Poincaré representation of the equations of motion of a spherical robot actuated by internal rotors
01 Jan 2018-
TL;DR: The Poincare representation of equations of motion provides a global characterization of the dynamics of a rigid body subjected to external torques as discussed by the authors, where the rotor torques are incorporated into the dynamics by way of the total angular momentum of the robot about the point of contact.
Abstract: The Poincare representation of equations of motion provides a global characterization of the dynamics of a rigid body subjected to external torques. We use this representation to obtain the global dynamics of a spherical robot with three independent internal rotors rolling on a plane. The robot is subjected to nonholonomic constraints arising out of pure rolling motion. The dynamics of the system is obtained by projecting the kinematic vector fields on the constrained distribution using the nonholonomic affine connection. The rotor torques are incorporated into the dynamics by way of the total angular momentum of the robot about the point of contact.
Citations
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TL;DR: A quaternion based extended Kalman Filter is explored for estimating the attitude of a nonholonomic spherical robot using a 3-axis gyroscope, accelerometer and magnetometer and a high cross correlation between the experimental data and true trajectory was obtained suggesting a strong match.
Abstract: This paper explores a quaternion based extended Kalman Filter (EKF) for estimating the attitude of a nonholonomic spherical robot using a 3-axis gyroscope, accelerometer and magnetometer. A low cost inertial measurement Unit (IMU) and magnetometer are mounted on the spherical robot and the measured data are fused with EKF to determine the attitude of the robot. The attitude of a spherical robot is a time-parameterized curve in SO(3) and hence is ideal for validating its attitude globally. An indoor experiment was carried by dead-reckoning on circular and trifolium trajectory. The ground truth was established by integrating the robot kinematics using the estimated attitude and then comparing it with the reference trajectory. A high cross correlation between the experimental data and true trajectory was obtained suggesting a strong match.
Cites methods from "Poincaré representation of the equa..."
...Various mathematical models were obtained for spherical robot with different actuator configurations were obtained in Euler-Poincaré equations [13, 14], for pendulum...
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References
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18 Mar 1996
TL;DR: The spherical construction offers extraordinary motion properties in cases where turning over or falling down are risks for the robot to continue its motion, and has full capability to recover from collisions with obstacles or another robots traveling in the environment.
Abstract: The paper deals with dynamics and control of a special type of mobile robot designed to act as a small platform to carry sensing devices or actuators in an environment where stability of the platform is critical, like in surveying unstructured hostile industrial environment exploring other planets, or simply being a part of a human place, like office or home, which has not been designed for mobile machines. The spherical construction offers extraordinary motion properties in cases where turning over or falling down are risks for the robot to continue its motion. Also it has full capability to recover from collisions with obstacles or another robots traveling in the environment.
292 citations
"Poincaré representation of the equa..." refers background in this paper
...Interest in the challenging problems related to the spherical robot can be seen in the works [1], [2]....
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Book•
04 Oct 2009
TL;DR: Holm as mentioned in this paper provides a unified viewpoint of Lagrangian and Hamiltonian mechanics in the coordinate-free language of differential geometry in the spirit of the Marsden-Ratiu school.
