Research Projects NTT-MIT Research Collaboration: a partnership in the future of communication and computation

Model Reduction for Human and Animal Locomotion


Start date: 11/2001

Jovan Popovic

Satoshi Iwaki

Project summary

This research develops physical models of locomotion that are simple and low-dimensional.

Project description

MIT2001-08 image

Modeling human and animal motion is a fundamental scientific objective, with applications in computer graphics, robotics, and medicine. Graphics applications include education, training, and visualization, as well as animation in art, film, and entertainment; in robotics, robot design and the design of controllers for legged locomotion; in medicine, the diagnosis of medical problems and the design of prosthetic devices. In all these applications, a predictive physical model of locomotion is essential. The success of each application is contingent on the simplicity of this locomotion model: models of great complexity are difficult to simulate, analyze, and optimize.

This research develops a general framework for constructing simple, low-dimensional models of locomotion. Joint removal, a simple model-reduction method, is a standard computer graphics practice for reducing the dimensionality of the model by removing the joints with negligible effect. The purpose of this research is to construct more powerful techniques that not only eliminate insignificant joints, but also discover simple locomotion models that approximate the dynamics equations controllably. The research employs statistical methods such as principal component analysis to analyze empirical and simulated motion data.

Demos, movies and other examples


The motion of a walking robot with 12 degrees of freedom (right) is expressed in a reduced 6-dimensional (middle) and 1-dimensional (left) configuration space with minor artifacts. The results indicate there may be a simpler configuration space for the walking robot.

Broad Jump.avi:

A human broad jump (right in red) is expressed in a reduced configuration space (middle in yellow) with some stretching and interpenetration artifacts. The 3D trajectories of 41 markers describe the original motion. This sequence of vectors with 123 elements each is reduced into a sequence vectors with only 8 elements each. On the left in green, the same motion reduced to a configuration space obtained from a smaller data set.

The principal investigators

Presentations and posters



Proposals and progress reports


NTT Bi-Annual Progress Report, July to December 2001:

NTT Bi-Annual Progress Report, January to June 2002:

NTT Bi-Annual Progress Report, July to December 2002:

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