A fast, iterative solver for the Inverse Kinematics problem
摘要
. FABRIK avoids the use of rotational angles or matrices, and instead finds each joint position via locating a point on a line. Thus, it converges in few iterations, has low computational cost and produces visually realistic poses. Constraints can easily be incorporated within FABRIK and multiple chains with multiple end effectors are also supported.
1.介紹
This paper presents a new heuristic iterative method, Forward And Backward Reaching Inverse Kinematics (FABRIK), for solving the IK problem in different scenarios.
啓發式迭代算法
It can easily handle end effector orientations and support, to the best of our knowledge, all chain classes . A reliable method for incorporating constraints is also presented and utilised within FABRIK. The proposed method retains all the advantages of FABRIK, producing visually smooth movements without oscillations and discontinuities.
怎麼做到的呢？
Another important advantage of the proposed methodology is the simplicity of the algorithm, which enables easy configuration to any IK problem.
2. 背景和動機
However, the most popular numerical approach is to use the Jacobian matrix to find a linear approximation to the IK problem.
雅可比方法
However, the Newton methods are complex, difficult to implement and have high computational cost per iteration.
牛頓方法
延申
CCD算法
However, CCD has some disadvantages; it can suffer from unrealistic animation, even if manipulator constraints have been added, and often produces motion with erratic discontinuities.
【15】【16】文章看
[15] Ronan Boulic, Javier Varona, Luis Unzueta, Manuel Peinado, Angel
Suescun, Francisco Perales, Evaluation of on-line analytic and
numeric inverse kinematics approaches driven by partial vision
input, Virtual Reality 10 (1) (2006) 48–61.
[16] Richard Kulpa, Franck Multon, Fast inverse kinematics and kinetics
solver for human-like figures, in: International Conference on
Humanoid Robots, IEEE-RAS, December 2005, pp. 38–43.
蒙特卡洛方法
[17] Nicolas Courty, Elise Arnaud, Inverse kinematics using sequential
monte carlo methods, in: Proc. of the V Conf. on Articulated Motion
and Deformable Objects, AMDO’08, LNCS, vol. 5098, Mallorca, Spain,
2008, pp. 1–10.
[18] Chris Hecker, Bernd Raabe, Ryan W. Enslow, John Deweese, Jordan
Maynard, Kees van Prooijen, Real-time motion retargeting to highly
varied user-created morphologies, ACM Transactions on Graphics
(TOG) 27 (3) (2008) 1–11.
別的方法
Grochow et al. [19] presents a style-based IK method
which is based on a learned model of human poses. Given
a set of constraints, the proposed system can produce, in
real-time, the most likely pose satisfying those constraints.
三角法
The Triangulation algorithm [22] is an IK solver that
uses the cosine rule to calculate each joint angle, starting
at the root of the kinematic chain and moving outward towards the end effector.
改進的三角測量法
An improved version is given in [23] where the n-link
IK problem is reduced to a two-link problem in which each
link is rotated at most once in an attempt to reach the target position.
實時FTL方法*
Brown et al. [24] presents a real-time method which
uses a ‘Follow-the-Leader’ (FTL) non-iterative technique
which is similar to each individual iteration of FABRIK.
這個方法有待完善
3. The articulated body model
4.FABRIK: a new heuristic IK solution
一種新的啓發式算法
FABRIK algorithm
It uses the previously calculated positions of the joints to find the updates in a forward and backward iterative mode.
FABRIK involves minimising the system error by adjusting each joint angle one at a
time.
The proposed method starts from the last joint of the chain and works forwards, adjusting each joint along the way.