Motion Planning Algorithms for a Rolling Sphere With Limited Contact Area

The paper deals with the motion planning problem for a rolling sphere with limited contact area. The system under consideration is represented by a hemispherical object that can roll without slipping or spinning on the plane. Under the constraints imposed on the size of the contact area, the construction of motion can be regarded as a problem of parallel parking in a finite number of movement steps. A motion strategy, realizing the movement steps by tracing generalized figure eights on the hemisphere, is introduced. Two different algorithms for this motion strategy, the circle-based and the generalized Viviani-curve-based ones, are proposed. The convergence of the algorithms is analyzed, and the computational feasibility of these algorithms is verified under simulation.

[1]  L. Dai,et al.  Non-holonomic Kinematics and the Role of Elliptic Functions in Constructive Controllability , 1993 .

[2]  David J. Montana,et al.  Contact stability for two-fingered grasps , 1992, IEEE Trans. Robotics Autom..

[3]  R. Mukherjee,et al.  Motion Planning for a Spherical Mobile Robot: Revisiting the Classical Ball-Plate Problem , 2002 .

[4]  A. Pressley.  Elementary Differential Geometry , 2000 .

[5]  Zexiang Li,et al.  Motion of two rigid bodies with rolling constraint , 1990, IEEE Trans. Robotics Autom..

[6]  Jeffrey C. Trinkle,et al.  Dextrous manipulation with rolling contacts , 1997, Proceedings of International Conference on Robotics and Automation.

[7]  T. Flash,et al.  The coordination of arm movements: an experimentally confirmed mathematical model , 1985, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[8]  Marilena Vendittelli,et al.  From nominal to robust planning: the plate-ball manipulation system , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[9]  M. Levi.  Geometric phases in the motion of rigid bodies , 1993 .

[10]  Dimitrios Hristu-Varsakelis,et al.  The dynamics of a forced sphere-plate mechanical system , 2001, IEEE Trans. Autom. Control..

[11]  Alfred A. Rizzi,et al.  Legless locomotion for legged robots , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[12]  Marilena Vendittelli,et al.  A framework for the stabilization of general nonholonomic systems with an application to the plate-ball mechanism , 2005, IEEE Transactions on Robotics.

[13]  Richard M. Murray,et al.  Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems , 1994, Math. Control. Signals Syst..

[14]  Vijay R. Kumar,et al.  Velocity and Acceleration Analysis of Contact Between Three-Dimensional Rigid Bodies , 1996 .

[15]  Antonio Bicchi,et al.  Rolling bodies with regular surface: controllability theory and applications , 2000, IEEE Trans. Autom. Control..

[16]  Kensuke Harada,et al.  Rolling Based Manipulation under Neighborhood Equilibrium , 2002, Int. J. Robotics Res..

[17]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[18]  G. R. Walsh,et al.  On Hammersley's minimum problem for a rolling sphere , 1986 .

[19]  Shigeyuki Hosoe,et al.  Planning of smooth motions for a ball-plate system with limited contact area , 2008, 2008 IEEE International Conference on Robotics and Automation.

[20]  Ranjan Mukherjee,et al.  Exponential stabilization of the rolling sphere , 2004, Autom..

[21]  David J. Montana,et al.  The Kinematics of Contact and Grasp , 1988, Int. J. Robotics Res..

[22]  K. Nagase,et al.  Control of a Sphere Rolling on a Plane with Constrained Rolling Motion , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[23]  Kevin M. Lynch,et al.  Rolling Manipulation with a Single Control , 2002, Int. J. Robotics Res..

[24]  Antonio Bicchi,et al.  Introducing the "SPHERICLE": an experimental testbed for research and teaching in nonholonomy , 1997, Proceedings of International Conference on Robotics and Automation.

[25]  Sunil K. Agrawal,et al.  Spherical rolling robot: a design and motion planning studies , 2000, IEEE Trans. Robotics Autom..

[26]  Pierre Rouchon.  Necessary Condition and Genericity of Dynamic Feedback Linearization , 1994 .

[27]  Mitsuji Sampei,et al.  Simultaneous control of position and orientation for ball-plate manipulation problem based on time-State control form , 2004, IEEE Transactions on Robotics and Automation.

[28]  Jean-Paul Laumond,et al.  Topological property for collision-free nonholonomic motion planning: the case of sinusoidal inputs for chained form systems , 1998, IEEE Trans. Robotics Autom..

[29]  Vijay Kumar,et al.  Dynamic control of 3-D rolling contacts in two-arm manipulation , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[30]  Bernard Roth,et al.  Analysis of Multifingered Hands , 1986 .

[31]  Velimir Jurdjevic.  The geometry of the plate-ball problem , 1993 .

[32]  Kensuke Harada,et al.  Rolling-based manipulation for multiple objects , 2000, IEEE Trans. Robotics Autom..

[33]  Antonio Bicchi,et al.  Dexterous Grippers: Putting Nonholonomy to Work for Fine Manipulation , 2002, Int. J. Robotics Res..

[34]  A. Chelouah,et al.  On the motion planning of rolling surfaces , 2003 .

[35]  Antonio Bicchi,et al.  Robotic dexterity via nonholonomy , 1998 .