In comparison to wheeled robots, spherical mobile robots offer greater mobility, stability, and scope for operation in hazardous environments. Inspite of these advantages, spherical designs have failed to gain popularity due to complexity of their motion planning and control problems. In this paper, we address the motion planning problem for the rolling sphere, often referred in the literature as the “ball-plate problem,” and propose two different algorithms for reconfiguration. The first algorithm, based on simple geometry, uses a standard kinematic model and invokes alternating inputs to obtain a solution comprised of circular arcs and straight line segments. The second algorithm is based on the Gauss-Bonet theorem of parallel transport and achieves reconfiguration through spherical triangle maneuvers. While the second algorithm is inherently simple and provides a solution comprised of straight line segments only, the first algorithm provides the basis for development of a stabilizing controller. Our stabilizing controller, which will be presented in our next paper, will be the first solution to a problem that has eluded many researchers since the kinematic model of the sphere cannot be converted to chained form. Both our algorithms require numerical computation of a small number of parameters and provide the scope for easy implementation.
Skip Nav Destination
Article navigation
December 2002
Technical Papers
Motion Planning for a Spherical Mobile Robot: Revisiting the Classical Ball-Plate Problem
Ranjan Mukherjee,
Ranjan Mukherjee
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226
Search for other works by this author on:
Mark A. Minor,
Mark A. Minor
Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112
Search for other works by this author on:
Jay T. Pukrushpan
Jay T. Pukrushpan
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109
Search for other works by this author on:
Ranjan Mukherjee
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226
Mark A. Minor
Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112
Jay T. Pukrushpan
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109
Contributed by the Dynamic Systems and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division, July 2000; final revision, March 2002. Associate Editor: Y. Hurmuzlu.
J. Dyn. Sys., Meas., Control. Dec 2002, 124(4): 502-511 (10 pages)
Published Online: December 16, 2002
Article history
Received:
July 1, 2000
Revised:
March 1, 2002
Online:
December 16, 2002
Citation
Mukherjee, R., Minor, M. A., and Pukrushpan, J. T. (December 16, 2002). "Motion Planning for a Spherical Mobile Robot: Revisiting the Classical Ball-Plate Problem ." ASME. J. Dyn. Sys., Meas., Control. December 2002; 124(4): 502–511. https://doi.org/10.1115/1.1513177
Download citation file:
Get Email Alerts
An Adaptive Sliding-Mode Observer-Based Fuzzy PI Control Method for Temperature Control of Laser Soldering Process
J. Dyn. Sys., Meas., Control
Fault detection of automotive engine system based on Canonical Variate Analysis combined with Bhattacharyya Distance
J. Dyn. Sys., Meas., Control
Multi Combustor Turbine Engine Acceleration Process Control Law Design
J. Dyn. Sys., Meas., Control (July 2025)
Related Articles
Motion Planning and Control of a Tractor With a Steerable Trailer Using Differential Flatness
J. Comput. Nonlinear Dynam (July,2008)
Velocity and Acceleration Cones for Kinematic and Dynamic Constraints on Omni-Directional Mobile Robots
J. Dyn. Sys., Meas., Control (December,2006)
Towing an Object With a Rover
J. Mechanisms Robotics (February,2025)
Ground Mobile Schatz Mechanism
J. Mechanisms Robotics (February,2016)
Related Proceedings Papers
Related Chapters
The Research of Local Path Planning for Mobile Robots Based on Grid Method
International Conference on Computer Research and Development, 5th (ICCRD 2013)
Methods for Mobile Robots Path Planning Based on Co-Located Environment
International Conference on Future Computer and Communication, 3rd (ICFCC 2011)
Optimal Path Planning of Mobile Robot with Multiple Targets Using Ant Colony Optimization
Intelligent Engineering Systems through Artificial Neural Networks, Volume 16