Rolling Manipulation with a Single Control

Underactuated manipulation is the process of controlling several object degrees-of-freedom with fewer robot actuators. Underactuated manipulation allows us to build dexterous robots with only a few actuators. In this paper we explore the possibility of useful dynamic manipulation with only a single actuator. Our case study is a ball rolling in an asymmetrical bowl which can be accelerated along one linear degree-of-freedom. We show that the state of the ball relative to the bowl is controllable by this single controlled acceleration. In particular, it is possible to control the equilibrium orientation of the ball on the three-dimensional manifold SO(3) using this single input. We have built an experimental demonstration of this system and we have constructed a motion planner to find a sequence of motions of the bowl to accomplish a desired reorientation.

[1]  William H. Press,et al.  Book-Review - Numerical Recipes in Pascal - the Art of Scientific Computing , 1989 .

[2]  Naoji Shiroma,et al.  Roles of shape and motion in dynamic manipulation , 1998 .

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

[4]  J. M. Hammersley,et al.  Probability, Statistics and Analysis: Oxford Commemoration Ball , 1983 .

[5]  Sunil Kumar Agrawal,et al.  Design, experiments and motion planning of a spherical rolling robot , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

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

[7]  Berthold K. P. Horn,et al.  Closed-form solution of absolute orientation using unit quaternions , 1987 .

[8]  Shen Guo-quan.  Rolling manipulation , 2003 .

[9]  Kevin M. Lynch,et al.  Controllability of a planar body with unilateral thrusters , 1999, IEEE Trans. Autom. Control..

[10]  J.Basto Gonçalves.  Local controllability of scalar input systems on 3-manifolds , 1991 .

[11]  Naoji Shiroma,et al.  The roles of shape and motion in dynamic manipulation: the butterfly example , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

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

[13]  Antonio Bicchi,et al.  Dexterous manipulation through rolling , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[14]  Myung-Soo Kim,et al.  Interpolating solid orientations with circular blending quaternion curves , 1995, Comput. Aided Des..

[15]  Richard M. Murray,et al.  Controllability of simple mechanical control systems , 1997 .

[16]  S. LaValle,et al.  Randomized Kinodynamic Planning , 2001 .

[17]  V. Jurdjevic.  Geometric control theory , 1996 .

[18]  P. Crouch,et al.  Spacecraft attitude control and stabilization: Applications of geometric control theory to rigid body models , 1984 .

[19]  P. Crouch,et al.  Controllability on principal fibre bundles with compact structure group , 1984 .

[20]  L. Fu,et al.  Controllability of spacecraft systems in a central gravitational field , 1994, IEEE Trans. Autom. Control..

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

[22]  R. Brockett.  Nonlinear systems and differential geometry , 1976, Proceedings of the IEEE.

[23]  A. D. Lewis.  Local configuration controllability for a class of mechanical systems with a single input , 1997, 1997 European Control Conference (ECC).

[24]  A. D. Lewis,et al.  Configuration Controllability of Simple Mechanical Control Systems , 1997 .

[25]  C. Lobry.  Controllability of Nonlinear Systems on Compact Manifolds , 1974 .

[26]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .

[27]  Yan-Bin Jia,et al.  Local observability of rolling , 1998 .

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

[29]  Steven M. LaValle,et al.  Rapidly-Exploring Random Trees: Progress and Prospects , 2000 .

[30]  Sung Yong Shin,et al.  A general construction scheme for unit quaternion curves with simple high order derivatives , 1995, SIGGRAPH.

[31]  Antonio Bicchi,et al.  Nonholonomic kinematics and dynamics of the Sphericle , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

[32]  Jean-Claude Latombe,et al.  Nonholonomic multibody mobile robots: Controllability and motion planning in the presence of obstacles , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[33]  F. Park.  Distance Metrics on the Rigid-Body Motions with Applications to Mechanism Design , 1995 .

[34]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[35]  Giuseppe Oriolo,et al.  with Application to Chained-Form Systems , 1996 .

[36]  H. Sussmann.  Lie Brackets and Local Controllability: A Sufficient Condition for Scalar-Input Systems , 1983 .

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

[38]  Kevin M. Lynch,et al.  Controllability of single input rolling manipulation , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[39]  H. Sussmann,et al.  Control systems on Lie groups , 1972 .

[40]  Nilanjan Sarkar,et al.  Control of Contact Interactions with Acatastatic Nonholonomic Constraints , 1997, Int. J. Robotics Res..

[41]  Naoji Shiroma,et al.  Collision-Free Trajectory Planning for a 3-DoF Robot with a Passive Joint , 2000, Int. J. Robotics Res..

[42]  S. Shankar Sastry,et al.  Kinematics and control of multifingered hands with rolling contact , 1989 .

[43]  P. Krishnaprasad,et al.  Controllability of Lie-Poisson reduced dynamics , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).