An analysis of the motion planning problem for a spherical rolling robot driven by internal rotors

The paper deals with the motion planning for a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. It is shown that if the robot is actuated by three rotors, any feasible kinematic trajectory is dynamically realizable. For the case of two rotors the conditions of controllability and dynamic realizability of a feasible kinematic trajectory are established. It is shown that in moving the robot by tracing straight lines and circles in the contact plane the dynamically realizable trajectories are not represented by the circles on the sphere, which is a feature of the kinematic model of pure rolling. The dynamic motion planning problem is then formulated in the optimal control settings, and the properties of the optimal trajectories are illustrated under simulation.

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

[2]  Shigeyuki Hosoe,et al.  Motion Planning Algorithms for a Rolling Sphere With Limited Contact Area , 2008, IEEE Transactions on Robotics.

[3]  Ravi N. Banavar,et al.  Motion analysis of a spherical mobile robot , 2009, Robotica.

[4]  Jean Levine,et al.  Analysis and Control of Nonlinear Systems , 2009 .

[5]  Anthony M. Bloch,et al.  Controllability and motion planning of a multibody Chaplygin's sphere and Chaplygin's top , 2008 .

[6]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

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

[8]  V. Jurdjevic.  NON-EUCLIDEAN ELASTICA , 1995 .

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

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

[11]  Jean Lévine,et al.  On Motion Planning for Robotic Manipulation with Permanent Rolling Contacts , 2002, Int. J. Robotics Res..

[12]  Philippe Martin,et al.  Any (controllable) driftless system with 3 inputs and 5 states is flat , 1995 .

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

[14]  Sunil K. Agrawal,et al.  Differentially Flat Systems , 2004 .

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

[16]  Motoji Yamamoto,et al.  On the dynamic model and motion planning for a class of spherical rolling robots , 2012, 2012 IEEE International Conference on Robotics and Automation.