Inverse
Related papers: 20
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Inverse methods in robotics and AI refer to a family of mathematical techniques that work backwards from a desired outcome to determine the inputs or configurations needed to achieve it. The most prominent application is **inverse kinematics (IK)**, which computes the joint angles or configurations a robot manipulator must adopt to place its end-effector at a specified position and orientation — the reverse of forward kinematics. Related techniques include inverse dynamics, which determines the forces and torques required to produce desired motion, and inverse optimal control, which infers underlying objectives from observed behavior. These methods rely heavily on tools such as the Moore-Penrose pseudoinverse and generalized inverses to handle redundant or underdetermined systems, where multiple solutions may exist. Challenges include singularities — configurations where solutions become unstable or non-unique — addressed through methods like Levenberg-Marquardt optimization or neural network approximations. Inverse methods are foundational across manipulation, locomotion, motion planning, and sensor calibration, enabling robots to translate high-level task goals into executable low-level commands efficiently and robustly.
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Top Cited Papers
Inverse Kinematic Solutions With Singularity Robustness for Robot Manipulator Control
Yoshihiko Nakamura, Hideo Hanafusa
Citations: 1064 • 1986
Properties of Generalized Predictive Control
D.W. Clarke, C. Mohtadi
Citations: 577 • 1987
A combined optimization method for solving the inverse kinematics problems of mechanical manipulators
L.-C.T. Wang, C.C. Chen
Citations: 483 • 1991
From human to humanoid locomotion—an inverse optimal control approach
Katja Mombaur, Anh Truong, Jean‐Paul Laumond
Citations: 428 • 2009
Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses
Arthur Albert
Citations: 395 • 1969
Some Applications of the Pseudoinverse of a Matrix
T. N. E. Greville
Citations: 349 • 1960
The Pinocchio C++ library : A fast and flexible implementation of rigid body dynamics algorithms and their analytical derivatives
Justin Carpentier, Guilhem Saurel, Gabriele Buondonno, Joseph Mirabel, Florent Lamiraux, Olivier Stasse, Nicolas Mansard
Citations: 344 • 2019
A Theory of Generalized Inverses Applied to Robotics
Keith L. Doty, Claudio Melchiorri, Claudio Bonivento
Citations: 307 • 1993
Dynamics computation of closed-link robot mechanisms with nonredundant and redundant actuators
Yoshihiko Nakamura, M. Ghodoussi
Citations: 283 • 1989
Learning inverse kinematics
A. D'Souza, Sethu Vijayakumar, Stefan Schaal
Citations: 282 • 2002
A dynamically stable single-wheeled mobile robot with inverse mouse-ball drive
Tom Lauwers, George Kantor, Ralph Hollis
Citations: 261 • 2006
Finding the Position and Orientation of a Sensor on a Robot Manipulator Using Quaternions
J.C.K. Chou, Mohamed S. Kamel
Citations: 260 • 1991
Robot Kinematics: Forward and Inverse Kinematics
Serdar Küçük, Zafer Bingül
Citations: 254 • 2006
DELTA: a simple and efficient parallel robot
François Pierrot, C. Reynaud, Alain Fournier
Citations: 252 • 1990
The Pseudoinverse of a Rectangular or Singular Matrix and Its Application to the Solution of Systems of Linear Equations
T. N. E. Greville
Citations: 250 • 1959
Decomposition of transformation matrices for robot vision
Sriram Ganapathy
Citations: 248 • 2005
Inverse dynamics control of floating base systems using orthogonal decomposition
Michael Mistry, Jonas Buchli, Stefan Schaal
Citations: 243 • 2010
Stability Analysis for Prioritized Closed-Loop Inverse Kinematic Algorithms for Redundant Robotic Systems
Gianluca Antonelli
Citations: 237 • 2009
Hamiltonian adaptive control of spacecraft
Jean-Jacques Slotine, Maria Domenica Di Benedetto
Citations: 226 • 1990
On the Continuity of the Generalized Inverse
G. W. Stewart
Citations: 225 • 1969