The set of rigid body motions forms the Lie group SE(3), the special Euclidean group in three dimensions. In this paper we investigate Riemannian metrics and affine connections on SE(3) that are suited for kinematic analysis and robot trajectory planning. In the first part of the paper, we study metrics whose geodesics are screw motions. We prove that no Riemannian metric can have such geodesics and we show that metrics whose geodesics are screw motions form a two-parameter family of semi-Riemannian metrics. In the second part of the paper we investigate affine connections which through the covariant derivative give the expression for the acceleration of a rigid body that agrees with the expression used in kinematics. We prove that there is...
This paper develops a method for generating smooth trajectories for a moving rigid body with specifi...
International audienceThe Euler-Poinsot rigid body motion is a standard mechanical system and is a m...
Abstract. The Euler-Poinsot rigid body motion is a standard mechanical system and it is a model for ...
This paper addresses the problem of generating smooth trajectories between an initial and final posi...
Abstract: Previous approaches to trajectory generation for rigid bodies have been either based on th...
There are various useful metrics for finding the distance between two points in Euclidean space. Met...
Previous approaches to trajectory generation for rigid bodies have been either based on the so-calle...
Abstract We present two methods for generating trajectories and motion interpolants that minimize en...
The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure ca...
International audienceThe Euler-Poinsot rigid body motion is a standard mechanical system and is the...
AbstractA systematic theoretical approach is presented, in an effort to provide a complete and illum...
The objective of this paper is to show that the group (3) with an imposed Lie-Poisson structure can ...
In this paper, we present a novel differential geometric characterization of two- and three-degree-o...
International audienceThe book explores the use of Lie groups in the kinematics and dynamics of rigi...
Motivated by the motion planning problem for oriented vehicles travelling in a 3-Dimensional space; ...
This paper develops a method for generating smooth trajectories for a moving rigid body with specifi...
International audienceThe Euler-Poinsot rigid body motion is a standard mechanical system and is a m...
Abstract. The Euler-Poinsot rigid body motion is a standard mechanical system and it is a model for ...
This paper addresses the problem of generating smooth trajectories between an initial and final posi...
Abstract: Previous approaches to trajectory generation for rigid bodies have been either based on th...
There are various useful metrics for finding the distance between two points in Euclidean space. Met...
Previous approaches to trajectory generation for rigid bodies have been either based on the so-calle...
Abstract We present two methods for generating trajectories and motion interpolants that minimize en...
The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure ca...
International audienceThe Euler-Poinsot rigid body motion is a standard mechanical system and is the...
AbstractA systematic theoretical approach is presented, in an effort to provide a complete and illum...
The objective of this paper is to show that the group (3) with an imposed Lie-Poisson structure can ...
In this paper, we present a novel differential geometric characterization of two- and three-degree-o...
International audienceThe book explores the use of Lie groups in the kinematics and dynamics of rigi...
Motivated by the motion planning problem for oriented vehicles travelling in a 3-Dimensional space; ...
This paper develops a method for generating smooth trajectories for a moving rigid body with specifi...
International audienceThe Euler-Poinsot rigid body motion is a standard mechanical system and is a m...
Abstract. The Euler-Poinsot rigid body motion is a standard mechanical system and it is a model for ...