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In order for a bimanual robot to manipulate an object that is held by both hands, it must construct motion plans such that the transformation between its end effectors remains fixed. This amounts to complicated nonlinear equality…
Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g. robotics where motion planning issues are topical. This computational problem is…
Robotic motion-planning problems, such as a UAV flying fast in a partially-known environment or a robot arm moving around cluttered objects, require finding collision-free paths quickly. Typically, this is solved by constructing a graph,…
In this paper we describe an algorithm for the computation of canonical forms of finite subsets of $\mathbb{Z}^d$, up to affinities over $\mathbb{Z}$. For fixed dimension $d$, this algorithm has worst-case asymptotic complexity $O(n \log^2…
We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…
We study the Universal Solvability of Robot Motion Planning on Graphs (USolR) problem: given an undirected graph $G = (V, E)$ and $p$ robots, determine whether any arbitrary configuration of the robots can be transformed into any other…
A graph is called (generically) rigid in $\mathbb{R}^d$ if, for any choice of sufficiently generic edge lengths, it can be embedded in $\mathbb{R}^d$ in a finite number of distinct ways, modulo rigid transformations. Here we deal with the…
Dexterous in-hand manipulation in robotics, particularly with multi-fingered robotic hands, poses significant challenges due to the intricate avoidance of collisions among fingers and the object being manipulated. Collision-free paths for…
Reliable real-time planning for robots is essential in today's rapidly expanding automated ecosystem. In such environments, traditional methods that plan by relaxing constraints become unreliable or slow-down for kinematically constrained…
Tightness is a generalisation of the notion of convexity: a space is tight if and only if it is "as convex as possible", given its topological constraints. For a simplicial complex, deciding tightness has a straightforward exponential time…
Planning trajectories for nonholonomic systems is difficult and computationally expensive. When facing unexpected events, it may therefore be preferable to deform in some way the initially planned trajectory rather than to re-plan entirely…
We study a variant of the Coordinated Motion Planning problem on undirected graphs, referred to herein as the \textsc{Coordinated Sliding-Motion Planning} (CSMP) problem. In this variant, we are given an undirected graph $G$, $k$ robots…
The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state…
We describe a deterministic algorithm that computes an approximate root of n complex polynomial equations in n unknowns in average polynomial time with respect to the size of the input, in the Blum-Shub-Smale model with square root. It…
An autonomous robot should be able to evaluate the affordances that are offered by a given situation. Here we address this problem by designing a system that can densely predict affordances given only a single 2D RGB image. This is achieved…
Let $\mathrm{R}$ be a real closed field and $\mathrm{D} \subset \mathrm{R}$ an ordered domain. We give an algorithm that takes as input a polynomial $Q \in \mathrm{D}[X_1,\ldots,X_k]$, and computes a description of a roadmap of the set of…
The ongoing deep learning revolution has allowed computers to outclass humans in various games and perceive features imperceptible to humans during classification tasks. Current machine learning techniques have clearly distinguished…
This paper reports a novel result: with proper robot models on matrix Lie groups, one can formulate the kinodynamic motion planning problem for rigid body systems as \emph{exact} polynomial optimization problems that can be relaxed as…
Given a multivariate real (or complex) polynomial $p$ and a domain $\cal D$, we would like to decide whether an algorithm exists to evaluate $p(x)$ accurately for all $x \in {\cal D}$ using rounded real (or complex) arithmetic. Here…
Coordinating the motion of multiple agents in constrained environments is a fundamental challenge in robotics, motion planning, and scheduling. A motivating example involves $n$ robotic arms, each represented as a line segment. The…