Inverse Kinematics Problems with Exact Hessian Matrices

Kenny Erleben and Sheldon Andrews

Inverse kinematics (IK) is a central component of systems for motion capture, character animation, motion planning, and robotics control. The field of computer graphics has developed fast stationary point solvers methods, such as the Jacobian transpose method and cyclic coordinate descent. Much work with Newton methods focus on avoiding directly computing the Hessian, and instead approximations are sought, such as in the BFGS class of solvers. This paper presents a numerical method for computing the exact Hessian of an IK system with spherical joints. It is applicable to human skeletons in computer animation applications and some, but not all, robots. Our results show that using exact Hessians can give performance advantages and higher accuracy compared to standard numerical methods used for solving IK problems. Furthermore, we provide code and supplementary details that allows researchers to plug-in exact Hessians in their own work with little effort.

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Constraint Reordering for Iterative Multi-Body Simulation with Contact

Sheldon Andrews, Kenny Erleben, Paul G. Kry, Marek Teichmann
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A Fast Linear Complementarity Problem (LCP) Solver for Separating Fluid-Solid Wall Boundary Conditions

Authors Michael Andersen, Sarah Niebe and Kenny Erleben
We address the task of computing solutions for a separating fluid-solid wall boundary condition model. We present an embarrassingly parallel, easy to implement, fluid LCP solver. We are able to use greater domain sizes than previous works have shown, due to our new solver. The solver exploits matrix-vector products as computational building blocks. We block the matrix-vector products in a way that allows us to evaluate the products, without having to assemble the full systems. Any iterative sub-solver can be used. Our work shows speedup factors ranging up to 500 for larger grid sizes.

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Rigid Body Contact Problems using Proximal Operators

Kenny Erleben

Iterative methods are popular for solving contact force problems in rigid body dynamics. They are loved for their robustness and surrounded by mystery as to whether they converge or not. We provide a mathematical foundation for iterative (PROX) schemes based on proximal operators. This is a class of iterative Jacobi and blocked Gauss–Seidel variants that theoretically proven always converge and provides a flexible plug and play framework for exploring different friction laws. We provide a portfolio of experience for choosing r-Factor strategies for such schemes and we analyze the distribution of convergence behaviors. Our results indicate the Gauss-Seidel variant is superior in terms of delivering predictable convergence behaviour and hence should be preferred over Jacobi variants. Our results also suggest that Global r -Factor strategies are better for structured stacking scenarios and can achieve absolute convergence in more cases.

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A numerical strategy for finite element modeling of frictionless asymmetric vocal fold collision

Alba Granados, Marek Krzysztof Misztal, Jonas Brunskog, Vincent Visseq and Kenny Erleben

Analysis of voice pathologies may require vocal fold models that include relevant features such as vocal fold asymmetric collision. The present study numerically addresses the problem of frictionless asymmetric collision in a self-sustained three-dimensional continuum model of the vocal folds. Theoretical background and numerical analysis of the finite-element position-based contact model are presented, along with validation. A novel contact detection mechanism capable to detect collision in asymmetric oscillations is developed. The effect of inexact contact constraint enforcement on vocal fold dynamics is examined by different variational methods for inequality constrained minimization problems, namely the Lagrange multiplier method and the penalty method. In contrast to the penalty solution, which is related to classical spring-like contact forces, numerical examples show that the parameter-independent Lagrange multiplier solution is more robust and accurate in the estimation of dynamical and mechanical features at vocal fold contact. Furthermore, special attention is paid to the temporal integration schemes in relation to the contact problem, the results suggesting an advantage of highly diffusive schemes. Finally, vocal fold contact enforcement is shown to affect asymmetric oscillations. The present model may be adapted to existing vocal fold models, which may contribute to a better understanding of the effect of the non-linear contact phenomenon on phonation.

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Teaching Inverse Kinematics

Screen casts and slides by Kenny Erleben for Teaching in Inverse Kinematics

This material was used to give students in Numerical Optimization classes a case-study to apply their own implemented methods on.

Special Issue on Physics based Animation in IEEE Computer Graphics & Animations

Guest Editors: Jan Bender, Barbara Solenthaler, and Kenny Erleben.

This special issue of IEEE Computer Graphics and Applications will provide an opportunity for researchers and practitioners in the field of physically based animation to publish their latest work.

Have a look at the call for papers.

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