A coordinate-free approach to instantaneous kinematics of two rigid objects with rolling contact and its implications for trajectory planning

This paper adopts a coordinate-free approach to investigate the kinematics of rigid bodies with rolling contact. A new equation of angular velocity of the moving body is derived in terms of the magnitude of rolling velocity and two sets of geometric invariants belonging to the respective contact curves. This new formulation can be differentiated up to any order. Furthermore, qualitative information about trajectory planning can be deduced from this equation if the characteristics of rolling objects and the motion are taken into consideration

Dynamics and Control of Whole Arm Grasps

In this paper we consider the dynamics and control of whole arm grasping systems. We develop a control scheme that employs a minimal set of inputs to control the trajectory of the system while using the surplus inputs to control the interaction forces in order to maintain the unilateral constraints at both rolling and sliding contacts. Since the number of surplus inputs is less than the number of output force variables, we propose a controller that controls the critical contact force components. We emphasize the dynamic models and algorithms for computing contact forces, which are crucial to the development of the control algorithms. Finally, we show how compliant contact models and a previously developed integrated simulation approach [14] are used to overcome the difficulties with uniqueness and existence of solutions. A planar whole arm manipulation system is used as an example to illustrate the basic ideas

A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects with Point Contact

This paper investigates the kinematics of spin-rolling motion of rigid objects. This paper does not consider slipping but applies a Darboux frame to develop kinematics of spin-rolling motion, which occurs in a nonholonomic system. A new formulation of spin-rolling motion of the moving object is derived in terms of contravariant vectors, rolling velocity, and geometric invariants, including normal curvature, geodesic curvature, and geodesic torsion of the respective contact curve. The equation is represented with geometric invariants. It can be readily generalized to suit both arbitrary parametric surface and contact trajectory and can be differentiated to any order. Effect of the relative curvatures and torsion on spin-rolling kinematics is explicitly presented. The translation velocity of an arbitrary point on the moving object is also derived based on the Darboux frame

The Instantaneous Kinematics of Manipulation

Dextrous manipulation planning is a problem of paramount importance in the study of multifingered robotic hands. In this paper, we show in general, that all system variables #the finger joint, object,and contact velocities# needtobe included in the differential kinematic equation used for manipulation planning, even if the manipulation task is only specified in terms of the goal configuration of the object or the contacts only. The dextrous manipulation kinematics that relates the finger joint movements to object and contact movements is derived. With the results of inverse and forward instantaneous kinematics, we precisely formulate the problem of dextrous manipulation and cast it in a form suitable for integrating the relevant theory of contact kinematics, nonholonomic motion planning, and grasp stability to develop a general technique for dextrous manipulation planning with multifingered hands