Cartesian coordinate system
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The Cartesian coordinate system is a mathematical framework that describes positions and orientations in space using perpendicular axes (X, Y, Z), providing a standardized reference frame for locating points in two or three dimensions. In robotics and AI, it serves as the foundational spatial language for nearly every aspect of robot operation — from defining end-effector positions and planning collision-free paths to controlling interaction forces and calibrating sensors. Robot manipulators are commanded to reach target locations expressed as Cartesian coordinates, while algorithms for visual servoing, impedance control, and trajectory planning all operate within or transform between Cartesian and joint spaces. Mobile robots use Cartesian frameworks to build environmental maps and estimate their own position. The system matters because it provides a universal, intuitive representation of physical space that bridges mechanical design, motion planning, perception, and control. Without a common spatial reference, coordinating multi-arm systems, human-robot interaction, or sensor fusion would be intractable, making the Cartesian coordinate system an indispensable foundation across virtually all robotics disciplines.
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On the Adaptive Control of Robot Manipulators
Jean-Jacques Slotine, Weiping Li
Citations: 2258 • 1987
A new technique for fully autonomous and efficient 3D robotics hand/eye calibration
R. Tsai, R. Lenz
Citations: 1343 • 1989
Impedance Control: An Approach to Manipulation: Part II—Implementation
Neville Hogan
Citations: 953 • 1985
A Global Performance Index for the Kinematic Optimization of Robotic Manipulators
Clément Gosselin, Jorge Angeles
Citations: 948 • 1991
Kinematics for multisection continuum robots
Cliff B. Jones, Ian D. Walker
Citations: 937 • 2006
DLR-Hand II: next generation of a dextrous robot hand
J. Butterfaß, Markus Grebenstein, Haoliang Liu, G. Hirzinger
Citations: 814 • 2002
Relative end-effector control using Cartesian position based visual servoing
W.J. Wilson, Carol Hulls, Gregory Bell
Citations: 621 • 1996
Visual tracking of a moving target by a camera mounted on a robot: a combination of control and vision
Nikos Papanikolopoulos, P.K. Khosla, Takeo Kanade
Citations: 561 • 1993
Formulation and optimization of cubic polynomial joint trajectories for industrial robots
Choun‐Sea Lin, P.-R. Chang, J. Luh
Citations: 483 • 1983
World modeling and position estimation for a mobile robot using ultrasonic ranging
James L. Crowley
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A new partitioned approach to image-based visual servo control
Peter Corke, Seth Hutchinson
Citations: 464 • 2001
Variable Impedance Control of Redundant Manipulators for Intuitive Human–Robot Physical Interaction
Fanny Ficuciello, Luigi Villani, Bruno Siciliano
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Feedback control of a nonholonomic wheeled cart in Cartesian space
Claude Samson, Karim Ait-Abderrahim
Citations: 422 • 2002
A depth space approach to human-robot collision avoidance
Fabrizio Flacco, Torsten Kröger, Alessandro De Luca, Oussama Khatib
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Configuration control of redundant manipulators: theory and implementation
H. Seraji
Citations: 414 • 1989
Torsion angle dynamics: Reduced variable conformational sampling enhances crystallographic structure refinement
Luke M. Rice, Axel T. Brünger
Citations: 367 • 1994
Distance functions and their application to robot path planning in the presence of obstacles
Éric Gilbert, Daniel Johnson
Citations: 366 • 1985
Cartesian Impedance Control of Redundant and Flexible-Joint Robots
Christian Ott
Citations: 339 • 2008
Joint stiffness identification of six-revolute industrial serial robots
Claire Dumas, Stéphane Caro, Sébastien Garnier, Benoît Furet
Citations: 334 • 2011
Hybrid position/Force control of multi-arm cooperating robots
S. Hayati
Citations: 332 • 1986