We propose a systematic modelling of the nonholonomic mobile manipulators built from a robotic arm mounted on a wheeled mobile platform. It extends the fundamental notions of nonholonomy, mobility and manœuvrability to the case of these hybrid holonomic/nonholonomic systems. It offers unambiguous definitions and models to the designer of kinematic control laws.

We consider the robot motion planning problem in the presence of non-integrable kinematic constraints, known as non-holonomic constraints. Car-like non-holonomic mobile robots are used for solving this problem, and several implemented planners are discussed. We claim that the randomized methods are more capable of efficiently solving many challenging, high-dimensional problems. Results with ran...

The aim of the paper is to prove that every smooth generalized vector subbundle D of a vector bundle E is the image of a smooth endomorphism Φ on the fibers of E that induces authomorphisms of fibers of D and is called here a natural anchor. Two new constructions of finite sets of smooth generators of the fibers of D are obtained, using any finite set of generators of the module Γ(E). Natural a...

In this work we present a detailed theoretical analysis for the spectral properties of Andreev bound states in multiterminal Josephson junctions by employing symmetry-constrained scattering matrix approach. We find that synthetic multidimensional space superconducting phases, crossings bands may support non-Abelian SU(2) monopoles with topological charge characterized second class Chern number....

The Brockett integrator is a 3-dimensional system with a non-holonomic constraint and the non-holonomic constraint makes the stabilization and control of the system challenging. The 3-dimensional non-holonomic integrator can be generalized in more than one way and this work looks into the time-optimal control of the generalized Brockett integrator which evolves on R × Skewm(R). The problem has ...

Cooperative motion planning is still a challenging task for robots. Recently, Value Iteration Networks (VINs) were proposed to model motion planning tasks as Neural Networks. In this work, we extend VINs to solve cooperative planning tasks under non-holonomic constraints. For this, we interconnect multiple VINs to pay respect to each other’s outputs. Policies for cooperation are generated via i...

A holonomic function is a differentiable or generalized function which satisfies a holonomic system of linear partial or ordinary differential equations with polynomial coefficients. The main purpose of this paper is to present algorithms for computing a holonomic system for the definite integral of a holonomic function with parameters over a domain defined by polynomial inequalities. If the in...