Spherical Robot Research Articles

Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem

Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem

Experimental Study on the Longitudinal Motion Performance of a Spherical Robot Rolling on Sandy Terrain

To provide the necessary theoretical models of sphere–soil interaction for the structural design, motion control, and simulation of spherical robots, this paper derives analytical expressions for traction force and driving torque when spherical robots slide and sink into sandy terrain, based on terramechanics and multibody dynamics. Furthermore, orthogonal experimental analysis identifies the load, joint angular acceleration, and maximum joint angular velocity of spherical robots as influencing factors, highlighting that the load significantly affects their longitudinal motion performance. Experimental results indicate that rolling friction and additional resistance on sandy terrain cannot be ignored. The corrected theoretical model effectively replicates the temporal variation of driving torque exerted by spherical robots on sandy terrain. Numerical computations and experimental analyses demonstrate that increasing the radius of the sphere shell, the load, and the slip ratio all lead to increased traction force and driving torque. However, traction force and driving torque begin to decrease once the slip ratio reaches approximately 0.5. Therefore, in the design of spherical robot structures and control laws, appropriate parameters such as load and slip ratio should be chosen based on the established sphere–soil interaction theoretical model to achieve high-quality longitudinal motion performance on sandy terrain.

XK-III: A Spherical Robot with Redundant Degrees of Freedom

The spherical robot XK-III, designed with redundant degrees of freedom, addresses the limitations of existing pendulum spherical robot structures by enhancing mobility and environmental adaptability. A nonlinear dynamic model is developed for XK-III’s new drive structure, along with a nonlinear disturbance observer (NDOB) to mitigate perturbations. Additionally, a Fuzzy PID controller (FPID) is implemented to further enhance XK-III’s environmental adaptability. Experimental results confirm the effectiveness of the new design, showing that XK-III equipped with FPID and NDOB outperforms traditional control systems in terms of anti-disturbance capabilities. This research provides valuable insights for the use of spherical robots in complex environments.

Research on the Influence of Radial Variation of Centroid on the Motion of Spherical Robot

Through the pendulum mechanism inside the spherical shell, the centroid can be varied circumferentially, enabling the spherical robot to achieve omnidirectional flexible movement. Additionally, the radial variation ability of the centroid enables spherical robots to adopt two distinct driving modes: the traditional lower pendulum driving mode and the inverted pendulum driving mode. There are two manifestations of radial variation in the centroid: having different radial positions of the centroid and achieving radial movement of the centroid. Focusing on these two manifestations, experimental data are obtained through different motion velocities and different motion slopes to conduct research on the influence of radial variation in the centroid on the motion of spherical robots. Based on the experimental data, multiple indicators are analyzed, including response speed, convergence speed, stability, and overshoot, as well as steering ability, climbing ability, and output power. The impact of the radial variation ability of the centroid on the control performance, locomotion capability, and energy consumption of spherical robots is summarized, and the correlation model relating the motion requirements to the radial position of the centroid is established, providing a theoretical basis for the selection of driving modes and centroid positions for spherical robots facing complex task requirements.

Algorithm for Controlling a Spherical Robot with a Pendulum Actuator in the Problem of Pursuing and Hitting a Moving Target

Algorithm for Controlling a Spherical Robot with a Pendulum Actuator in the Problem of Pursuing and Hitting a Moving Target

Attitude oscillation suppression control of a XK-I spherical robot

PurposeIn complex environments, a spherical robot has great application value. When the pendulum spherical robot is stopped or disturbed, there will be a periodic oscillation. This situation will seriously affect the stability of the spherical robot. Therefore, this paper aims to propose a control method based on backstepping and disturbance observers for oscillation suppression.Design/methodology/approachThis paper analyzes the mechanism of oscillation. The oscillation model of the spherical robot is constructed and the relationship between the oscillation and the internal structure of the sphere is analyzed. Based on the oscillation model, the authors design the oscillation suppression control of the spherical robot using the backstepping method. At the same time, a disturbance observer is added to suppress the disturbance.FindingsIt is found that the control system based on backstepping and disturbance observer is simple and efficient for nonlinear models. Compared with the PID controller commonly used in engineering, this control method has a better control effect.Practical implicationsThe proposed method can provide a reliable and effective stability scheme for spherical robots. The problem of instability in real motion is solved.Originality/valueIn this paper, the oscillation model of a spherical robot is innovatively constructed. Second, a new backstepping control method combined with a disturbance observer for the spherical robot is proposed to suppress the oscillation.

