arXiv subjects

Alessandro De Luca

Publications and source records attributed to Alessandro De Luca.

At least 19 recordsLinked to original sources

arXiv2026

Assembling Solar Panels by Dual Robot Arms Towards Full Autonomous Lunar Base Construction

Since the successful Apollo program, humanity is once again aiming to return to the Moon for scientific discovery, resource mining, and inhabitation. Upcoming decades focus on building a lunar outpost, with robotic systems playing a crucial role to safely and efficiently establish essential infrastructure such as solar power generating towers. Similar to the construction of the International Space Station (ISS), shipping necessary components via modules and assembling them in situ should be a practical scenario. In this context, this paper focuses on the integration of vision, control, and hardware systems within an autonomous sequence for a dual-arm robot system. We explore a perception and control pipeline specifically designed for assembling solar panel modules, one of the benchmark tasks. Ad hoc hardware was designed and tested in real-world experiments. A mock-up of modular solar panels and active-passive connectors are employed, with the control of this grappling fixture integrated into the proposed pipeline. The successful implementation of our method demonstrates that the two robot manipulators can effectively connect arbitrarily placed panels, highlighting the seamless integration of vision, control, and hardware systems in complex space applications.

cs.RO↗

arXiv2025

Dorst-Smeulders Coding for Arbitrary Binary Words

A binary word is Sturmian if the occurrences of each letter are balanced, in the sense that in any two factors of the same length, the difference between the number of occurrences of the same letter is at most 1. In digital geometry, Sturmian words correspond to discrete approximations of straight line segments in the Euclidean plane. The Dorst-Smeulders coding, introduced in 1984, is a 4-tuple of integers that uniquely represents a Sturmian word $w$, enabling its reconstruction using $|w|$ modular operations, making it highly efficient in practice. In this paper, we present a linear-time algorithm that, given a binary input word $w$, computes the Dorst-Smeulders coding of its longest Sturmian prefix. This forms the basis for computing the Dorst-Smeulders coding of an arbitrary binary word $w$, which is a minimal decomposition (in terms of the number of factors) of $w$ into Sturmian words, each represented by its Dorst-Smeulders coding. This coding could be leveraged in compression schemes where the input is transformed into a binary word composed of long Sturmian segments. Although the algorithm is conceptually simple and can be implemented in just a few lines of code, it is grounded in a deep analysis of the structural properties of Sturmian words.

cs.DM↗

arXiv2025

Recursive Model-agnostic Inverse Dynamics of Serial Soft-Rigid Robots

Robotics is shifting from rigid, articulated systems to more sophisticated and heterogeneous mechanical structures. Soft robots, for example, have continuously deformable elements capable of large deformations. The flourishing of control techniques developed for this class of systems is fueling the need of efficient procedures for evaluating their inverse dynamics (ID), which is challenging due to the complex and mixed nature of these systems. As of today, no single ID algorithm can describe the behavior of generic (combinations of) models of soft robots. We address this challenge for generic series-like interconnections of possibly soft structures that may require heterogeneous modeling techniques. Our proposed algorithm requires as input a purely geometric description (forward-kinematics-like) of the mapping from configuration space to deformation space. With this information only, the complete equations of motion can be given an exact recursive structure which is essentially independent from (or `agnostic' to) the underlying reduced-order kinematic modeling techniques. We achieve this goal by exploiting Kane's method to manipulate the equations of motion, showing then their recursive structure. The resulting ID algorithms have optimal computational complexity within the proposed setting, i.e., linear in the number of distinct modules. Further, a variation of the algorithm is introduced that can evaluate the generalized mass matrix without increasing computation costs. We showcase the applicability of this method to robot models involving a mixture of rigid and soft elements, described via possibly heterogeneous reduced order models (ROMs), such as Volumetric FEM, Cosserat strain-based, and volume-preserving deformation primitives. None of these systems can be handled using existing ID techniques.

cs.RO↗

arXiv2025

Digital Convexity and Combinatorics on Words

An upward (resp. downward) digitally convex word is a binary word that best approximates from below (resp. from above) an upward (resp. downward) convex curve in the plane. We study these words from the combinatorial point of view, formalizing their geometric properties and highlighting connections with Christoffel words and finite Sturmian words. In particular, we study from the combinatorial perspective the operations of inflation and deflation on digitally convex words.

