Mobility and Motion Modelling of Pendulum-Driven Ball-Robots: Decoupled Models for Steering and Obstacle Crossing

Research output: ThesisDoctoral ThesisMonograph


  • Tomi Ylikorpi

Research units


During the last two decades, mobile ball-shaped robots have gained an increasing interest among researchers, mathematicians, robot engineers, and public. Ball-robot provides an interesting research case to study rolling kinematics, advanced modelling and control problems, as well as interaction and communications between humans and mobile robots. While the first patents on self-propelled spherical toys were filed already in the end of the 19th century, commercial spherical robots have been lately introduced in the market for surveillance, entertainment, and gaming applications. The motivation behind this study anticipates a domestic rolling robot providing observation and surveillance at home or in industrial environment. In development of a ball-robot, dynamic modelling is essential in evaluation and prediction of robot performance, as well as in controller development, path planning, and decision making. This thesis studies decoupled forward rolling models and steering models of pendulum-driven ball-shaped robots. Customarily, a decoupled steering model assumes between the ball and rolling plane a point contact and restricted ball spinning, which leads to a kinematic motion model. Considering ball-robot inertia and non-symmetry, this thesis introduces a new dynamic precession model and compares the simulated rolling paths of the dynamic and kinematic steering models. In addition, another new dynamic precession model is presented to consider a non-zero contact area and to evaluate the conditions where no-spinning constraint is applicable. Regarding the forward motion model, this work collects the decoupled models available in the literature and reformulates them with a unified notation and formulation. The unified presentation allows easy comparison and application of the existing models. A detailed discussion is dedicated for the application of pendulum motor reaction torque within different model formulations. To design a spherical robot to surpass obstacles it may encounter during its operation, there exists a need to estimate the dynamic step-overcoming capability of the robot. Customarily, a quasi-static analysis has been conducted to evaluate the slope-climbing and step-crossing capability of a ball-shaped robot, but this approach seriously underrates the robot's dynamic step-crossing capability. This work introduces new simplified contact models for rigid-shelled and flexible-shelled ball-robots when in contact with a step-shaped obstacle. The contact models are implemented together with the decoupled forward rolling model, and the robot's step-overcoming capability is evaluated through simulations. The simulation results are validated with practical step-overcoming tests on free-rolling and pendulum-driven balls.


Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
Print ISBNs978-952-60-7617-1
Electronic ISBNs978-952-60-7616-4
Publication statusPublished - 2017
MoE publication typeG4 Doctoral dissertation (monograph)

    Research areas

  • ball-robot, ball-shaped robot, spherical robot, rolling robot, mobile robot kinematics and dynamics, contact model

ID: 17675362