Related papers: Deciding Cuspidality of Manipulators through Compu…
Existing learning approaches to dexterous manipulation use demonstrations or interactions with the environment to train black-box neural networks that provide little control over how the robot learns the skills or how it would perform post…
We consider the problem of computing sample points in each connected component of a semi-algebraic set defined by the non-vanishing or the positivity of an n-variate polynomial of degree d, with rational coefficients of bit size bounded by…
Deep Reinforcement Learning (RL) has shown great success in learning complex control policies for a variety of applications in robotics. However, in most such cases, the hardware of the robot has been considered immutable, modeled as part…
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
A basic task in the design of an industrial robot application is the relative placement of robot and workpiece. Process points are defined in Cartesian coordinates relative to the workpiece coordinate system, and the workpiece has to be…
Let $f, f_1, \ldots, f_\nV$ be polynomials with rational coefficients in the indeterminates $\bfX=X_1, \ldots, X_n$ of maximum degree $D$ and $V$ be the set of common complex solutions of $\F=(f_1,\ldots, f_\nV)$. We give an algorithm…
Quality Diversity (QD) has shown great success in discovering high-performing, diverse policies for robot skill learning. While current benchmarks have led to the development of powerful QD methods, we argue that new paradigms must be…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
In the coordinated motion planning problem, we are given a graph together with the starting and destination vertices of $k$ robots. At each time step, any subset of robots may move, each traversing an edge of the graph, provided that no two…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
The workspace topologies of a family of 3-revolute (3R) positioning manipulators are enumerated. The workspace is characterized in a half-cross section by the singular curves. The workspace topology is defined by the number of cusps that…
We investigate the problem of multi-robot coordinated planning in environments where the robots may have to operate in close proximity to each other. We seek computationally efficient planners that ensure safe paths and adherence to…
Autonomous robotic inspection, where a robot moves through its environment and inspects points of interest, has applications in industrial settings, structural health monitoring, and medicine. Planning the paths for a robot to safely and…
As surgical interventions trend towards minimally invasive approaches, Concentric Tube Robots (CTRs) have been explored for various interventions such as brain, eye, fetoscopic, lung, cardiac and prostate surgeries. Arranged concentrically,…
We consider two basic algorithmic problems concerning tuples of (skew-)symmetric matrices. The first problem asks to decide, given two tuples of (skew-)symmetric matrices $(B_1, \dots, B_m)$ and $(C_1, \dots, C_m)$, whether there exists an…
Quadruped robots are increasingly used in various applications due to their high mobility and ability to operate in diverse terrains. However, most available quadruped robots are primarily focused on mobility without object manipulation…
Let $\mathcal{W} \subset \mathbb{R}^2$ be a planar polygonal environment (i.e., a polygon potentially with holes) with a total of $n$ vertices, and let $A,B$ be two robots, each modeled as an axis-aligned unit square, that can translate…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
For robots to successfully execute tasks assigned to them, they must be capable of planning the right sequence of actions. These actions must be both optimal with respect to a specified objective and satisfy whatever constraints exist in…
General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$…