math.CO↗

arXiv2025

On-Line Learning for Planning and Control of Underactuated Robots with Uncertain Dynamics

We present an iterative approach for planning and controlling motions of underactuated robots with uncertain dynamics. At its core, there is a learning process which estimates the perturbations induced by the model uncertainty on the active and passive degrees of freedom. The generic iteration of the algorithm makes use of the learned data in both the planning phase, which is based on optimization, and the control phase, where partial feedback linearization of the active dofs is performed on the model updated on-line. The performance of the proposed approach is shown by comparative simulations and experiments on a Pendubot executing various types of swing-up maneuvers. Very few iterations are typically needed to generate dynamically feasible trajectories and the tracking control that guarantees their accurate execution, even in the presence of large model uncertainties.

cs.RO↗

arXiv2024

Some Results on Digital Segments and Balanced Words

We exhibit combinatorial results on Christoffel words and binary balanced words that are motivated by their geometric interpretation as approximations of digital segments. We give a closed formula for counting the exact number of balanced words with $a$ zeroes and $b$ ones. We also study minimal non-balanced words.

cs.FL↗

arXiv2024

Maximal Closed Substrings

A string is closed if it has length 1 or has a nonempty border without internal occurrences. In this paper we introduce the definition of a \emph{maximal closed substring} (MCS), which is an occurrence of a closed substring that cannot be extended to the left nor to the right into a longer closed substring. MCSs with exponent at least $2$ are commonly called \emph{runs}; those with exponent smaller than $2$, instead, are particular cases of \emph{maximal gapped repeats}. We provide an algorithm that, given a string of length $n$ locates all MCSs the string contains in $\mathcal O(n\log n)$ time.

cs.DS↗

arXiv2024

Input Decoupling of Lagrangian Systems via Coordinate Transformation: General Characterization and its Application to Soft Robotics

Suitable representations of dynamical systems can simplify their analysis and control. On this line of thought, this paper aims to answer the following question: Can a transformation of the generalized coordinates under which the actuators directly perform work on a subset of the configuration variables be found? Not only we show that the answer to this question is yes, but we also provide necessary and sufficient conditions. More specifically, we look for a representation of the configuration space such that the right-hand side of the dynamics in Euler-Lagrange form becomes $[\boldsymbol{I} \; \boldsymbol{O}]^{T}\boldsymbol{u}$, being $u$ the system input. We identify a class of systems, called collocated, for which this problem is solvable. Under mild conditions on the input matrix, a simple test is presented to verify whether a system is collocated or not. By exploiting power invariance, we provide necessary and sufficient conditions that a change of coordinates decouples the input channels if and only if the dynamics is collocated. In addition, we use the collocated form to derive novel controllers for damped underactuated mechanical systems. To demonstrate the theoretical findings, we consider several Lagrangian systems with a focus on continuum soft robots.

cs.RO↗

arXiv2024

Nonlinear Modes as a Tool for Comparing the Mathematical Structure of Dynamic Models of Soft Robots

Continuum soft robots are nonlinear mechanical systems with theoretically infinite degrees of freedom (DoFs) that exhibit complex behaviors. Achieving motor intelligence under dynamic conditions necessitates the development of control-oriented reduced-order models (ROMs), which employ as few DoFs as possible while still accurately capturing the core characteristics of the theoretically infinite-dimensional dynamics. However, there is no quantitative way to measure if the ROM of a soft robot has succeeded in this task. In other fields, like structural dynamics or flexible link robotics, linear normal modes are routinely used to this end. Yet, this theory is not applicable to soft robots due to their nonlinearities. In this work, we propose to use the recent nonlinear extension in modal theory -- called eigenmanifolds -- as a means to evaluate control-oriented models for soft robots and compare them. To achieve this, we propose three similarity metrics relying on the projection of the nonlinear modes of the system into a task space of interest. We use this approach to compare quantitatively, for the first time, ROMs of increasing order generated under the piecewise constant curvature (PCC) hypothesis with a high-dimensional finite element (FE)-like model of a soft arm. Results show that by increasing the order of the discretization, the eigenmanifolds of the PCC model converge to those of the FE model.

