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Biomimetic Motion Generation

The biomimetic motion generation project draws together research from Computer Animation, Human Motor Production, Robotics and Dynamics. The synthesis of realistic humanoid motion is investigated by studying theories about how the central nervous system plans movement, how the biomechanics of the human musculo-skeletal system and neural control interact in the physical environment, how muscle and joint forces may be calculated to bring about movements, and how these movements may be simulated or produced by humanoid robots.

The project was conducted in collaboration with the Human Information Science Laboratories at ATR in Japan, and Dr Frank Pollick of the Psychology Department, University of Glasgow .

A number of synthetic motion production models were developed, including minimisation of Cartesian end-effector (hand) derivatives, minimisation of joint angle derivatives, equilibrium point control, minimum jerk virtual trajectories, minimum torque, minimum torque change, and computationally optimised posture based torque minimizations.

Motions have been realised by computer generated synthetic humanoids, and by a humanoid robot as may be seen the the following animations. MetaCreation's Poser software was used to render the synthetic humanoid.

A novel mathematical technique was developed for a class of motions generated according to multidimensional splines with minimum Nth derivative. This includes the minimisation of end-point velocity, acceleration, jerk and snap and the minimisation of joint angle velocity, acceleration, jerk and snap. A single technique capable of handling arbitrary dimensional splines was used to minimise the Nth derivative.

It is possible to prove using the Calculus of Variations, that a 2N-1 order polynomial is sufficient to minimise the Nth derivative of a trajectory under some end-point conditions such as end-point positions, velocities or higher order derivatives. The basic approach for finding the coefficients of such a polynomial was to express the end-point derivatives in terms of the spline control points using a linear system.

Expressing the coefficients in this way allows the coefficients of adjacent spline segments to be related. The Nth derivative of a given spline segment may be determined analytically.

The polynomial coefficients necessary to satisfy the minimum Nth derivative condition may now be found by formulating these equations as a linear system. The constraints (end-point positions, etc. ) may be inserted into this system by replacing the corresponding row of the matrix with an identity, and setting the target position in the constraint vector.

This solves the problem of minimising the N-th derivative for a single polynomial spline segment. In order to solve the problem for a multi-segment spline, these linear programmes may be combined into a single compound matrix. The matrices for each dimension of the spline may be formulated and solved separately.

One problem remains. It was assumed that the passage times of the spline's knots was fixed, but this may not be the case. The optimum knot passage times may be found using gradient descent to reduce the cost of successive solutions until a minimum is found. This process is quick because the matrices involved may be solved quickly.

A number of psychovisual experiments were carried out using the motions derived with synthetic models. A set of eight motions was designed and performed with each of the synthetic models using both the CG humanoid and the humanoid robot. The motions included short and long, straight and curved, slow and fast, cyclic and non-cyclic examples. The experiments included subjects' assessing the naturalness of motions, and the similarity between different motion generation algorithms performing the same motion specification.

The results of the experiments revealed some interesting facts. For example, it was not necessary to consider derivative minimisation above the second or third degree (acceleration or jerk) in order to generate natural appearing motions. Also, the computationally demanding minimisation of torque or torque change was not necessary to generative natural appearing motion.

The results are summarised below. Please click on an image to enlarge it. The left column corresponds to the motions displayed using the computer generated synthetic humanoid, and the right column corresponds to motions displayed using videos of the humanoid robot. The first row shows the results of the naturalness evaluation experiment, and the second shows the results of the similarity experiment where the similarities between models are expressed as Cartesian distance in a dimensionally-reduced image.

 

Further information relating to this project (such as experimental design, analysis, computational statistics and conclusions) may be found in the following sources:

Last Update 10th March 2006
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