Related papers: Topological robotics: motion planning in projectiv…
We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe''…
This paper presents a method for constrained motion planning from vision, which enables a robot to move its end-effector over an observed surface, given start and destination points. The robot has no prior knowledge of the surface shape,…
Robots can provide assistance to a human by moving objects to locations around the person's body. With a well chosen initial configuration, a robot can better reach locations important to an assistive task despite model error, pose…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
We describe and implement a randomized algorithm that inputs a polyhedron, thought of as the space of states of some automated guided vehicle $\mathcal{R}$, and outputs an explicit system of piecewise linear motion planners for…
We present an algorithm to compute planar linkage topology and geometry, given a user-specified end-effector trajectory. Planar linkage structures convert rotational or prismatic motions of a single actuator into an arbitrarily complex…
Consider a set of $n$ simple autonomous mobile robots (asynchronous, no common coordinate system, no identities, no central coordination, no direct communication, no memory of the past, non-rigid, deterministic) initially in distinct…
In this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well-understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is…
We study the topological complexity, in the sense of Smale, of three enumerative problems in algebraic geometry: finding the 27 lines on cubic surfaces, the 28 bitangents and the 24 inflection points on quartic curves. In particular, we…
We study the problem of bipedal robot navigation in complex environments with uncertain and rough terrain. In particular, we consider a scenario in which the robot is expected to reach a desired goal location by traversing an environment…
We consider the problem of multi-robot path planning in a complex, cluttered environment with the aim of reducing overall congestion in the environment, while avoiding any inter-robot communication or coordination. Such limitations may…
We obtain an explicit formula for the best lower bound for the higher topological complexity, TC_k(P^n), of real projective space implied by mod 2 cohomology.
The problem of optimal motion planing and control is fundamental in robotics. However, this problem is intractable for continuous-time stochastic systems in general and the solution is difficult to approximate if non-instantaneous nonlinear…
Farber introduced a notion of topological complexity $\TC(X)$ that is related to robotics. Here we introduce a series of numerical invariants $\TC_n(X), n=1,2, ...$ such that $\TC_2(X)=\TC(X)$ and $\TC_n(X)\le \TC_{n+1}(X)$. For these…
This paper studies motion planning of a mobile robot under uncertainty. The control objective is to synthesize a {finite-memory} control policy, such that a high-level task specified as a Linear Temporal Logic (LTL) formula is satisfied…
Ground robots navigating in complex, dynamic environments must compute collision-free trajectories to avoid obstacles safely and efficiently. Nonconvex optimization is a popular method to compute a trajectory in real-time. However, these…
In this paper, we deal with the robot motion planning problem in multi-valued function theory. We first enrich the multi-homotopy studies by introducing a multi-homotopy lifting property and a multi-fibration. Then we compute both a…
Parametrized motion planning algorithms \cite{CFW} have a high degree of universality and flexibility; they generate the motion of a robotic system under a variety of external conditions. The latter are viewed as parameters and constitute…
Motion planning seeks a collision-free path in a configuration space (C-space), representing all possible robot configurations in the environment. As it is challenging to construct a C-space explicitly for a high-dimensional robot, we…
We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on…