Systems and Control: Theory and Applications

Mobile Robot Design Using a Continuously Variable Transmission

Robot and Sensor Calibration

Computer-Aided Design of curves, Surfaces, and Rigid-body Motions


 

Systems and Control: Theory and Applications

 

The papers collected here describe our work on various aspects of systems and control. Several of the papers address attitude estimation and control, where we explicitly take into account the geometry of the rotation group and characteristics of GPS measurements. The paper by Han and Park (2001) shows how to to formulate least squares tracking on the Euclidean group in a coordinate-invariant way. The paper by Mishra et al describes work performed by his group at the Courant Institute (which I visited during 2001-2002) on hybrid systems for the mathematical modeling and simulation of biochemical pathways.


Related Publications

H.S. Kim, San Lim, C. Iurascu, F.C. Park, and Youngman Cho, "A robust, descrete, near time-optimal controller for hard-disk drives," Precision Engineering, vol. 28, pp. 459-468, 2004.

B. Mishra, F.C.~Park et al, "A sense of life: computational and experimental investigations with models of biochemical and evolutionary processes," OMICS: A Journal of Integrative Biology, vol. 7, no. 3, pp. 253-268, 2003.

Changmook Chun and F.C. Park, "Dynamics-based attitude determination using global positioning system," AIAA J. Guidance, Control, and Dynamics, vol. 24, no. 3, pp. 466-473, 2001.

Youngmo Han and F.C. Park, "Least-squares tracking on the Euclidean group," IEEE Trans. Automatic Control, vol. 46, no. 7, pp. 1127-1132, 2001.

F.C. Park, Junggon Kim, and Changdon Kee, "Geometric descent algorithms for attitude determination using the global positioning system," AIAA J. Guidance, Control, and Dynamics, vol. 23, no. 1, pp. 26-33, 2000.

S. Bharadwaj, M. Osipchuk, K.D. Mease, and F.C. Park, "Geometry and inverse optimality in global attitude stabilization," AIAA J. Guidance, Control, and Dynamics, vol. 21, no. 6, pp. 930-939, 1998.




 
 

Mobile Robot Design Using a Continuously Variable Transmission

 
 
  Photograph of MOSTS and S-CVT prototype.
 
  Pivot device for planar accessibility of MOSTS.Pivot inspiration and Realization by use of an internal gear

Continuous variable transmissions (CVT) have been the object of considerable research interest within the mechanical design community, primarily driven by automotive applications. Unlike conventional stepped transmissions, a CVT allows for a continuous range of gear ratios that can, up to certain device-dependent physical limits, be selected independently of the applied torque. This featuer of the CVT allows for engine oeration at the optimal fuel consumption point, improving overall vehicle efficiency.

The CVT can be regarded as a nonholonomic mechanical transmission device, involving rolling wheels in contact with a sphere, and as such leads to a rich set of problems involving nonholonomic systems. While the kinematics of nonholonomic CVTs are well-understood, by contrast very little attention has been given to the understanding of their dynamic and elastic behaviors, e.g., spin and other sources of power loss, as well as elasto-dynamic modeling. Clearly such an understanding is essential to making nonholonomic CVTs a practical, relaible, and widely used machine element for robotic systems.

The papers here describe a novel type of nonholonomic CVT, the S-CVT, and the development of a new type of wheeled mobile robot, which we call MOSTS (Mobile rObot with a Spherical Transmission System), based on the S-CVT. Typical mobile robots achieve planar mobility by employing an additional controlled actuator, such as a steering wheel or a motor for differentiating each wheel velocity. MOSTS is a minimal design in the sense that, with the design of a novel pivoting device that takes advantage of the flexibility of the S-CVT, it can turn about its cetner and change its direction of movement without the need for a steering actuator and controller. A feedback linearization based shifting controller, and an experimental analysis of the sources of power loss within the S-CVT, are also reported.



Related Publications

Jungyun Kim, Yeongil Park, and F.C. Park, "Design, analysis, and control of a spherical continuously variable transmission," ASME J. Mechanical Design, vol. 124, no. 1, pp. 21-29, 2002.

Jungyun Kim, Yeongil Park, F.C. Park, "Design, analysis and control of a wheeled mobile robot with a nonholonomic spherical CVT," Int. J. Robotics Research, vol. 21, no. 5-6, pp. 409-426, 2002.


 

 
 

Robot and Sensor Calibration

 

The papers listed here describe our work on various aspects of calibration, from camera sensors (Park and Martin 1994, Gwak et al 2003), to the kinematic calbration of both open chains (Okamura and Park 1996) and closed chains (Iurascu and Park 2003). All of these works share the common feature of exploiting the underlying geometric structure of the Euclidean group, and also the curved joint configuration space in the case of closed chains.



Related Publications

Koichiro Okamura and F.C. Park, "Kinematic calibration using the product of exponentials formula," Robotica, vol. 14, no. 4, pp. 415-421, 1996.

F.C. Park and B. Martin, "Robot sensor calibration: solving AX=XB on the Euclidean group," IEEE Trans. Robotics & Automation, vol. 10, no. 5, pp. 717-721, 1994.

Cornel Iurascu and F.C. Park, "Geometric algorithms for closed chain kinematic calibration," ASME J. Mechanical Design, vol. 125, no.1, pp. 23-32, 2003.

Seungwoong Gwak, Junggon Kim and F.C. Park, "Numerical optimization on the Euclidean group with applications to camera calibration," IEEE Trans. Robotics and Automation, vol. 19, no. 1, pp.65-74, 2003.



 
 

Computer-Aided Design of curves, Surfaces, and Rigid-body Motions

 

The papers listed here describe our work on geometric algorithms for generating curves and surfaces, and also of interpolating motions on the Euclidean group. The two papers on curve and surface flows (Kwon and Park 1999, Kwon, Park, and Chi 2005) give a partial differential equation description of the inextensible motion of curves and surfaces; such equations have potential applications in describing the motion of strings and developable surfaces. An optimal control method for constructing developable surfaces that approximate a given arbitrary surface is presented in (Park et al 2002). The remaining papers show how to efficiently construct trajectories on the Euclidean group, by generalizing standard notions such as Bezier curves and cubic splines to the Euclidean group in a frame-invariant way.



Related Publications

D.Y. Kwon and F.C. Park, "Evolution of inelastic plane curves," Applied Mathematics Letters, vol. 12, pp. 115-119, 1999.

D.Y. Kwon, F.C. Park, and D.P. Chi, "Inextensible flows of curves and developable surfaces," Applied Mathematics Letters, pp. 2005.

F.C. Park, Junghyun Yoo, Changmook Chun, and B. Ravani, "Design of Developable Surfaces Using Optimal Control" ASME J. Mechanical Design, vol. 124, no. 4, pp. 602-608, 2002.

F.C. Park and I.G. Kang, "Cubic spline algorithms for orientation interpolation," Int. J. Numerical Methods in Engineering, vol. 46, pp. 45-64, 1999.

F.C. Park and B. Ravani, "Smooth invariant interpolation of rotations," ACM Trans. Graphics, vol. 16, no. 3, pp. 277-295, 1997.

F.C. Park and B. Ravani, "Bezier curves on Riemannian manifolds and Lie groups with kinematics applications," ASME J. Mechanical Design, vol. 117, no. 1, pp. 36-40, 1995.