arXiv subjects

Daniel Condurache

Publications and source records attributed to Daniel Condurache.

5 recordsLinked to original sources

arXiv2026

Lie-Algebraic Bell Recurrences for Arbitrary-Order Twist Jets and Parallel-Mechanism Closure

This paper develops an arbitrary-order kinematic construction that links serial propagation, parallel-mechanism closure, and rigid-platform point fields within one dual screw framework. A cylindrical joint is retained as one native physical block, with revolute and prismatic joints obtained as special cases. For each fixed joint axis, ordinary Bell polynomials organize the derivatives of the exponential factor; across a chain, the noncommuting factors remain in their physical order. Initial-frame prefix and terminal-resolved covariant formulas then produce equivalent representations of the serial twist jet. For a parallel mechanism, repeated Leibniz differentiation, with joint-level derivatives organized by Bell polynomials, yields an arbitrary-order triangular active-passive closure recurrence: the same passive Jacobian is solved at every derivative order at a regular configuration, while the right-hand side contains only prescribed active data and lower-order jets. The resulting platform twist jet is mapped exactly to the point-independent affine invariants of the velocity, acceleration, jerk, and snap fields. The validation is deliberately complementary: a generic 3C chain with noncoplanar axes and nonzero rotational and translational cylindrical coordinates tests ordered serial propagation, an RR+RRR spherical wrist tests active-passive closure, and a Hunt-type 6-RUS mechanism with six active revolute joints tests an independently reconstructed platform jet and its affine fields. Independent differentiation of the rigid motion, evaluation of the affine fields, and the differentiated branch closures all agree through fourth order with residuals below $10^{-12}$ in the corresponding SI units. The formulation is purely kinematic and applies at configurations where the selected active-passive partition is regular.

cs.RO↗

arXiv2026

New Symbolic Procedures in the Study of Dynamical Systems

The thesis develops symbolic representations of dynamical systems in finite-dimensional commutative real algebras. The algebraic framework (orthogonal idempotents, zero divisors, and the structure of finite-order algebras) supports algebra-valued Fourier and Laplace transforms and Walsh-function-based system identification. The methods yield exact, coordinate-free vectorial solutions for motion in non-inertial reference frames, including a generalized Larmor theorem, the Foucault pendulum, motion in central positional-force fields, and the two-body problem in arbitrarily rotating reference frames. This English edition is an audited LaTeX reconstruction of the 1995 original, with an editorial note documenting provenance.

math.DS↗

arXiv2026

Dual Park-Ravani Interpolation of Rigid Motions: Acceleration-Field Continuity and Holonomic Hermite Repair

The Park-Ravani construction generates a twice continuously differentiable, frame-invariant spline on SO(3) by exponentiating cubic canonical-coordinate polynomials. We show that the construction transfers, without changing form, to the group of orthogonal dual tensors, a representation of rigid displacements. The transferred recurrence is stated compactly through the dual extension of the right Jacobian of the exponential map and its first Fr\'echet derivative. This yields interpolation of prescribed rigid poses and continuity of the body dual twist and its first derivative. Using the higher-order rigid-body kinematics of dual spatial twists, we then prove that the resulting curve has a continuous physical acceleration field, not merely a continuous quantity obtained by formally differentiating the dual part of a twist. We also distinguish algebraic dual transfer from temporal differential prolongation: their simultaneous first-order use takes place in a hyper-dual algebra, and interpolation of arbitrary prolonged nodal data need not be holonomic. A noncommuting three-pose example verifies the recurrence, all knot continuity statements, and dimensional covariance under a change from meters to millimeters. We define and analyze the first-order holonomy defect of a generic hyper-dual interpolant, exhibit an exact counterexample, and remove the defect by cubic or quintic Hermite interpolation in dual logarithmic coordinates.

cs.RO↗

arXiv2026

Arbitrary-Order Hermite Interpolation of Rigid-Motion Jets via Hyper-Multidual Quaternions

We study bilateral interpolation of finite-order rigid-motion jets represented by unit dual quaternions. An order-$n$ multidual (MD) algebra is the truncated polynomial algebra $\mathbb{R}[\varepsilon]/(\varepsilon^{n+1})$; hyper-multidual (HMD) quaternions are dual quaternions with coefficients in this algebra. Temporal HMD transforms encode a pose and its derivatives, whereas a generic HMD curve need not be the temporal jet of its pose projection; we call this requirement holonomicity. We show that a temporal transform and its relative descriptor are unitary and derive recursive coefficient constraints, together with a local realizability converse in an admissible logarithm chart. We then extend screw linear interpolation (ScLERP) algebraically to unit HMD quaternions. Although it matches complete endpoint transforms, direct HMD--ScLERP is generically non-holonomic for arbitrary endpoint jets. We give a coefficient criterion and explicit endpoint and first-order interior contact defects. A holonomic alternative is obtained by mapping endpoint transforms to logarithmic dual-quaternion coordinates, applying the degree-$(2n+1)$ Hermite polynomial that matches derivatives through order $n$, and lifting by the exponential. HMD arithmetic also recovers higher-order rigid-motion acceleration fields without explicit differentiation of $\mathrm{dexp}$. Rotation and full $\mathrm{SE}(3)$ tests through second order, with an additional third-order polynomial check, reproduce the stated defects and endpoint jets.

cs.RO↗

arXiv2025

An analysis of higher-order kinematics formalisms for an innovative surgical parallel robot

The paper presents a novel modular hybrid parallel robot for pancreatic surgery and its higher-order kinematics derived based on various formalisms. The classical vector, homogeneous transformation matrices and dual quaternion approaches are studied for the kinematic functions using both classical differentiation and multidual algebra. The algorithms for inverse kinematics for all three studied formalisms are presented for both differentiation and multidual algebra approaches. Furthermore, these algorithms are compared based on numerical stability, execution times and number and type of mathematical functions and operators contained in each algorithm. A statistical analysis shows that there is significant improvement in execution time for the algorithms implemented using multidual algebra, while the numerical stability is appropriate for all algorithms derived based on differentiation and multidual algebra. While the implementation of the kinematic algorithms using multidual algebra shows positive results when benchmarked on a standard PC, further work is required to evaluate the multidual algorithms on hardware/software used for the modular parallel robot command and control.

cs.RO↗