Gyroscopic Precession In Motion Modelling Of Ball-Shaped Robots

This study discusses kinematic and dynamic precession models for a rolling ball with a finite contact area and a point contact respectively. In literature, both conventions have been applied. In this paper, we discuss in detail the kinematic and dynamic models to describe the ball precession and the radius of a circular rolling path. The kinematic model can be used if the contact area and friction coefficient are sufficient to prevent slippage. The dynamic precession model has significance in multi-body simulation environments handling rolling balls with ideal point contacts. We have applied both the kinematic and dynamic precession model to evaluate the no-slip condition of the existing GimBall-robot. According to the result, the necessity of an external precession torque may cause slipping at lower velocities than expected if ignoring this torque.Peer reviewe

Unified Representation Of Decoupled Dynamic Models For Pendulum-Driven Ball-Shaped Robots

Dynamic models describing the ball-robot motion form the basis for developments in ball-robot mechanics and motion control systems. For this paper, we have conducted a literature review of decoupled forward-motion models for pendulum-driven ball-shaped robots. The existing models in the literature apply several different conventions in system definition and parameter notation. Even if describing the same mechanical system, the diversity in conventions leads into dynamic models with different forms. As a result, it is difficult to compare, reproduce and apply the models available in the literature. Based on the literature review, we reformulate all common variations of decoupled dynamic forward-motion models using a unified notation and formulation. We have verified all reformulated models through simulations, and present the simulation results for a selected model. In addition, we demonstrate the different system behavior resulting from different ways to apply the pendulum reaction torque, a variation that can be found in the literature. For anyone working with the ball-robots, the unified compilation of the reformulated dynamic models provides an easy access to the models, as well as to the related work.Peer reviewe

Quaternion model of programmed control over motion of a Chaplygin ball

This paper deals with the problem of program control of the motion of a dynamically asymmetric balanced ball on the plane using three flywheel motors, provided that the ball rolls without slipping. The center of mass of the mechanical system coincides with the geometric center of the ball. Control laws are found to ensure the motion of the ball along the basic trajectories (line and circle), as well as along an arbitrarily given piecewise smooth trajectory on the plane. In this paper, we propose a quaternion model of ball motion. The model does not require using the traditional trigonometric functions. Kinematic equations are written in the form of linear differential equations eliminating the disadvantages associated with the use of Euler angles. The solution of the problem is carried out using the quaternion function of time, which is determined by the type of trajectory and the law of motion of the point of contact of the ball with the plane. An example of ball motion control is given and a visualization of the ball-flywheel system motion in a computer algebra package is presented. © 2019 Udmurt State University. All rights reserved

Kinematics and Robot Design I, KaRD2018

This volume collects the papers published on the Special Issue “Kinematics and Robot Design I, KaRD2018” (https://www.mdpi.com/journal/robotics/special_issues/KARD), which is the first issue of the KaRD Special Issue series, hosted by the open access journal “MDPI Robotics”. The KaRD series aims at creating an open environment where researchers can present their works and discuss all the topics focused on the many aspects that involve kinematics in the design of robotic/automatic systems. Kinematics is so intimately related to the design of robotic/automatic systems that the admitted topics of the KaRD series practically cover all the subjects normally present in well-established international conferences on “mechanisms and robotics”. KaRD2018 received 22 papers and, after the peer-review process, accepted only 14 papers. The accepted papers cover some theoretical and many design/applicative aspects

Analysis Of A Dual Scissored-Pair,variable-Speed, Control Moment Gyroscope Driven Spherical Robot

The objective of this research is to compare barycenter offset based designs of spherical robots to control moment gyroscope (CMG) based designs in order to determine which approach is most effective. The first objective was to develop a list of current state of the art designs in order to gain an overall understanding of what the obstacles in this area of research were. The investigation showed that barycenter offset designs can produce a low, continuous output torque, whereas CMG based designs can usually only produce a high, momentary output torque. The second objective was to develop a CMG based design that has the potential to outperform current state barycenter offset based designs. A design consisting of a dual, scissored-pair CMG (DSP-VSCMG) configuration was proposed and the dynamics derived from first principles. The third objective was to develop a set of equations that can describe performance characteristics of spherical robots . The equations that were modeled were power consumption, translational velocity, maximum incline plane, step size from rest, as well as CMG inertias and geometries. The fourth objective was to perform a series of parametric analysis using the developed equation set to compare barycenter and DSP-VSCMG based designs in a controlled environment. The analysis showed that DSP-VSCMG based designs can be more agile than barycenter designs, but require more power to do so

Dynamic Modeling and Control of Spherical Robots

In this work, a rigorous framework is developed for the modeling and control of spherical robotic vehicles. Motivation for this work stems from the development of Moball, which is a self-propelled sensor platform that harvests kinetic energy from local wind fields. To study Moball's dynamics, the processes of Lagrangian reduction and reconstruction are extended to robotic systems with symmetry-breaking potential energies, in order to simplify the resulting dynamic equations and expose mathematical structures that play an important role in subsequent control-theoretic tasks. These results apply to robotic systems beyond spherical robots. A formulaic procedure is introduced to derive the reduced equations of motion of most spherical robots from inspection of the Lagrangian. This adaptable procedure is applied to a diverse set of robotic systems, including multirotor aerial vehicles. Small time local controllability (STLC) results are derived for barycentric spherical robots (BSR), which are spherical vehicles whose locomotion depends on actuating the vehicle's center of mass (COM) location. STLC theorems are introduced for an arbitrary BSR on flat, sloped, or smooth terrain. I show that STLC depends on the surjectivity of a simple steering matrix. An STLC theorem is also derived for a class of commonly encountered multirotor vehicles. Feedback linearizing and PID controllers are proposed to stabilize an arbitrary spherical robot to a desired trajectory over smooth terrain, and direct collocation is used to develop a feedforward controller for Moball specifically. Moball's COM is manipulated by a novel system of magnets and solenoids, which are actuated by a "ballistic-impulse" controller that is also presented. Lastly, a motion planner is developed for energy-harvesting vehicles. This planner charts a path over smooth terrain while balancing the desire to achieve scientific objectives, avoid hazards, and the imperative of exposing the vehicle to environmental sources of energy such as local wind fields and topology. Moball's design details and experimental results establishing Moball's energy-harvesting performance (7W while rolling at a speed of 2 m/s), are contained in an Appendix.</p

Inverse dynamics-based motion control of a fluid-actuated rolling robot

In this paper, the rest-to-rest motion planning problem of a fluid-actuated spherical robot is studied. The robot is driven by moving a spherical mass within a circular fluid-filled pipe fixed internally to the spherical shell. A mathematical model of the robot is established and two inverse dynamics-based feed-forward control methods are proposed. They parameterize the motion of the outer shell or the internal moving mass as weighted Beta functions. The feasibility of the proposed feed-forward control schemes is verified under simulations