swarm members or Indirect- control or influence one or more swarm members relying on existing control laws to propagate that influence. Both approaches have been followed by HSI researchers. The Indirect case uses standard consensus methods where the operator exerts influence over a few robots and then the swarm reaches a consensus based on its intrinsic rules. The Direct method corresponds to flooding in which the operator directly sends the intention to a subset of the swarm and the command then propagates through the remainder of the swarm as a privileged message. In this paper we compare these two methods regarding their convergence time and properties in noisy and noiseless conditions with static and dynamic graphs. We have found that average consensus method (indirect control) converges much slower than flooding (direct) method but it has more noise tolerance in comparison with simple flooding algorithms. Also, we have found that the convergence time of the consensus method behaves erratically when the graph’s connectivity (Fiedler value) is high

A Study On Distributed Model Predictive Consensus

We investigate convergence properties of a proposed distributed model predictive control (DMPC) scheme, where agents negotiate to compute an optimal consensus point using an incremental subgradient method based on primal decomposition as described in Johansson et al. [2006, 2007]. The objective of the distributed control strategy is to agree upon and achieve an optimal common output value for a group of agents in the presence of constraints on the agent dynamics using local predictive controllers. Stability analysis using a receding horizon implementation of the distributed optimal consensus scheme is performed. Conditions are given under which convergence can be obtained even if the negotiations do not reach full consensus.Comment: 20 pages, 4 figures, longer version of paper presented at 17th IFAC World Congres

Optimal output consensus for linear systems: A topology free approach

In this paper, for any homogeneous system of agents with linear continuous time dynamics, we formulate an optimal control problem. In this problem a convex cost functional of the control signals of the agents shall be minimized, while the outputs of the agents shall coincide at some given finite time. This is an instance of the rendezvous or finite time consensus problem. We solve this problem without any constraints on the communication topology and provide a solution as an explicit feedback control law for the case when the dynamics of the agents is output controllable. It turns out that the communication graph topology induced by the solution is complete. Based on this solution for the finite time consensus problem, we provide a solution to the case of infinite time horizon. Furthermore, we investigate under what circumstances it is possible to express the controller as a feedback control law of the output instead of the states.Comment: 8 page

A Smooth Distributed Feedback for Global Rendezvous of Unicycles

This paper presents a solution to the rendezvous control problem for a network of kinematic unicycles in the plane, each equipped with an onboard camera measuring its relative displacement with respect to its neighbors in body frame coordinates. 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 contains a reverse-directed spanning tree. The proposed feedback is very simple, and relies only on the onboard measurements. No global positioning system is required, nor any information about the unicycles' orientations