1,720,975 research outputs found
A general framework for task-constrained motion planning with moving obstacles
No full textConsider the practically relevant situation in which a robotic system is assigned a task to be executed in an environment that contains moving obstacles. Generating collision-free motions that allow the robot to execute the task while complying with its control input limitations is a challenging problem, whose solution must be sought in the robot state space extended with time. We describe a general planning framework which can be tailored to robots described by either kinematic or dynamic models. The main component is a control-based scheme for producing configuration space subtrajectories along which the task constraint is continuously satisfied. The geometric motion and time history along each subtrajectory are generated separately in order to guarantee feasibility of the latter and at the same time make the scheme intrinsically more flexible. A randomized algorithm then explores the search space by repeatedly invoking the motion generation scheme and checking the produced subtrajectories for collisions. The proposed framework is shown to provide a probabilistically complete planner both in the kinematic and the dynamic case. Modified versions of the planners based on the exploration–exploitation approach are also devised to improve search efficiency or optimize a performance criterion along the solution. We present results in various scenarios involving non-holonomic mobile robots and fixed-based manipulators to show the performance of the planner
An optimal mesh generation algorithm for domains with Koch type boundaries
No full textIn this paper we propose a mesh algorithm to generate a regular and conformal family of nested triangulations for a planar domain divided into two non-convex polygonal subdomains by a prefractal Koch type interface. The presence of the interface, a polygonal curve, induces a natural triangulation in which the vertices of the prefractal are also nodes of the triangulation. In order to achieve an optimal rate of convergence of the numerical approximation a suitably refined mesh around the reentrant corners is required. This is achieved by generating a mesh compliant with the Grisvard's condition. We present the mesh algorithm and a detailed proof of the Grisvard conditions
An Optimal Mesh Generation for Domains with Koch Type Boundaries
No full textWe consider the numerical approximation for a 2D second order parabolic transmission problem across a pre-fractal interface K_n of Koch type; the layer K_n, a polygonal curve, divides a given domain into two non-convex sub-domains \Omega^i_n.
The approximation is carried out by a FEM discretization for the space variable and a finite difference scheme in time.
The two main difficulties in the approximation and simulations of this type of problems are the generation of a suitable mesh to possibly achieve an optimal rate of convergence and to limit the intrinsic computational cost of numeric approximations.
In this talk we will focus on the construction of a mesh compliant with the so-called "Grisvard" conditions which will allow us to obtain an optimal rate of convergence both in space and in time
Numerical approximation of transmission problems across Koch-type highly conductive layers
No full textWe prove a priori error estimates for a parabolic second order transmission problem across a prefractal interface K-n of Koch type which divides a given domain Omega into two non-convex sub-domains Omega(i)(n). By exploiting some regularity results for the solution in Omega(i)(n) we build a suitable mesh, compliant with the so-called "Grisvard" conditions, which allows to achieve an optimal rate of convergence for the semidiscrete approximation of the prefractal problem by Galerkin method. The discretization in time is carried out by the theta-method. (C) 2011 Elsevier Inc. All rights reserved
Heat-flow problems across fractal mixtures: Regularity results of the solutions and numerical approximation
No full textA parabolic transmission problem with Ventcel'-type boundary conditions on a prefractal mixture Koch-type interface is studied. Regularity results for the solution are proved. The numerical approximation of the problem is considered, and optimal a priori error estimates of the order of convergence are obtained
Task-constrained motion planning for underactuated robots
No full textThis paper addresses the motion planning problem in the presence of obstacles for underactuated robots that are assigned a geometric task. It is assumed that the robot is subject to kinematic (joint limits, joint velocity bounds) as well as dynamic (torque bounds) constraints. Building on our previous work on task-constrained motion planning, we describe a randomized planner that works directly at the torque level and generates solutions by separating geometric motions from time history. The effectiveness of the proposed approach is shown by planning collision-free swing-up maneuvers for a Pendubot system
Sensor-Based Task-Constrained Motion Planning using Model Predictive Control
No full textA redundant robotic system must execute a task in a workspace populated by obstacles whose motion is unknown in advance. For this problem setting, we present a sensor-based planner that uses Model Predictive Control (MPC) to generate motion commands for the robot. We also propose a real-time implementation of the planner based on ACADO, an open source toolkit for solving general nonlinear MPC problems. The effectiveness of the proposed algorithm is shown through simulations and experiments carried out on a UR10 manipulator
Task-constrained motion planning with moving obstacles
No full textWe consider the problem of planning the motion of redundant robotic systems subject to geometric task constraints in the presence of obstacles moving along known trajectories. Building on our previous results on task-constrained motion planning, we propose a control-based motion planner that works directly in the task-constrained configuration space extended with the time dimension. The generated trajectories are collision-free and satisfy the task constraint with arbitrary accuracy. Bounds on the achievable generalized velocities may also be taken into account. The proposed approach is validated through planning experiments on a 7-dof articulated robot and an 8-dof mobile manipulator
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