Geometric tracking control for a nonholonomic system: a spherical robot

Gajbhiye, Sneha; Banavar, Ravi N.

doi:10.1016/j.ifacol.2016.10.267

Cited by 12 publications

(10 citation statements)

References 28 publications

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“…More recently, [13] provides a detailed analysis of the trajectory of the Chaplygin sphere's contact point, and it has been shown that the dynamics of the Chaplygin top exhibit a strange attractor [14] and the phenomenon of reversal [15]. The dynamics of the rolling ball with dynamic internal structure is also an active topic in the nonholonomic mechanics literature [16,17,7,18,19,20,21,22,23].…”

Section: Introductionmentioning

confidence: 99%

On the dynamics of a rolling ball actuated by internal point masses

Putkaradze

Rogers

2018

Meccanica

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The motion of a rolling ball actuated by internal point masses that move inside the ball's frame of reference is considered. The equations of motion are derived by applying Euler-Poincaré's symmetry reduction method in concert with Lagrange-d'Alembert's principle, which accounts for the presence of the nonholonomic rolling constraint. As a particular example, we consider the case when the masses move along internal rails, or trajectories, of arbitrary shape and fixed within the ball's frame of reference. Our system of equations can treat most possible methods of actuating the rolling ball with internal moving masses encountered in the literature, such as circular motion of the masses mimicking swinging pendula or straight line motion of the masses mimicking magnets sliding inside linear tubes embedded within a solenoid. Moreover, our method can model arbitrary rail shapes and an arbitrary number of rails such as several ellipses and/or figure eights, which may be important for future designs of rolling ball robots. For further analytical study, we also reduce the system to a single differential equation when the motion is planar, that is, considering the motion of the rolling disk actuated by internal point masses, in which case we show that the results obtained from the variational derivation coincide with those obtained from Newton's second law. Finally, the equations of motion are solved numerically, illustrating a wealth of complex behaviors exhibited by the system's dynamics. Our results are relevant to the dynamics of nonholonomic systems containing internal degrees of freedom and to further studies of control of such systems actuated by internal masses.

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Section: Introductionmentioning

confidence: 99%

On the dynamics of a rolling ball actuated by internal point masses

Putkaradze

Rogers

2018

Meccanica

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“…Gajbhiye 2016 [30] designed two control laws for spherical robot trajectory tracking that are the orientation tracking using a modified traced potential function and the contact position tracking using transport map. The proposed method claimed to be able to reduced orientation stabilization and demonstrated using simulation.…”

Section: Path Planning and Trajectory Tracking Control Discussionmentioning

confidence: 99%

The Kinematics and Dynamics Motion Analysis of a Spherical Robot

Dewi¹,

Risma²,

Oktarina³

et al. 2019

EECSI

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Mobile robot application has reach more aspect of life in industry and domestic. One of the mobile robot types is a spherical robot whose components are shielded inside a rigid cell. The spherical robot is an interesting type of robot that combined the concept of a mobile robot and inverted pendulum for inner mechanism. This combination adds to more complex controller design than the other type of mobile robots. Aside from these challenges, the application of a spherical robot is extensive, from being a simple toy, to become an industrial surveillance robot. This paper discusses the mathematical analysis of the kinematics and dynamics motion analysis of a spherical robot. The analysis combines mobile robot and pendulum modeling as the robot motion generated by a pendulum mechanism. This paper is expected to give a complete discussion of the kinematics and dynamics motion analysis of a spherical robot.

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“…Roozegar et al [47] studied the optimal motion planning and control of a nonholonomic spherical mobile robot by the method of dynamic programming (DP). Gajbhiye and Banavar [48] established the tracking control law of two different targets (spherical robot) in the nonholonomic system. Other control methods were also adopted for the stability control of spherical robot: the nonlinear high order (second order) sliding mode feedback control [49] and a grey PID fuzzy controller [50].…”

Section: Introductionmentioning

confidence: 99%

Design and Performance Evaluation of a Spherical Robot Assisted by High-Speed Rotating Flywheels for Self-Stabilization and Obstacle Surmounting

Wei

Liu

2021

Journal of Mechanisms and Robotics

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In order to reinforce the operation stability and obstacle capability of a spherical robot, this paper presents a spherical robot with high-speed rotating flywheel, the mechanical structure of which is mainly composed of a spherical shell, a double pendulum on both sides and two high-speed flywheels. The robot has three excitation modes: level running, self-stability operating and obstacle surmounting. The dynamic characteristics of the pendulum, flywheel and brake of the robot are discussed through the establishment of kinematic and dynamic model of the spherical robot and the influence of parameters like weight, flywheel speed and flywheel position on its dynamic characteristics and robot performance is optimized and analyzed in detail. The research results indicate that the two flywheels located in the center of the sphere apart can bring the maximum stability gain to the sphere. Finally, the simulation and experiment of the stability gain brought by the high-speed flywheel to the sphere verify that the operation stability of the sphere is effectively improved after using the flywheel, and the robot that stops the flywheel through a brake fixed on the pendulum has better obstacle surmounting performance.

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Geometric tracking control for a nonholonomic system: a spherical robot

Cited by 12 publications

References 28 publications

On the dynamics of a rolling ball actuated by internal point masses

On the dynamics of a rolling ball actuated by internal point masses

The Kinematics and Dynamics Motion Analysis of a Spherical Robot

Design and Performance Evaluation of a Spherical Robot Assisted by High-Speed Rotating Flywheels for Self-Stabilization and Obstacle Surmounting

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