Abstract: ,by Darryl D. Holm, Tanya Schmah and Cristina Stoica, Oxford University Press,Oxford, 2009, xi + 515 pp., ISBN: 978-0-19-921290-3The purpose of the book is to provide the unifying viewpoint of Lagrangian andHamiltonian mechanics in the coordinate-free language of differential geometryin the spirit of the Marsden-Ratiu school. The book is similar in content - althoughless formal - to the book by J. Marsden and T. Ratiu [7]. One can also mentionthe companion two-volumes book by Holm [4,5] written at a more basic level,and that one can recommend as an introductory reading. The classical treatises onthe subject are the books by Abraham-Marsden [1], Arnold [2] and Libermann-Marle [6].Typical applications are N-particle systems, rigid bodies, continua such as u-ids and electromagnetic systems that illustrate the powerfulness of the adoptedpoint of view. The geometrical structure allows the covering of both the nite-dimensional conservative case (rst part of the book) and the innite dimensionalsituation in the second part. The notion of symmetry here is central, as it allowsa reduction of the number of dimensions of the mechanical systems, and furtherexploits the conserved quantities (momentum map) associated to symmetry. Liegroup symmetries, Poisson reduction and momentum maps are rst discussed.The concepts are introduced in a progressive and clear manner in the rst part ofthe book. The second part devoted to innite dimensional systems is motivatedby the identication of Euler’s ideal uid motion with the geodesic o w on thegroup of volume-preserving diffeomorphism. The Euler-PoincarO (EP) variationalprinciple for the Euler uid equations is exposed in the framework of geometricmechanics, in association with Lie-Poisson Hamiltonian structure of Noether’stheorem and momentum maps. Original applications of the Euler-PoincarO equa-tions to solitons, computational anatomy, image matching, or geophysical uiddynamics are given at the end of the second part of the book.Here the rst chapter recapitulates the Newtonian, Lagrangian and Hamiltonian117
254 citations
20 Apr 1997
TL;DR: An experimental apparatus developed in the laboratory for research and advanced teaching purposes that consists of an untethered spherical vehicle that autonomously rolls on the laboratory floor, and can reach arbitrary positions and orientations in the environment.
Abstract: In this paper we describe an experimental apparatus developed in our laboratory for research and advanced teaching purposes. The device consists of an untethered spherical vehicle that autonomously rolls on the laboratory floor, and can reach arbitrary positions and orientations in the environment. The kinematics of the vehicle are nonholonomic and result from the combination of the kinematics of two classical nonholonomic systems, namely, a unicycle and a plate-ball system. The "SPHERICLE" introduces features that are new with respect to the two systems.
230 citations
"Poincaré representation of the equa..." refers background or methods in this paper
...Among the varied actuating mechanisms for applications, a notable few are: a mobile robot enclosed in a sphere [3], [4], momentum wheels [5] and multiple mass displacement [6], [7]....
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...Euler angle parameterization has been used to establish kinematic controllability in [4], [3]....
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01 Dec 2000
TL;DR: A mathematical model of the robot's motion was developed using the nonholonomic constraints on its motion, and it is shown experimentally that the model agrees well with the results.
Abstract: Describes a prototype and analytical studies of a spherical rolling robot, a new design of a nonholonomic robot system. The spherical robot is driven by two remotely controlled, internally mounted rotors that induce the ball to roll and spin on a flat surface. It is tracked on the plane by an overhead camera. A mathematical model of the robot's motion was developed using the nonholonomic constraints on its motion. For a number of simple motions, it is shown experimentally that the model agrees well with the results. Methods were developed for planning feasible, minimum time and minimum energy trajectories for the robot. These methods are illustrated both by mathematical simulation and hardware experiments.
224 citations
"Poincaré representation of the equa..." refers background in this paper
...Among the varied actuating mechanisms for applications, a notable few are: a mobile robot enclosed in a sphere [3], [4], momentum wheels [5] and multiple mass displacement [6], [7]....
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07 Aug 2002
TL;DR: A prototype and analytical studies of a spherical rolling robot, a new design of an omnidirectional robot system that can arbitrarily begin to move in any direction to the target, and autonomously roll and reach any desired position is described.
Abstract: This paper describes a prototype and analytical studies of a spherical rolling robot, a new design of an omnidirectional robot system. The robot can arbitrarily begin to move in any direction to the target, and autonomously roll and reach any desired position. Our design considers a spherical robot with an internal mechanism for propulsion. The propulsion mechanism distributes weights radially along spokes fixed inside the sphere and enables the robot to accelerate, decelerate, and move with constant velocity. A mathematical model of the robot's dynamic and motion is instructed. An algorithmic motion planning is developed and, partly, pseudo-code of that is presented. For a number of missions, it is shown experimentally that the model agrees well with the results.
131 citations
"Poincaré representation of the equa..." refers background in this paper
...Among the varied actuating mechanisms for applications, a notable few are: a mobile robot enclosed in a sphere [3], [4], momentum wheels [5] and multiple mass displacement [6], [7]....
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