A Robot Dynamic Target Grasping Method Based on Affine Group Improved Gaussian Resampling Particle Filter

Tracking and grasping a moving target is currently a challenging topic in the field of robotics. The current visual servo grasping method is still inadequate, as the real-time performance and robustness of target tracking both need to be improved. A target tracking method is proposed based on improved geometric particle filtering (IGPF). Following the geometric particle filtering (GPF) tracking framework, affine groups are proposed as state particles. Resampling is improved by incorporating an improved conventional Gaussian resampling algorithm. It addresses the problem of particle diversity loss and improves tracking performance. Additionally, the OTB2015 dataset and typical evaluation indicators in target tracking are adopted. Comparative experiments are performed using PF, GPF and the proposed IGPF algorithm. A dynamic target tracking and grasping method for the robot is proposed. It combines an improved Gaussian resampling particle filter algorithm based on affine groups and the positional visual servo control of the robot. Finally, the robot conducts simulation and experiments on capturing dynamic targets in the simulation environment and actual environment. It verifies the effectiveness of the method proposed in this paper.

Finite dimensional varieties on hypergroups

Let X be a hypergroup, K its compact subhypergroup and assume that (X, K) is a Gelfand pair. Connections between finite dimensional varieties and K-polynomials on X are discussed. It is shown that a K-variety on X is finite dimensional if and only if it is spanned by finitely many K-monomials. Next, finite dimensional varieties on affine groups over $${\mathbb {R}}^d$$ R d , where d is a positive integer are discussed. A complete description of those varieties using partial differential equations is given.

Ranks, Subdegrees and Suborbital graphs of the product action of Affine Groups

The action of affine groups on Galois field has been studied. For instance, studied the action of on Galois field for a power of prime. In this paper, the rank and subdegree of the direct product of affine groups over Galois field acting on the cartesian product of Galois field is determined. The application of the definition of the product action is used to achieve this. The ranks and subdegrees are used in determination of suborbital graph, the non-trivial suborbital graphs that correspond to this action have been constructed using Sims procedure and were found to have a girth of 0, 3, 4 and 6.

A note on extremely primitive affine groups

Let G be a finite primitive permutation group on a set $$\Omega $$ Ω with non-trivial point stabilizer $$G_{\alpha }$$ G α . We say that G is extremely primitive if $$G_{\alpha }$$ G α acts primitively on each of its orbits in $$\Omega {\setminus } \{\alpha \}$$ Ω \ { α } . In earlier work, Mann, Praeger, and Seress have proved that every extremely primitive group is either almost simple or of affine type and they have classified the affine groups up to the possibility of at most finitely many exceptions. More recently, the almost simple extremely primitive groups have been completely determined. If one assumes Wall’s conjecture on the number of maximal subgroups of almost simple groups, then the results of Mann et al. show that it just remains to eliminate an explicit list of affine groups in order to complete the classification of the extremely primitive groups. Mann et al. have conjectured that none of these affine candidates are extremely primitive and our main result confirms this conjecture.

Variations à la Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane

Any quantization maps linearly functions on a phase space to symmetric operators in a Hilbert space. Covariant integral quantization combines operator-valued measure with symmetry group of the phase space. Covariant means that the quantization map intertwines classical (geometric operation) and quantum (unitary transformations) symmetries. Integral means that we use all ressources of integral calculus, in order to implement the method when we apply it to singular functions, or distributions, for which the integral calculus is an essential ingredient. In this paper we emphasize the deep connection between Fourier transform and covariant integral quantization when the Weyl-Heisenberg and affine groups are involved. We show with our generalisations of the Wigner-Weyl transform that many properties of the Weyl integral quantization, commonly viewed as optimal, are actually shared by a large family of integral quantizations.

Cherlin's conjecture for almost simple groups of Lie rank 1

A permutation group G on a set Ω is said to be binary if, for every n ∈ ℕ and for every I, J ∈ Ωn, the n-tuples I and J are in the same G-orbit if and only if every pair of entries from I is in the same G-orbit to the corresponding pair from J. This notion arises from the investigation of the relational complexity of finite homogeneous structures.Cherlin has conjectured that the only finite primitive binary permutation groups are the symmetric groups Sym(n) with their natural action, the groups of prime order, and the affine groups V ⋊ O(V) where V is a vector space endowed with an anisotropic quadratic form.We prove Cherlin's conjecture, concerning binary primitive permutation groups, for those groups with socle isomorphic to PSL2(q), 2B2(q), 2G2(q) or PSU3(q). Our method uses the notion of a “strongly non-binary action”.