Massimo Cefalo

Numerical approximation of transmission problems across Koch-type highly conductive layers

Abstract We prove a priori error estimates for a parabolic second order transmission problem across a prefractal interface Kn of Koch type which divides a given domain Ω into two non-convex sub-domains Ω n i . By exploiting some regularity results for the solution in Ω n i 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 θ-method.

ENERGY-BASED CONTROL OF THE BUTTERFLY ROBOT

Abstract We address the control problem for the Butterfly, an interesting example of 2-dof underactuated mechanical system. This robot consists of a butterfly-shaped rotational link on whose rim a ball rolls freely. The control objective is to stabilize the robot at a certain unstable equilibrium. To this end, exploiting the existence of heteroclinic trajectories, we extend a previously proposed energy-based technique. Simulation results show the effectiveness of the presented method.

Planning safe cyclic motions under repetitive task constraints

We consider motion planning in the presence of obstacles for redundant robotic systems subject to repetitive task constraints. For this open problem, we present a novel control-based randomized planner which produces cyclic, collision-free paths in configuration space and guarantees continuous satisfaction of the task constraints. In particular, the proposed algorithm relies on bidirectional search and loop closure in the task-constrained configuration space. Planning experiments on a simple 3R planar robot and the KUKA LWR-IV 7-dof manipulator are reported to show the effectiveness of the proposed method.

An optimal mesh generation algorithm for domains with Koch type boundaries

In 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 Grisvards condition. We present the mesh algorithm and a detailed proof of the Grisvard conditions.

Dynamically feasible task-constrained motion planning with moving obstacles

We present a randomized algorithm for planning dynamically feasible motions of robots subject to geometric task constraints in the presence of moving obstacles. The proposed method builds upon our previous results on task-constrained motion planning with moving obstacles. With respect to our previous formulation, the inclusion of bounds on the available actuator torques leads to the adoption of an acceleration-level motion generation scheme. Therefore, the new planner must operate in a task-constrained state space extended with time. The generated trajectories are collision-free, obey velocity and torque bounds, and satisfy the task constraint with arbitrary accuracy. The effectiveness of the proposed approach is shown by results on various scenarios involving a 7-dof manipulator.

Task-constrained motion planning with moving obstacles

We 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.

Repeatable Motion Planning for Redundant Robots Over Cyclic Tasks

We consider the problem of repeatable motion planning for redundant robotic systems performing cyclic tasks in the presence of obstacles. For this open problem, we present a control-based randomized planner, which produces closed collision-free paths in configuration space and guarantees continuous satisfaction of the task constraints. The proposed algorithm, which relies on bidirectional search and loop closure in the task-constrained configuration space, is shown to be probabilistically complete. A modified version of the planner is also devised for the case in which configuration-space paths are required to be smooth. Finally, we present planning results in various scenarios involving both free-flying and nonholonomic robots to show the effectiveness of the proposed method.

Task-constrained motion planning for underactuated robots

This 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.

Parallel collision check for sensor based real-time motion planning

In this paper we present a real-time collision check algorithm based on the parallel computation capabilities of recent graphics cards GPUs. We show an effective application of the proposed algorithm to solve the task-constrained real-time motion planning problem for a redundant manipulator. We propose a proof-of-concept motion planner based on fast collision check of predicted robot motion over a given planning horizon. Obstacles are avoided exploiting the redundancy of the robot. Reactive velocities are computed for some control points placed on the robot and projected in the null space of the task Jacobian. The approach is validated through simulations in V-Rep environments and experiments on the KUKA LWR-IV 7-DoF manipulator.