Natural-CCD算法

Abstract

Therefore, they exhibit an infinite number of solutions for the inverse kinematics problem, and to choose the best one can be a great challenge. A new algorithm based on the cyclic coordinate descent (CCD) and named as natural-CCD is proposed to solve this issue.
The proposed algorithm is very simple, precise, and computationally efficient. It works for robots either in two or three spatial dimensions and handles a large amount of degrees-of-freedom. Because of this, it is aimed to break down barriers between discrete hyper-redundant and continuum soft robots.
無窮多的解法裏挑取最好的。
打破冗餘機器人和軟體機器人之間的障礙（隔閡）。

Introduction

背景
Hyper-redundant manipulators or snake-arm robots rely on a number of DOFs higher than the minimum required to perform a particular task.
目的

In recent years, exhaustive methods have been replaced by optimization algorithms because the computational cost of the first ones grows faster versus the number of joints. Thus,the most recent optimization methods studied are PseudoInverse Jacobian,Pattern Search, Global Search,Genetic Algorithms,Simulated Annealing, Artificial Neural Networks, and Particle-Swarm Optimization.The common limitation of these methods is that none of them provides a commitment to the desired criteria for solving the inverse kinematics problem: low computational times for a large number of DOF, high precision, and a good-quality solution.

介紹CCD算法

The natural-CCD and selective coordinate descent algorithms

CCD算法的侷限：
1.kinematic singularities are not managed.運動奇點沒有得到管理
2. Second, it does not propose any kinematic constraint to avoid self-collisions. 沒有任何關節限制避免自碰撞
3. Third, since the h angle can take high values ， the movements of each joint can be abrupt, originating convoluted robot configurations.
修正方法
1.奇點主要是兩個向量平行。 In those special cases, the use of a random direction ~d
(Eq. 4) and angle h (Eq. 3) is recommended to avoid the initial singularity.
2.To solve the second limitation, the existence of selfcollisions, a maximum-angle upper bound is proposed.

？？？
3.k-factor
NCCD

SCD

先選擇要轉動的關節，以滿足各種要求。