Certain evolutionary trends from analytical methods to a combination of analytical, computational and measurement methods are addressed in this paper. Implications of these trends in modeling, stability, actuation and control of multi rigid body systems are explored here. This approach makes use of recent technical developments in two areas. Electronic hardware is currently available for comput...

An open research question is how to define a useful metric on SE(n) with respect to (1) the choice of coordinate frames and (2) the units used to measure linear and angular distances. We present two techniques for approximating elements of the special Euclidean group SE(n) with elements of the special orthogonal group SO(n+1). These techniques are based on the singular value and polar decomposi...

In this paper, we consider the problem of obtaining optimal controllers which minimize a quadratic cost function for the rotational motion of a rigid body. We are not concerned with the attitude of the body and consider only the evolution of the angular velocity as described by Euler's equations. We obtain conditions which guarantee the existence of linear stabilizing optimal and suboptimal con...

This paper tackles the problem of computing smooth, optimal trajectories on the Euclidean group of motions SE(3). The problem is formulated as an optimal control problem where the cost function to be minimized is equal to the integral of the classical curvature squared. This problem is analogous to the elastic problem from differential geometry and thus the resulting rigid body motions will tra...

Physics-based multibody simulations have a wide range of applications. In order to be capable of analyzing complex problem formulations, e.g. the motion of the human skeleton, joints are a necessary requirement for multibody simulation frameworks. The major focus of this thesis lies on the development and implementation of a general scheme to integrate joint motion constraints into the pe frame...

We address stable synchronization of a network of rotating and translating rigid bodies in three-dimensional space. Motivated by applications that require coordinated spinning spacecraft or diving underwater vehicles, we prove control laws that stably couple and coordinate the dynamics of multiple rigid bodies. We design decentralized, energy shaping control laws for each individual rigid body ...

recently a method has been developed to decouple the equations of motion for multi-rigid body systems. in this paper, the method is first studied, then the equations of motion for a planar two degree-of-freedom robot with flexible joints are carried out using lagaranges equations and kanes equation with congruency transformations. finally, the results obtained from both methods are throroughly ...

The interactive manipulation of rigid objects in virtual reality environments requires an object behaviour which is at least physically plausible to be useful for applications like interactive assembly simulation or virtual training. Physically plausible behaviour implies that collisions between simulated solid objects are taken into account, and that the motion of objects with obstacle contact...

This paper investigates methods for computing a smooth motion that interpolates a given set of positions and orientations of a rigid body. To make the interpolation independent of the representation of the motion, we use the coordinate-free framework of differential geometry. Inertial and body-fixed reference frames must be chosen to describe the position and orientation of the rigid body. We s...