On the manipulability of dual cooperative robots

The definition of manipulability ellipsoids for dual robot systems is given. A suitable kineto-static formulation for dual cooperative robots is adopted which allows for a global task space description of external and internal forces, and relative velocities. The well known concepts of force and velocity manipulability ellipsoids for a single robot are formally extended and the contributions of the two single robots to the cooperative system ellipsoids are illustrated. Duality properties are discussed. A practical case study is developed

Acta Informatica manuscript No. (will be inserted by the editor) A Complete Classification of the Expressiveness of Interval Logics of Allen’s Relations The General and the Dense Cases

Abstract Interval temporal logics take time intervals, instead of time instants, as their primitive temporal entities. One of the most studied interval temporal logics is Halpern and Shoham’s modal logic of time intervals HS, which associates a modal operator with each binary relation between intervals over a linear order (the so-called Allen’s interval relations). In this paper, we compare and classify the expressiveness of all fragments of HS on the class of all linear orders and on the subclass of all dense linear orders. For each of these classes, we identify a complete set of definabilities between HS modalities, valid in that class, thus obtaining a complete classification of the family of all 4096 fragments of HS with respect to their expressiveness. We show that on the class of all linear orders there are exactly 1347 expressively different fragments of HS, while on the class of dense linear orders there are exactly 966 such expressively different fragments

Horn fragments of the Halpern-Shoham Interval Temporal Logic

We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval temporal logic depending on the type (box or diamond) of the interval modal operators, the type of the underlying linear order (discrete or dense), and the type of semantics for the interval relations (reflexive or irreflexive). For example, we show that satisfiability of Horn formulas with diamonds is undecidable for any type of linear orders and semantics. On the contrary, satisfiability of Horn formulas with boxes is tractable over both discrete and dense orders under the reflexive semantics and over dense orders under the irreflexive semantics but becomes undecidable over discrete orders under the irreflexive semantics. Satisfiability of binary Horn formulas with both boxes and diamonds is always undecidable under the irreflexive semantics

Use of Self-Selected Postures to Regulate Multi-Joint Stiffness During Unconstrained Tasks

The human motor system is highly redundant, having more kinematic degrees of freedom than necessary to complete a given task. Understanding how kinematic redundancies are utilized in different tasks remains a fundamental question in motor control. One possibility is that they can be used to tune the mechanical properties of a limb to the specific requirements of a task. For example, many tasks such as tool usage compromise arm stability along specific directions. These tasks only can be completed if the nervous system adapts the mechanical properties of the arm such that the arm, coupled to the tool, remains stable. The purpose of this study was to determine if posture selection is a critical component of endpoint stiffness regulation during unconstrained tasks.Three-dimensional (3D) estimates of endpoint stiffness were used to quantify limb mechanics. Most previous studies examining endpoint stiffness adaptation were completed in 2D using constrained postures to maintain a non-redundant mapping between joint angles and hand location. Our hypothesis was that during unconstrained conditions, subjects would select arm postures that matched endpoint stiffness to the functional requirements of the task. The hypothesis was tested during endpoint tracking tasks in which subjects interacted with unstable haptic environments, simulated using a 3D robotic manipulator. We found that arm posture had a significant effect on endpoint tracking accuracy and that subjects selected postures that improved tracking performance. For environments in which arm posture had a large effect on tracking accuracy, the self-selected postures oriented the direction of maximal endpoint stiffness towards the direction of the unstable haptic environment.These results demonstrate how changes in arm posture can have a dramatic effect on task performance and suggest that postural selection is a fundamental mechanism by which kinematic redundancies can be exploited to regulate arm stiffness in unconstrained tasks