Inverse kinematics by numerical and analytical cyclic coordinate descent

Robotica ◽  
2010 ◽  
Vol 29 (4) ◽  
pp. 619-626 ◽  
Author(s):  
Anders Lau Olsen ◽  
Henrik Gordon Petersen
Keyword(s):  
Numerical Method ◽  
Inverse Kinematics ◽  
Coordinate Descent ◽  
Cost Functions ◽  
Serial Chain ◽  
Prismatic Joints ◽  
Cyclic Coordinate Descent

SUMMARYCyclic coordinate descent (CCD) inverse kinematics methods are traditionally derived only for manipulators with revolute and prismatic joints. We propose a new numerical CCD method for any differentiable type of joint and demonstrate its use for serial-chain manipulators with coupled joints. At the same time more general and simpler to derive, the method performs as well in experiments as the existing analytical CCD methods and is more robust with respect to parameter settings. Moreover, the numerical method can be applied to a wider range of cost functions.

scholarly journals A General Approach Based on Newton’s Method and Cyclic Coordinate Descent Method for Solving the Inverse Kinematics

2019 ◽  
Vol 9 (24) ◽  
pp. 5461
Author(s):  
Yuhan Chen ◽  
Xiao Luo ◽  
Baoling Han ◽  
Yan Jia ◽  
Guanhao Liang ◽  
...  
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Inverse Kinematics ◽  
Optimization Problem ◽  
Robot Manipulators ◽  
Descent Method ◽  
Coordinate Descent ◽  
Coordinate Descent Method ◽  
Prismatic Joints ◽  
Cyclic Coordinate Descent

The inverse kinematics of robot manipulators is a crucial problem with respect to automatically controlling robots. In this work, a Newton-improved cyclic coordinate descent (NICCD) method is proposed, which is suitable for robots with revolute or prismatic joints with degrees of freedom of any arbitrary number. Firstly, the inverse kinematics problem is transformed into the objective function optimization problem, which is based on the least-squares form of the angle error and the position error expressed by the product-of-exponentials formula. Thereafter, the optimization problem is solved by combining Newton’s method with the improved cyclic coordinate descent (ICCD) method. The difference between the proposed ICCD method and the traditional cyclic coordinate descent method is that consecutive prismatic joints and consecutive parallel revolute joints are treated as a whole in the former for the purposes of optimization. The ICCD algorithm has a convenient iterative formula for these two cases. In order to illustrate the performance of the NICCD method, its simulation results are compared with the well-known Newton–Raphson method using six different robot manipulators. The results suggest that, overall, the NICCD method is effective, accurate, robust, and generalizable. Moreover, it has advantages for the inverse kinematics calculations of continuous trajectories.

Inverse Kinematics for Planar Parallel Manipulators

1997 ◽  
Author(s):  
Robert L. Williams ◽  
Brett H. Shelley
Keyword(s):  
Inverse Kinematics ◽  
Broad Class ◽  
Parallel Manipulators ◽  
End Effector ◽  
Serial Chain ◽  
Prismatic Joints ◽  
Inverse Solutions ◽  
Three Degree Of Freedom ◽  
Serial Chains ◽  
Planar Parallel Manipulators

Abstract This paper presents algebraic inverse position and velocity kinematics solutions for a broad class of three degree-of-freedom planar in-parallel-actuated manipulators. Given an end-effector pose and rate, all active and passive joint values and rates are calculated independently for each serial chain connecting the ground link to the end-effector link. The solutions are independent of joint actuation. Seven serial chains consisting of revolute and prismatic joints are identified and their inverse solutions presented. To reduce computations, inverse Jacobian matrices for overall manipulators are derived to give only actuated joint rates. This matrix yields conditions for invalid actuation schemes. Simulation examples are given.