Algorithm for controlling a spherical robot with a pendulum actuator in the problem of pursuing and hitting a moving target

An algorithm is developed to control a spherical robot with a pendulum actuator through servoconstraints, generating the necessary control torque. Servoconstraints set a movement program that allows the robot to pursue a moving target until it is hit. The rectilinear and curvilinear trajectories of the robot, constructed on the basis of numerical integration, are considered, their length and time to hit the target are determined. Keywords:spherical robot, pendulum actuator, control, pursuit, hit, nonholonomic constraint, servoconstraint evaeva_84@mail.ru

Research on a Biomimetic Flexible Ball Joint With Variable Stiffness for Robots

Abstract The human ball joint is a compact and flexible 3-degree-of-freedom (DOF) composite joint. The ball joints commonly used in robot design lack active driving capability. Ball joints with active drive generally consist of three single-degree-of-freedom joints connected in series, which is a noncompacted structure and easily leads to singular postures. In order to meet the demand for high-performance composite joint modules for service robots, this article designs a flexible biomimetic spherical robot joint with variable stiffness characteristics: the mechanism of muscle parallel antagonistic drive and ligament wrapping constraint is simulated; three parallel branch chains are used to drive three composite degrees-of-freedom; ropes, soft airbags, and series elastic drive gears are used to form a flexible transmission system; the contour of the rope winch has been optimized with the aim of transmission stability; and a pneumatic variable stiffness soft structure has been designed and fabricated. A compliance control algorithm for joints was developed based on the principle of impedance control. The research results indicate that the biomimetic ball-and-socket joint has a compact structure, a wide range of motion and good motion tracking performance, variable stiffness performance, and flexible interaction ability.

Lie-group modeling and simulation of a spherical robot, actuated by a yoke–pendulum system, rolling over a flat surface without slipping

The present paper aims at introducing a mathematical model of a spherical robot expressed in the language of Lie-group theory. Since the main component of motion is rotational, the space SO(3)3 of three-dimensional rotations plays a prominent role in its formulation. Because of friction to the ground, rotation of the external shell results in translational motion. Rolling without slipping implies a constraint on the tangential velocity of the robot at the contact point to the ground which makes it a non-holonomic dynamical system. The mathematical model is obtained upon writing a Lagrangian function that describes the mechanical system and by the Hamilton minimal-action principle modified through d’Alembert virtual work principle to account for non-conservative control actions as well as frictional reactions. The result of the modeling appears as a series of non-holonomic Euler–Poincaré equations of dynamics plus a series of auxiliary equations of reconstruction and advection type. A short discussion on the numerical simulation of such mathematical model complements the main analytic-mechanic development.

Panoramic visual system for spherical mobile robots

Abstract Aimed at the challenges of wide-angle mobile robot visual perception for diverse field applications, we present the spherical robot visual system that uses a 360° field of view (FOV) for realizing real-time object detection. The spherical robot image acquisition system model is developed with optimal parameters, including camera spacing, camera axis angle, and the distance of the target image plane. Two 180 $^{\circ}$ -wide panoramic FOVs, front and rear view, are formed using four on-board cameras. The speed of the SURF algorithm is increased for feature extraction and matching. For seamless fusion of the images, an improved fade-in and fade-out algorithm is used, which not only improves the seam quality but also improves object detection performance. The speed of the dynamic image stitching is significantly enhanced by using a cache-based sequential image fusion method. On top of the acquired panoramic wide FOVs, the YOLO algorithm is used for real-time object detection. The panoramic visual system for the spherical robot is then tested in real time, which outputs panoramic views of the scene at an average frame rate of 21.69 fps and panoramic views with object detection at an average of 15.39 fps.

Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem

Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem

A Deep Reinforcement Learning-Based Decentralized Hierarchical Motion Control Strategy for Multiple Amphibious Spherical Robot Systems With Tilting Thrusters

A Deep Reinforcement Learning-Based Decentralized Hierarchical Motion Control Strategy for Multiple Amphibious Spherical Robot Systems With Tilting Thrusters

Reinforcement Learning in the Task of Spherical Robot Motion Control

The output control algorithm is a pair of trained neural networks — actor and critic, where the actor-network is used to obtain the control torques applied to the robot wheel and the critic-network is only involved in the learning process. The results of the training are shown below, namely how the robot performs the motion along ten arbitrary trajectories, where the main quality functional is the average error magnitude over the trajectory length scale. The algorithm is implemented using the PyTorch machine learning library.

Geometry and Kinematics of the Mecanum Wheel on a Plane and a Sphere

This article is devoted to a study of the geometry and kinematics of the Mecanum wheels, also known as Ilon wheels or the Swedish wheels. The Mecanum wheels are one of the types of omnidirectional wheels. This property is provided by peripheral rollers whose axes are deviated from the wheel one by 45 degrees. A unified approach to studying the geometry and kinematics of the Mecanum wheels on a plane and on the internal or external surface of a sphere is proposed. Kinematic relations for velocities at the contact point of the wheel and the supporting surface, and angular velocities of the roller relative to the supporting surface are derived. They are necessary to describe the dynamics of the Mecanum systems taking into account forces and moments of contact friction in the presence of slipping. From the continuous contact condition, relations determining the geometry of the wheel rollers on a plane and on the internal or external surface of a sphere are obtained. The geometric relations for the Mecanum wheel rollers could help to adjust the existing shape of the Mecanum wheel rollers of spherical robots and ballbots to improve the conditions of contact between the rollers and the spherical surface. An analytical study of the roller geometry was carried out, and equations of their generatrices were derived. Under the no-slipping condition, expressions for rotational velocities of the wheel and the contacting roller are obtained. They are necessary for analyzing the motion of systems within the framework of nonholonomic models, solving problems of controlling Mecanum systems and improving its accuracy. Using the example of a spherical robot with an internal three-wheeled Mecanum platform, the influence of the rollers on the robot movement was studied at the kinematic level. It has been established that the accuracy of the robot movement is influenced not only by the geometric parameters of the wheels and the number of rollers, but also by the relationship between the components of the platform center velocity and its angular velocity. Results of the numerical simulation of the motion of the spherical robot show a decrease in control accuracy in

