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Robokcs research has made extensive use of techniques based on me Moore-Penrose inverse, or generalized inverse, of matri als. Recently it has been pointed out how noninvariant results may, in general, be obtained by applying these techniques to other areas of robotics, namely hybrid control and inverse ve locity kinematics. Unfortunately, the problems are not restricted to just these particular areas in robotics but are connected with misleading definitions of the metric properties of the six- dimensional wrench and twist vector spaces used in robotics. The current definitions lead to inconsistent results (i.e., results that are not invariant with respect to changes in the reference frame andlor changes in the dimensional units used to express the problem. As a matter of fact, given a linear systemu = Ax, where the matrix A may be singular, the Moore-Penrose theory of generalized inverses may be properly and directly applied only when the vector space U of vectoru and the vector space X of vector x are inner product spaces. Arbitrary assignment of Euclidean inner products to the space U and X when the vectorsu andx have elements with different physical units can lead to inconsistent and noninvariant results. In this article the problem of inconsistent, noninvariant solutionsX s tou = Ax in robotics is briefly reviewed and a general theory for com puting consistent, gauge-invariant solutions to nonhomogeneous systems of the formu = Ax is developed. In addition, the dual relationship between rigid-body kinematics and statics is de fined formally as a particular, linear algebraic system whose solution system is also a dual system. Examples illustrate the theory.

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Physical human-robot interaction requires the development of safe and dependable robots. This involves the mechanical design of lightweight and compliant manipulators and the definition of motion control laws that allow to combine compliant behavior in reaction to possible collisions, while preserving accuracy and performance of rigid robots in free space. In this framework, great attention has been given to robots manipulators with relevant elasticity at the joints/transmissions. While the modeling and control of robots with elastic joints of finite but constant stiffness is a well-established topic, few results are available for the case of robot structures with variable joint stiffness -mostly limited to the 1-dof case. We present here a basic control study for a general class of multi-dof manipulators with variable joint stiffness, taking into account different possible modalities for changing the joint stiffness on the fly by an additional set of commands. It is shown that nonlinear control laws, based either on static or dynamic state feedback, are able to exactly linearize the closedloop equations and allow to simultaneously impose a desired behavior to the robot motion and to the joint stiffness in an decoupled way. Illustrative simulations results are presented. ©2008 IEEE

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In this paper, the tendon-sheath driving system for a robotic hand is presented and its force transmission characteristics are analyzed. The use of tendon-based transmission permits to reduce the size and the complexity of the actuation chain in many mechanical devices. A simple static model that describes the tendon-sheath driving system is presented, and its behavior is compared both with simulative results, obtained with a lumped parameters model of the tendon, and with experimental results. Different static and dynamic friction models are used in the simulations and the related results are compared to highlight some phenomena that are not visible from the static model of the tendon. A simple force control algorithm with feedforward friction compensation based on the static friction model is also presented.

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Abstract-In this paper, the problem of online estimation of the mechanical impedance during the contact of a robotic system with an unknown environment is considered. This problem is of great interest when controlling a robot in an unstructured and unknown environment, such as in telemanipulation tasks, since it can be easily shown that the exploitation of the knowledge of the mechanical properties of the environment can greatly improve the performance of the robotic system. In particular, a single-point contact is considered, and the (nonlinear) Hunt-Crossley model is taken into account, instead of the classical (linear) Kelvin-Voigt model. Indeed, the former achieves a better physical consistency and also allows describing the behavior of soft materials. Finally, the online estimation algorithm is described and experimental results are presented and discussed.