Generating periodic motions for the butterfly robot

We analyze the problem of dynamic non-prehensile manipulation by considering the example of the butterfly robot. Our main objective is to study the problem of stabilizing periodic motions, which resemble some form of juggling acrobatics. To this end, we approach the problem by considering the framework of virtual holonomic constraints. Under this basis, we provide an analytical and systematic solution to the problems of trajectory planning and design of feedback controllers to guarantee orbital exponential stability. Results are presented in the form of simulation tests.