Modeling Ranges of Limb Motion for Real-Time Inverse Kinematics

彬彬

1 Introduction

Accurate modeling of range of joint motions (joint ROM) is a fundamental

problem of articulated figure animation. The joint ROM

should be carefully designed to avoid an impossible pose, requiring

tedious work because of the complexity and extensiveness of

human joints, especially shoulders and hips. Although many joint

ROM models have been proposed in the field of biomechanics and

graphics, they still have two issues. The first is that a ROMof spherical

joint is defined in a spherical domain. A traditional approach

respectively defines a range of yaw, pitch and roll of joint rotation,

which often causes an unexpected artifact due to the nonlinearity

of the Euler angles. Another method uses a sophisticated parameterization

of 3D rotation [Herda et al. 2005] or a 3D geometrical

model to represent a boundary of joint orientation. These methods,

however, require extra computational cost. The second issue

is that a joint ROM is separately defined for each joint. Previous

models often neglect a strong dependency between adjacent joints;

a shoulder’s joint ROM varies depending on elbow angle for example.

A complex mechanism is therefore required to simulate such

dependency [Herda et al. 2005].

We propose a model to represent ranges of limb motion (limb

ROM). The key idea of limb ROM is to define a space of possible

pose of a limb 1, instead of defining ROM of each joint. A

limb ROM is composed of a valid 3D workspace of the wrist and a

range of swivel angle at arbitrary location in the workspace; “swivel

angle” [Tolani et al. 2000] denotes a rotation angle of the elbow

around an axis with which shoulder and wrist are connected. Our

method has three contributions: 1) our method successfully simulates

a dependency between ROM of a joint and rotation of its

neighbor because a limb ROM model limits movements of multiple

joints simultaneously. 2) A compact limb ROM model is automatically

estimated from a sparse collection of example poses based on

an empirical assumption. 3) Our limb ROM model is well suited

to a real-time inverse kinematics (IK) technique [Tolani et al. 2000]

because our model consists of wrist position and swivel angle, both

of which are the control inputs of the IK solver. Prior to***cuting

the IK solver, an impossible limb pose is efficiently avoided by relocating

the wrist position into the valid workspace and adjusting

swivel angle while fixing the wrist position.

2 Technical approach

2.1 Model cons***ction

A limb ROM model represents a valid range of directions from

shoulder to wrist, and range of swivel angle and distance from

shoulder to wrist along a direction as shown in Figure (a). This

model is cons***cted from a collection of example poses using a

non-parametric regression technique. An example data of the nonparametric

model is composed of wrist position and swivel angle

in a shoulder’s local coordinate system. As a collection of examples

is very sparse in practice, missing data is interpolated from the

measurements. To improve the interpolation accuracy, the dimensionality

of the interpolation problem is reduced on an empirical

assumption: a range of swivel angle changes depending on only

direction from shoulder to wrist without being constrained by a dis-

∗e-mail: tmki@acm.org

1In this paper we explain about only upper limbs.

Swivel

angle

Distance between

shoulder and wrist

Direction from

shoulder to wrist

a) Limb ROM model b) Workspace of right wrist c) Workspace of left ankle

(These bumpy surfaces are caused by simple marching cubes)

tance to wrist. Based on this assumption, example data is mapped

onto a surface of unit sphere on which a direction from shoulder to

wrist is represented by a point. The point on the surface stores a

distance to wrist and a swivel angle of the example. Missing data is

then interpolated using uniform sampling by following four steps:

Sampling points are first distributed uniformly on the spherical surface.

Secondly, minimum and maximum values of swivel angle and

those of distance to wrist are respectively searched within a certain

radius around each sampling point. Thirdly, the searched values are

stored in each sampling point, and points having no value are removed.

Finally, a valid region on the spherical surface is defined by

detecting a closed outer hull which includes all available sampling

points.

2.2 Validation of limb poses

A limb pose is validated using our model in two steps: A direction

to wrist is first validated by checking whether it is mapped within

the valid region on the spherical surface. A distance to wrist and

a swivel angle are then checked whether they are within the range

that is calculated using a k-nearest neighbor interpolation of the

samples.

Our method provides a straightforward solution to synthesize a

possible pose using an IK solver designed for human limbs [Tolani

et al. 2000]. Our model enables a constant-time validation and correction

of wrist position and swivel angle prior to an***cution of

the IK solver, whereas the previous method incorporates a joint

ROM with an optimization framework.

3 Discussion

We created limb ROM models of arms and legs using motion capture

data of a loose-limbed actress. Figure (b) and (c) show an

approximated workspace of right wrist and left ankle, respectively.

These results demonstrate reasonable accuracy of our model. One

major limitation is that our model still requires a large amount

of memory which increases according to the number of sampling

points. Our future work includes an investigation of a more compact,

parametric limb ROM model, which would be accomplished

by using a polynomial approximation technique.

References

Herda, L., Urtasun, R., and Fua, P. 2005. Hierarchical implicit

surface joint limits for human body tracking. Computer Vision

and Image Understanding 99, 2, 189–209.

Tolani, D., Goswami, A., and Badler, N. I. 2000. Real-time inverse

kinematics techniques for anthropomorphic limbs. Graphical

Models 62, 5, 353–388.

彬彬

菜刀吻电线

年末感慨实在是多，三言两语道不完！最让我揪心的还是你，行李备好了没？火车票买了没？别感动，我只是问问，自己的事情还是要自己做滴！哈哈。

奇

赞一个，哈哈

tc

不会吧，太恐怖了

奇

我就看看，我不说话

菜刀吻电线

很有心,部分已收录自用,谢谢

C.R.CAN

跑着去顶朋友滴铁

奇

我看看就走，你们聊！

tc

你们都躲开，我来顶