On Performing Non-Prehensile Rolling Manipulations: Stabilizing Synchronous Motions of Butterfly Robots

The paper explores the challenging task of per- forming a non-prehensile manipulation of several balls syn- chronously rolling on the curved hands of Butterfly robots. Each Butterfly robot represents a standard benchmark hardware setup, comprising a DC motor rotating a butterfly-shaped frame in a vertical plane, with a ball moving freely upon it, equipped with integrated computer vision, communication, pro- grammable control, and computation interfaces. The combined dynamics of the considered system, consisting of N ≥2 such robots, is inherently underactuated, characterized by N active and N passive degrees of freedom, as well as N independent unilateral constraints that model the interactions between the frames and the balls, assuming no slipping. We focus on designing a model-based centralized feedback controller to achieve synchronized rotations of the balls. We assume the accuracy of our mathematical model and the feasibility of implementing a discretized version of the proposed continuous- time controller with a sufficiently small sampling time, that, in particular, is necessary for numerical differentiation. Relying on orbital stability of nominal periodic solution of the closed- loop system, we will experimentally check robustness to various inevitable challenges such as noises, disturbances, uncertainties, and communication delays. Hence, our concentration lies in designing an orbitally stabilizing controller for the underac- tuated models. The primary contribution is proposing one set of transverse coordinates, enabling transverse-linearization- based controller design, accompanied by pertinent closed-loop system analysis tools, thereby enhancing the efficacy of solving the manipulation task. Analytical and model-based arguments are validated through successful simulations and experiments conducted on two Butterfly robots, thereby emphasizing the validity and practicality of the proposed approach. I. MOTIVATION FOR PERFORMING ROBOTIC DYNAMIC MANIPULATIONS AND CHALLENGES Various tasks in service and medical applications demand human-like manipulation abilities from robotic systems for automating and advancing human-involved and human- centered assignments. Meanwhile, most of the tools and environments, used by humans in every-day life, are not universal; by centuries they have been tuned and adjusted for human hands to perform specific operations, e.g. eating soup by manipulating a spoon, opening a door by pushing a ⋆This work was supported by the grant of the state program of the ‘Sirius’ Federal Territory “Scientific and technological development of the ‘Sirius’ Federal Territory”. 1M. Surov and S. Gusev are with the Department of Information Technologies and AI, Sirius University of Science and Technology, Sochi, Russia, {surov.mo,gusev.sv}@talantiuspeh.ru 2S. Pchelkin and A. Shiriaev are with the Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway, anton.shiriaev@ntnu.no 3L. Freidovich is with the Robotics and Control Group, the Department of Applied Physics and Electronics, Ume ̊a University, Ume ̊a , Sweden, leonid.freidovich@umu.se handle, lightly touching an object and painting on a canvas by brushes, stitching/sewing clothes and soft materials/tissues by a needle etc. Clearly, such personalization of tools and strategies for handling external objects and environments reflects the challenge and the complexity of various actions easily performed by adults, which are often resulted from extended-in-time learning to perform various tracks as well as comprehending and advancing the skills. At the same time, in spite of the diversity of manipulating tasks, there are a few conceptual interaction patterns defining continuous contact of a human hand and an external tool or an object or an environment along a movement: Either it is firmly grasped by a human hand or it rolls or/and slides on a human hand being pushed, see, e.g., [1]. The last two interaction formats, i.e. when an external object rolls or slides or both on a human hand, represent ones of the most difficult and important tasks for humans. The main difficulty comes from the necessity to overcome and/or harvest the nonlin- ear effects appearing due to object/environment interaction dynamics and contact conditions. A human should learn feasible and often dexterious behaviors consistent with dy- namic constraints and ways to control such motions to make them repeatable and insensitive to noise and perturbations. The importance of dynamic manipulation skills is related to extended capabilities of hands and increased robustness of the human motor control system. Developing assistive robots assumes that robotic hands will be able to perform similar grasping, manipulating, trans- porting, assembling, and other handling of objects as it would be done by a human. Therefore, it is attractive to analyze and explore recorded human performances for searching artifacts and incentives that can be useful in planning similar robot hand movements and in their stabilization. Meanwhile, the superficial repetition of recorded movements by a robot is unlikely to lead to success. Indeed, even small perturbations of contact conditions and differences in formats of robot’s actuation substantially change the dynamical properties of the augmented system, defined by combined dynamics of the robot and the object. Such modifications preclude from the possibility for a robot hand to literally mimic and follow time references reconstructed from human motion recordings without a failure. Hence, we need alternative interpretations of human exercises both for planning similar but robot-like behaviors and for their robust control. It is worth to mention one of critical and explicit properties of a human motor control architecture: humans have no accurate sense of time. Therefore, developing human-like control architectures for robotic dynamic manipulation rules out most of classical 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) October 14-18, 2024. Abu Dhabi, UAE 979-8-3503-7769-9/24/$31.00 ©2024 IEEE 12678