The roles of shape and motion in dynamic manipulation: the butterfly example

Optimal Shape and Motion Planning for Dynamic Planar Manipulation

“…Chen [4] optimizes both the shape and control input for an underactuated throwing arm. Lynch [13] explores the design space (shape and motion) of a contact juggler for the task of butterfly juggling in a planar rolling system. This system is the closest work to this paper, and serves as primary inspiration for the proposed approach.…”

“…The algebraic representation we use in this paper is similar to the one proposed by Lynch et al [13] to describe contact juggling. For their expression, we will make use of the notation introduced in Section III to describe the shape and motion of the system.…”

“…The dynamics-kinematics of planar contact are represented as constraints, similar to previous works on trajectory optimization through contact [13,15].…”

Generating periodic motions for the butterfly robot

“…One of these examples is the Butterfly system, which was introduced by K. Lynch [1] to understand the problem of dynamical manipulation in the form of robotic juggling.…”

“…One of the many interesting challenges allocated to this setup is the generation of periodic juggling-like motions at different equilibrium points. To the best of our knowledge, two approaches have been proposed: 1) optimization-based motion planning under PD feedback control [1] and 2) passivity based control [2], [3]. Within this context, our aim is to present a dedicated study based on the virtual holonomic constraints (VHC) approach [4], [5], which is a method that has proven to be useful for deriving analytical solutions to similar problems.…”