cs.RO↗

arXiv2023

Extremal values of semi-regular continuants and codings of interval exchange transformations

Given a set $A$ of positive integers $a_1<\cdots<a_k$ and a partition $P: n_1+\cdots+n_k=n$, find the extremal denominators of the regular and semi-regular continued fraction $[0;x_1,\ldots,x_n]$ with partial quotients $x_i\in A$ and where each $a_i$ occurs exactly $n_i$ times in $x_1,\ldots,x_n$. In 1983, G. Ramharter gave an explicit description of the extremal arrangements of the regular continued fraction and the minimizing arrangement for the semi-regular continued fraction and showed that in each case the arrangement is unique up to reversal and independent of the actual values of the integers $a_i$. However, an explicit determination of a maximizing arrangement for the semi-regular continuant turned out to be more difficult. Ramharter conjectured that as in the other three cases, the maximizing arrangement is unique up to reversal and depends only on the partition $P$ and not on the values of the $a_i$. He further verified the conjecture in the case of a binary $A$. In this paper we confirm Ramharter's conjecture for sets $A$ with $|A|=3$ and give an algorithmic construction for the unique maximizing arrangement. We also show that Ramharter's conjecture fails for sets with $|A|\geq 4$, as the maximizing arrangement is in general neither unique nor independent of the values of the digits in $A$. The central idea is that the extremal arrangements satisfy a strong combinatorial condition, which may also be stated in the context of infinite sequences on an ordered set. We show that for bi-infinite binary words, this condition coincides with the Markoff property, discovered by A.A. Markoff in 1879 in his study of minima of binary quadratic forms. We further show that this same combinatorial condition is the fundamental property which describes the orbit structure of the natural codings of points under a symmetric $k$-interval exchange transformation.

math.CO↗

arXiv2022

On the Lie complexity of Sturmian words

Bell and Shallit recently introduced the Lie complexity of an infinite word $s$ as the function counting for each length the number of conjugacy classes of words whose elements are all factors of $s$. They proved, using algebraic techniques, that the Lie complexity is bounded above by the first difference of the factor complexity plus one; hence, it is uniformly bounded for words with linear factor complexity, and, in particular, it is at most 2 for Sturmian words, which are precisely the words with factor complexity $n+1$ for every $n$. In this note, we provide an elementary combinatorial proof of the result of Bell and Shallit and give an exact formula for the Lie complexity of any Sturmian word.

cs.DM↗

arXiv2022

Kinematic Control of Redundant Robots with Online Handling of Variable Generalized Hard Constraints

We present a generalized version of the Saturation in the Null Space (SNS) algorithm for the task control of redundant robots when hard inequality constraints are simultaneously present both in the joint and in the Cartesian space. These hard bounds should never be violated, are treated equally and in a unified way by the algorithm, and may also be varied, inserted or deleted online. When a joint/Cartesian bound saturates, the robot redundancy is exploited to continue fulfilling the primary task. If no feasible solution exists, an optimal scaling procedure is applied to enforce directional consistency with the original task. Simulation and experimental results on different robotic systems demonstrate the efficiency of the approach. The proposed algorithm can be viewed as a generic platform that is easily applicable to any robotic application in which robots operate in an unstructured environment and online handling of joint and Cartesian constraints is critical.

cs.RO↗

arXiv2021

Reduced-order observer design for a robotic manipulator

This paper investigates the design of reduced-order observers for robotic manipulators. Observer stability conditions are obtained based on a Lyapunov analysis and the proposed observer is enhanced with a hybrid scheme that may adjust the gains to cope with possible unbounded velocities of the robot joints. Thanks to such hybrid strategy, the observer works accurately both for robots driven by open-loop controllers and by output feedback controllers. Numerical simulations illustrate the efficacy of the reduced-order observer in several scenarios, including a comparison with the performances of a classical full-order observer.