Explorations of the holonomy of a rolling sphere

Consider a rigid body rolling with one point in contact with a fixed surface. Now suppose that the instantaneous point of contact traces out a closed path. As a demonstration of a phenomenon known as holonomy, the body will typically not return to its original orientation. The simplest demonstration of this phenomenon in rigid body dynamics occurs in the motion of a rolling sphere and finds application to path planning and reorientation of spherical robots. Motivated by earlier works of Bryant and Johnson, we establish expressions for the change in orientation of a rolling sphere after completing a rectangular path. We use numerical methods to show that all possible changes in orientation are possible using a single rectangular path. Based on the Euler angle parameterization of a rotation, we develop a more intuitive method to achieve a desired orientation using three rectangular paths. With regards to applications, the paths we discuss can be employed to achieve any desired reorientation of a spherical robot.

基于灰狼算法的球形机器人构件参数优化

基于灰狼算法的球形机器人构件参数优化

Control of a Spherical Robot with a Nonholonomic Omniwheel Hinge Inside

This study investigates the rolling along the horizontal plane of two coupled rigid bodies: a spherical shell and a dynamically asymmetric rigid body which rotates around the geometric center of the shell. The inner body is in contact with the shell by means of omniwheels. A complete system of equations of motion for an arbitrary number of omniwheels is constructed. The possibility of controlling the motion of this mechanical system along a given trajectory by controlling the angular velocities of omniwheels is investigated. The cases of two omniwheels and three omniwheels are studied in detail. It is shown that two omniwheels are not enough to control along any given curve. It is necessary to have three or more omniwheels. The quaternion approach is used to study the dynamics of the system.

Design and Implementation of a Model Predictive Formation Tracking Control System for Underwater Multiple Small Spherical Robots

Due to the characteristics of good concealment ability and strong mobility, multiple, small spherical underwater robot formations play an important role in near coast defense missions, such as cruising, reconnaissance, surveillance, and sensitive target capturing. Referring to the formation problem for underwater small spherical robots with limited energy, perception, and computation abilities, a trajectory tracking-based formation strategy that transforms the complex formation tracking problem into a simple trajectory tracking problem of a single robot is provided. Two layers are designed in the formation tracking strategy. The upper layer is a virtual structure-based formation algorithm. The bottom layer is a tracking controller based on model predictive control (MPC). The formation algorithm is in charge of calculating reference trajectory for each robot in the formation according to the global formation path. The MPC-based dynamic controller for each robot is designed to track the self reference trajectory. Compared with the model predictive control method used for the traditional trajectory tracking problem of a single robot, this paper additionally considers the formation constraints and the internal collision avoidance. In addition, the extended state observer (ESO) is utilized to estimate the lumped disturbance composed of environment disturbance and the inaccurate dynamic model of a small spherical robot. Not only are the numerical simulations based on MATLAB v.2015a, but physical simulations based on self-building multi-spherical robot formation platform are also carried out. Furthermore, through using two small spherical robots, a formation tracing experiment is conducted. All of the results prove that the proposed formation method is feasible and practical for small spherical robots.

Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base Using Feedback

This paper treats the problem of a spherical robot with an axisymmetric pendulum driverolling without slipping on a vibrating plane. The main purpose of the paper isto investigate the stabilization of the upper vertical rotations of the pendulumusing feedback (additional control action). For the chosen type of feedback,regions of asymptotic stability of the upper vertical rotations of the pendulum are constructedand possible bifurcations are analyzed. Special attention is also given to the question ofthe stability of periodic solutions arising as the vertical rotations lose stability.

Control of a Spherical Robot Rolling Over Irregular Surfaces

Pendulum-Driven Spherical Robots are a type of spherical robot whose motion is achieved by controlling two motors for longitudinal and lateral motion. This configuration makes the robot a non-holonomic system, which impedes it from navigating directly towards a target. In addition, controlling its motion on inclined irregular surfaces is also an issue that has not received much attention. In this work, we addressed these two issues by proposing a methodology to con-trol both motors using PID controllers. However, we propose tuning the controller’s gains using stochastic signals for the longitudinal controller because by varying the motor’s torque, the robot is more susceptible to destabilization in combination with a classical gain tuning methodology for the second controller. Our results indicate that this enables the robot to perform motion on inclined irregular surfaces. We also propose using semicircular trajectories to plan the robot’s motion to reach a target successfully even when moving on inclined irregular surfaces. We have carried out experiments in the Webots simulator, showing that our approach does not overshoot while reaching a settling time of almost 0. These results outperform the Ziegler-Nichols PID controller.