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A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
Given a quadratic map Q : K^n -> K^k defined over a computable subring D of a real closed field K, and a polynomial p(Y_1,...,Y_k) of degree d, we consider the zero set Z=Z(p(Q(X)),K^n) of the polynomial p(Q(X_1,...,X_n)). We present a…
The three domatic number problem asks whether a given undirected graph can be partitioned into at least three dominating sets, i.e., sets whose closed neighborhood equals the vertex set of the graph. Since this problem is NP-complete, no…
In this paper, we devise methods for the multi- objective control of humanoid robots, a.k.a. prioritized whole- body controllers, that achieve efficiency and robustness in the algorithmic computations. We use a form of whole-body…
In robotic tasks, changes in reference frames typically do not influence the underlying physical properties of the system, which has been known as invariance of physical laws.These changes, which preserve distance, encompass isometric…
Collaborative robots (cobots) are machines designed to work safely alongside people in human-centric environments. Providing cobots with the ability to quickly infer the inertial parameters of manipulated objects will improve their…
The control and sensing of large-scale systems results in combinatorial problems not only for sensor and actuator placement but also for scheduling or observability/controllability. Such combinatorial constraints in system design and…
The Semialgebraic Orbit Problem is a fundamental reachability question that arises in the analysis of discrete-time linear dynamical systems such as automata, Markov chains, recurrence sequences, and linear while loops. An instance of the…
We consider efficient route planning for robots in applications such as infrastructure inspection and automated surgical imaging. These tasks can be modeled via the combinatorial problem Graph Inspection. The best known algorithms for this…
Hybrid systems theory has become a powerful approach for designing feedback controllers that achieve dynamically stable bipedal locomotion, both formally and in practice. This paper presents an analytical framework 1) to address…
Robot positioning accuracy is a key factory when performing high-precision manufacturing tasks. To effectively improve the accuracy of a manipulator, often up to a value close to its repeatability, calibration plays a crucial role. In the…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
We give a new complexity bound for calculating the complex dimension of an algebraic set. Our algorithm is completely deterministic and approaches the best recent randomized complexity bounds. We also present some new, significantly sharper…
Continuum robots have emerged as a promising technology in the medical field due to their potential of accessing deep sited locations of the human body with low surgical trauma. When deriving physics-based models for these robots,…
The automatic shape control of deformable objects is a challenging (and currently hot) manipulation problem due to their high-dimensional geometric features and complex physical properties. In this study, a new methodology to manipulate…
We implement and evaluate different methods for the reconfiguration of a connected arrangement of tiles into a desired target shape, using a single active robot that can move along the tile structure. This robot can pick up, carry, or drop…
Multi-robot systems have begun to permeate into a variety of different fields, but collision-free navigation in a decentralized manner is still an arduous task. Typically, the navigation of high speed multi-robot systems demands replanning…
Over three decades of scientific endeavors to realize programmable matter, a substance that can change its physical properties based on user input or responses to its environment, there have been many advances in both the engineering of…
Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the…
We discuss the relationship between quaternion algebras and quadratic forms with a focus on computational aspects. Our basic motivating problem is to determine if a given algebra of rank 4 over a commutative ring R embeds in the 2x2-matrix…