eess.SY↗

arXiv2021

Motion Control of Redundant Robots with Generalised Inequality Constraints

We present an improved version of the Saturation in the Null Space (SNS) algorithm for redundancy resolution at the velocity level. In addition to hard bounds on joint space motion, we consider also Cartesian box constraints that cannot be violated at any time. The modified algorithm combines all bounds into a single augmented generalised vector and gives equal, highest priority to all inequality constraints. When needed, feasibility of the original task is enforced by the SNS task scaling procedure. Simulation results are reported for a 6R planar robot.

cs.RO↗

arXiv2021

On the extremal values of the cyclic continuants of Motzkin and Straus

In a 1983 paper, G. Ramharter asks what are the extremal arrangements for the cyclic analogues of the regular and semi-regular continuants first introduced by T.S. Motzkin and E.G. Straus in 1956. In this paper we answer this question by showing that for each set $A$ consisting of positive integers $1<a_1<a_2<\cdots <a_k$ and a $k$-term partition $P: n_1+n_2 + \cdots + n_k=n$, there exists a unique (up to reversal) cyclic word $x$ which maximizes (resp. minimizes) the regular cyclic continuant $K^{\circlearrowright}(\cdot)$ amongst all cyclic words over $A$ with Parikh vector $(n_1,n_2,\ldots,n_k)$. We also show that the same is true for the minimizing arrangement for the semi-regular cyclic continuant $\dot K^{\circlearrowright}(\cdot)$. As in the non-cyclic case, the main difficulty is to find the maximizing arrangement for the semi-regular continuant, which is not unique in general and may depend on the integers $a_1,\ldots,a_k$ and not just on their relative order. We show that if a cyclic word $x$ maximizes $\dot K^{\circlearrowright}(\cdot)$ amongst all permutations of $x$, then it verifies a strong combinatorial condition which we call the singular property. We develop an algorithm for constructing all singular cyclic words having a prescribed Parikh vector.

math.CO↗

arXiv2019

Characteristic Parameters and Special Trapezoidal Words

Following earlier work by Aldo de Luca and others, we study trapezoidal words and their prefixes, with respect to their characteristic parameters $K$ and $R$ (length of shortest unrepeated suffix, and shortest length without right special factors, respectively), as well as their symmetric versions $H$ and $L$. We consider the distinction between closed (i.e., periodic-like) and open prefixes, and between Sturmian and non-Sturmian ones. Our main results characterize right special and strictly bispecial trapezoidal words, as done by de Luca and Mignosi for Sturmian words.

cs.DM↗

arXiv2017

The sequence of open and closed prefixes of a Sturmian word

A finite word is closed if it contains a factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We are interested in the {\it oc-sequence} of a word, which is the binary sequence whose $n$-th element is $0$ if the prefix of length $n$ of the word is open, or $1$ if it is closed. We exhibit results showing that this sequence is deeply related to the combinatorial and periodic structure of a word. In the case of Sturmian words, we show that these are uniquely determined (up to renaming letters) by their oc-sequence. Moreover, we prove that the class of finite Sturmian words is a maximal element with this property in the class of binary factorial languages. We then discuss several aspects of Sturmian words that can be expressed through this sequence. Finally, we provide a linear-time algorithm that computes the oc-sequence of a finite word, and a linear-time algorithm that reconstructs a finite Sturmian word from its oc-sequence.

cs.DM↗

arXiv2016

On Christoffel and standard words and their derivatives

We introduce and study natural derivatives for Christoffel and finite standard words, as well as for characteristic Sturmian words. These derivatives, which are realized as inverse images under suitable morphisms, preserve the aforementioned classes of words. In the case of Christoffel words, the morphisms involved map $a$ to $a^{k+1}b$ (resp.,~$ab^{k}$) and $b$ to $a^{k}b$ (resp.,~$ab^{k+1}$) for a suitable $k>0$. As long as derivatives are longer than one letter, higher-order derivatives are naturally obtained. We define the depth of a Christoffel or standard word as the smallest order for which the derivative is a single letter. We give several combinatorial and arithmetic descriptions of the depth, and (tight) lower and upper bounds for it.

cs.DM↗