3 research outputs found
Near-Optimal Min-Sum Motion Planning for Two Square Robots in a Polygonal Environment
Let be a planar polygonal environment
(i.e., a polygon potentially with holes) with a total of vertices, and let
be two robots, each modeled as an axis-aligned unit square, that can
translate inside . Given source and target placements
of and , respectively, the goal is to
compute a \emph{collision-free motion plan} , i.e., a motion
plan that continuously moves from to and from to
so that and remain inside and do not collide with
each other during the motion. Furthermore, if such a plan exists, then we wish
to return a plan that minimizes the sum of the lengths of the paths traversed
by the robots, . Given and a parameter , we present an
-time -approximation algorithm
for this problem. We are not aware of any polynomial time algorithm for this
problem, nor do we know whether the problem is NP-Hard. Our result is the first
polynomial-time -approximation algorithm for an optimal motion
planning problem involving two robots moving in a polygonal environment.Comment: The conference version of the paper is accepted to SODA 202
Planification de pas pour robots humanoïdes : approches discrètes et continues
Dans cette thèse nous nous intéressons à deux types d'approches pour la planification de pas pour robots humanoïdes : d'une part les approches discrètes où le robot n'a qu'un nombre fini de pas possibles, et d'autre part les approches où le robot se base sur des zones de faisabilité continues. Nous étudions ces problèmes à la fois du point de vue théorique et pratique. En particulier nous décrivons deux méthodes originales, cohérentes et efficaces pour la planification de pas, l'une dans le cas discret (chapitre 5) et l'autre dans le cas continu (chapitre 6). Nous validons ces méthodes en simulation ainsi qu'avec plusieurs expériences sur le robot HRP-2. ABSTRACT : In this thesis we investigate two types of approaches for footstep planning for humanoid robots: on one hand the discrete approaches where the robot has only a finite set of possible steps, and on the other hand the approaches where the robot uses continuous feasibility regions. We study these problems both on a theoretical and practical level. In particular, we describe two original, coherent and efficient methods for footstep planning, one in the discrete case (chapter 5), and one in the continuous case (chapter 6). We validate these methods in simulation and with several experiments on the robot HRP-2
d_1-Optimal Motion for a Rod (Extended Abstract)
) Tetsuo Asano 1 , David Kirkpatrick 2 , and Chee K. Yap 3 1 Osaka Electro-Communication University, Japan, 2 University of British Columbia, Canada, 3 Courant Institute, New York University, USA December 5, 1994 Abstract We study optimal motion for a rod in the plane amidst polygonal obstacles. The optimality criterion is based on minimizing the orbit length of a fixed but arbitrary point (called the focus) on the rod. Our surprising result is that this problem is NP-hard if when focus is in the relative interior of the rod whereas it is solvable in polynomial time if the focus is an endpoint of the rod. Other results include a local characterization of d1-optimal motion and an approximation algorithm. 1 Introduction Although feasibility motion planning is very well studied, little is known about optimal motion planning except for the case where the robot body is a disc. In this paper we are interested in studying optimal motion for a rod (a directed line segment). Of c..