Planar motion of a parabolic catadioptric camera

2004 ◽  
Author(s):  
D. Gupta ◽  
K. Daniilidis
Keyword(s):  
Planar Motion ◽  
Catadioptric Camera

A compact motion controller-based planar motion mechanism for captive manoeuvring tests

2021 ◽  
Vol 220 ◽  
pp. 108195
Author(s):  
M. Cansın Özden ◽  
Sertaç Kurdoğlu ◽  
Ersin Demir ◽  
Kadir Sarıöz ◽  
Ömer Gören
Keyword(s):  
Planar Motion ◽  
Motion Controller ◽  
Motion Mechanism ◽  
Planar Motion Mechanism

scholarly journals Self-Localization of Mobile Robots Using a Single Catadioptric Camera with Line Feature Extraction

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4719
Author(s):  
Huei-Yung Lin ◽  
Yuan-Chi Chung ◽  
Ming-Liang Wang
Keyword(s):  
Mobile Robots ◽  
Ground Plane ◽  
Feature Correspondence ◽  
Projection Model ◽  
3D Space ◽  
Base Points ◽  
Real Scene ◽  
Correspondence Matching ◽  
Mobile Robot Localization ◽  
Catadioptric Camera

This paper presents a novel self-localization technique for mobile robots using a central catadioptric camera. A unified sphere model for the image projection is derived by the catadioptric camera calibration. The geometric property of the camera projection model is utilized to obtain the intersections of the vertical lines and ground plane in the scene. Different from the conventional stereo vision techniques, the feature points are projected onto a known planar surface, and the plane equation is used for depth computation. The 3D coordinates of the base points on the ground are calculated using the consecutive image frames. The derivation of motion trajectory is then carried out based on the computation of rotation and translation between the robot positions. We develop an algorithm for feature correspondence matching based on the invariability of the structure in the 3D space. The experimental results obtained using the real scene images have demonstrated the feasibility of the proposed method for mobile robot localization applications.

The Curvature Theory of Line Trajectories in Spatial Kinematics

1981 ◽  
Vol 103 (4) ◽  
pp. 718-724 ◽  
Author(s):  
J. M. McCarthy ◽  
B. Roth
Keyword(s):  
Planar Motion ◽  
Spatial Motion ◽  
Third Order ◽  
Local Shape ◽  
The Third ◽  
Moving Body ◽  
Physical Representation ◽  
Curvature Theory ◽  
Spatial Kinematics ◽  
Differential Properties

This paper develops the differential properties of ruled surfaces in a form which is applicable to spatial kinematics. Derivations are presented for the three curvature parameters which define the local shape of a ruled surface. Related parameters are also developed which allow a physical representation of this shape as generated by a cylindric-cylindric crank. These curvature parameters are then used to define all the lines in the moving body which instantaneously generate speciality shaped trajectories. Such lines may be used in the synthesis of spatial motions in the same way that the points on the inflection circle and cubic of stationary curvature are used to synthesize planar motion. As an example of this application several special sets of lines are defined: the locus of all lines which for a general spatial motion instantaneously generate helicoids to the second order and the locus of lines generating right hyperboloids to the third order.

Modeling and analysis of a 3-DOF Lorentz-force-driven planar motion stage for nanopositioning

Mechatronics ◽  
2010 ◽  
Vol 20 (5) ◽  
pp. 553-565 ◽  
Author(s):  
Jin Lei ◽  
Xin Luo ◽  
Xuedong Chen ◽  
Tianhong Yan
Keyword(s):  
Lorentz Force ◽  
Planar Motion ◽  
Modeling And Analysis ◽  
Motion Stage ◽  
Planar Motion Stage

scholarly journals Control-Oriented Planar Motion Modeling of Unmanned Surface Vehicles

2010 ◽  
Author(s):  
C Sonnenburg ◽  
A Gadre ◽  
D Horner ◽  
S Kragelund ◽  
A Marcus ◽  
...  
Keyword(s):  
Planar Motion ◽  
Motion Modeling ◽  
Unmanned Surface Vehicles

Instant Center Based Kinematic Formulation for Planar Wheeled Platforms

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Amit Kulkarni ◽  
Delbert Tesar
Keyword(s):  
Rigid Body ◽  
Input Parameter ◽  
Radial Distance ◽  
Planar Motion ◽  
Mobile Platform ◽  
General Point ◽  
Kinematic Modeling ◽  
Mobile Platforms ◽  
General Order ◽  
Operational Criteria

For a general J wheeled mobile platform capable of up to three-degrees-of-freedom planar motion, there are up to two J independent input parameters yet the output of the platform is completely represented by three independent variables. This leads to an input parameter resolution problem based on operational criteria, which are in development just as they have been developed for n input manipulator systems. To resolve these inputs into a meaningful decision structure means that all motions at the wheel attachment points must have clear physical meaning. To this effect, we propose a methodology for kinematic modeling of multiwheeled mobile platforms using instant centers to efficiently describe the motion of all system points up to the nth order using a generalized algebraic formulation. This is achieved by using a series of instant centers (velocity, acceleration, jerk, and jerk derivative), where each point in the system has a motion property with its magnitude proportional to the radial distance of the point from the associated instant center and at a constant angle relative to that radius. The method of instant center provides a straightforward and physically intuitive way to synthesize a general order planar motion of mobile platforms. It is shown that a general order motion property of any point on a rigid body follows two properties, namely, directionality and proportionality, with respect to the corresponding instant center. The formulation presents a concise expression for a general order motion property of a general point on the rigid body with the magnitude and direction separated and identified. The results are summarized for up to the fifth order motion in the summary table. Based on the initial formulation, we propose the development of operational criteria using higher order properties to efficiently synthesize the motion of a J wheeled mobile platform.

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