Faster Motion on Cartesian Paths Exploiting Robot Redundancy at the Acceleration Level

The problem of minimizing the transfer time along a given Cartesian path for redundant robots can be approached in two steps, by separating the generation of a joint path associated to the Cartesian path from the exact minimization of motion time under kinematic/dynamic bounds along the obtained parameterized joint path. In this framework, multiple suboptimal solutions can be found, depending on how redundancy is locally resolved in the joint space within the first step. We propose a solution method that works at the acceleration level, by using weighted pseudoinversion, optimizing an inertia-related criterion, and including null-space damping. Several numerical results obtained on different robot systems demonstrate consistently good behaviors and definitely faster motion times in comparison with related methods proposed in the literature. The motion time obtained with our method is reasonably close to the global time-optimal solution along same Cartesian path. Experimental results on a KUKA LWR IV are also reported, showing the tracking control performance on the executed motions

TOOL PATH PLANNING FOR MACHINING FREE-FORM SURFACES

This paper is about new iso-parametric tool path planning for machining trimmed free-form surfaces. The trimmed surface has been re-parameterized by two different parameterization techniques, namely, the partial differential equation method and the newly developed boundary interpolation method. The efficiency of the scheme has been measured in terms of path length and computational time needed for machining some typical surfaces. Conventionally, the forward-step is calculated by approximating the cutting curve with the osculating circle. The actual tolerance of the forward-step may go beyond the prescribed limit due to the circular arc approximation. In this study, the actual cutting curve has been considered to keep the tolerance in the forward-step below the prescribed value. The new algorithm has been tested on some typical surfaces and the results show a significant improvement in the surface profile in terms of tolerance of the forward-step

Symmetry Realization via a Dynamical Inverse Higgs Mechanism

The Ward identities associated with spontaneously broken symmetries can be saturated by Goldstone bosons. However, when space-time symmetries are broken, the number of Goldstone bosons necessary to non-linearly realize the symmetry can be less than the number of broken generators. The loss of Goldstones may be due to a redundancy or the generation of a gap. This phenomena is called an Inverse Higgs Mechanism (IHM). However, there are cases when a Goldstone boson associated with a broken generator does not appear in the low energy theory despite the lack of the existence of an associated IHM. In this paper we will show that in such cases the relevant broken symmetry can be realized, without the aid of an associated Goldstone, if there exists a proper set of operator constraints, which we call a Dynamical Inverse Higgs Mechanism (DIHM). We consider the spontaneous breaking of boosts, rotations and conformal transformations in the context of Fermi liquids, finding three possible paths to symmetry realization: pure Goldstones, no Goldstones and DIHM, or some mixture thereof. We show that in the two dimensional degenerate electron system the DIHM route is the only consistent way to realize spontaneously broken boosts and dilatations, while in three dimensions these symmetries could just as well be realized via the inclusion of non-derivatively coupled Goldstone bosons. We have present the action, including the leading order non-linearities, for the rotational Goldstone (angulon), and discuss the constraint associated with the possible DIHM that would need to be imposed to remove it from the spectrum. Finally we discuss the conditions under which Goldstone bosons are non-derivatively coupled, a necessary condition for the existence of a Dynamical Inverse Higgs Constraint (DIHC), generalizaing the results for Vishwanath and Wantanabe.Comment: Added a new result for the beta function for the UV theory of unitary fermion

Derived categories and rationality of conic bundles

We show that a standard conic bundle over a minimal rational surface is rational and its Jacobian splits as the direct sum of Jacobians of curves if and only if its derived category admits a semiorthogonal decomposition by exceptional objects and the derived categories of those curves. Moreover, such a decomposition gives the splitting of the intermediate Jacobian also when the surface is not minimal.Comment: New version; now also the case of cubic degeneration in P^2 is described in detail. 23 Page