709 research outputs found
Rank-preserving geometric means of positive semi-definite matrices
The generalization of the geometric mean of positive scalars to positive
definite matrices has attracted considerable attention since the seminal work
of Ando. The paper generalizes this framework of matrix means by proposing the
definition of a rank-preserving mean for two or an arbitrary number of positive
semi-definite matrices of fixed rank. The proposed mean is shown to be
geometric in that it satisfies all the expected properties of a rank-preserving
geometric mean. The work is motivated by operations on low-rank approximations
of positive definite matrices in high-dimensional spaces.Comment: To appear in Linear Algebra and its Application
On least-cost path for realistic simulation of human motion
We are interested in "human-like" automatic motion simulation with applications in ergonomics.
The apparent redundancy of the humanoid wrt its explicit tasks leads to the problem of choosing a plausible movement in the framework of redundant kinematics.
Some results have been obtained in the human motion literature for reach motion that involves the position of the hands. We discuss these results and a motion generation scheme associated. When orientation is also explicitly required, very few works are available and even the methods for analysis are not defined.
We discuss the choice for metrics adapted to the orientation, and also the problems encountered in defining a proper metric in both position and orientation. Motion capture and simulations are provided in both cases.
The main goals of this paper are: to provide a survey on human motion features at task level for both position and orientation, to propose a kinematic control scheme based on these features, to define properly the error between motion capture and automatic motion simulation
On geodesic paths and least-cost motions for human-like tasks
We are interested in ”human-like” automatic mo- tion generation. The apparent redundancy of the humanoid wrt its explicit tasks lead to the problem of choosing a plausible movement in the framework of redundant kinematics. Some results have been obtained in the human motion literature for reach motion that involves the position of the hands. We discuss these results and a motion generation scheme associated. When orientation is also explicitly required, very few works are available and even the methods for analysis are not defined. We discuss the choice for metrics adapted to the orientation, and also the problems encountered in defining a proper metric in both position and orientation. Motion capture and simulations are provided in both cases. The main goals of this paper are : - to provide a survey on human motion features at task level for both position and orientation,
- to propose a kinematic control scheme based on these features
- to define properly the error between motion capture and automatic motion simulation
- …