Posture Prediction Versus Inverse Kinematics

2001 ◽  
Author(s):  
Karim Abdel-Malek ◽  
Wei Yu ◽  
Zan Mi ◽  
E. Tanbour ◽  
M. Jaber
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Human Performance ◽  
Inverse Kinematic ◽  
Cost Functions ◽  
Optimization Approach ◽  
Final Position ◽  
Serial Robot ◽  
Posture Prediction

Abstract Inverse kinematics is concerned with the determination of joint variables of a manipulator given its final position or final position and orientation. Posture prediction also refers to the same problem but is typically associated with models of the human limbs, in particular for postures assumed by the torso and upper extremities. There has been numerous works pertaining to the determination and enumeration of inverse kinematic solutions for serial robot manipulators. Part of these works have also been directly extended to the determination of postures for humans, but have rarely addressed the choice of solutions undertaken by humans, but have focused on purely kinematic solutions. In this paper, we present a theoretical framework that is based on cost functions as human performance measures, subsequently predicting postures based on optimizing one or more of such cost functions. This paper seeks to answer two questions: (1) Is a given point reachable (2) If the point is reachable, we shall predict a realistic posture. We believe that the human brain assumes different postures driven by the task to be executed and not only on geometry. Furthermore, because of our optimization approach to the inverse kinematics problem, models with large number of degrees of freedom are addressed. The method is illustrated using several examples.

A Fuzzy Algorithm to Study the Inverse Kinematics Problem of a Serial Manipulator

2015 ◽  
Vol 783 ◽  
pp. 77-82
Author(s):  
Francesco Aggogeri ◽  
Nicola Pellegrini ◽  
Riccardo Adamini
Keyword(s):  
Inverse Kinematics ◽  
Linear Equations ◽  
Rigid Bodies ◽  
Robust Performance ◽  
Serial Chain ◽  
Interactive Algorithm ◽  
Inverse Kinematics Problem ◽  
Transcendental Functions ◽  
Computationally Expensive ◽  
Non Linear Equations

This paper presents a fuzzy logic to solve the inverse kinematics problem. As the complexity of robot increases, obtaining the inverse kinematics solution requires the solution of non linear equations having transcendental functions are difficult and computationally expensive. This study focuses on a serial manipulator modelled as a serial chain of rigid bodies connected by joints. A new fuzzy interactive algorithm is developed and the effectiveness is compared with other methods on a SCARA robot. It converge in all the developed simulations showing a robust performance.

scholarly journals Random permutations fix a worst case for cyclic coordinate descent

2018 ◽  
Vol 39 (3) ◽  
pp. 1246-1275 ◽  
Author(s):  
Ching-pei Lee ◽  
Stephen J Wright
Keyword(s):  
Nonlinear Function ◽  
Quadratic Function ◽  
Random Permutation ◽  
Coordinate Descent ◽  
Random Permutations ◽  
Worst Case ◽  
Computational Performance ◽  
Technical Report ◽  
Cyclic Coordinate Descent ◽  
Better Than

Abstract Variants of the coordinate descent approach for minimizing a nonlinear function are distinguished in part by the order in which coordinates are considered for relaxation. Three common orderings are cyclic (CCD), in which we cycle through the components of $x$ in order; randomized (RCD), in which the component to update is selected randomly and independently at each iteration; and random-permutations cyclic (RPCD), which differs from CCD only in that a random permutation is applied to the variables at the start of each cycle. Known convergence guarantees are weaker for CCD and RPCD than for RCD, though in most practical cases, computational performance is similar among all these variants. There is a certain type of quadratic function for which CCD is significantly slower than for RCD; a recent paper by Sun & Ye (2016, Worst-case complexity of cyclic coordinate descent: $O(n^2)$ gap with randomized version. Technical Report. Stanford, CA: Department of Management Science and Engineering, Stanford University. arXiv:1604.07130) has explored the poor behavior of CCD on functions of this type. The RPCD approach performs well on these functions, even better than RCD in a certain regime. This paper explains the good behavior of RPCD with a tight analysis.

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