Synchronizing N cart-pendulums using virtual holonomic constraints

A solution is presented to the problem of synchronizing a chain of N cart-pendulums using virtual holonomic constraints. The approach is based on a master-slave configuration whereby the first cart-pendulum is controlled so as to stabilize a desired oscillation around its unstable equilibrium. Then, each remaining cart-pendulum is controlled so as to fully synchronize it to the previous pendulum.