Workspace and Singularity analysis of a Delta like family robot

Workspace and joint space analysis are essential steps in describing the task and designing the control loop of the robot, respectively. This paper presents the descriptive analysis of a family of delta-like parallel robots by using algebraic tools to induce an estimation about the complexity in representing the singularities in the workspace and the joint space. A Gr{\"o}bner based elimination is used to compute the singularities of the manipulator and a Cylindrical Algebraic Decomposition algorithm is used to study the workspace and the joint space. From these algebraic objects, we propose some certified three dimensional plotting describing the the shape of workspace and of the joint space which will help the engineers or researchers to decide the most suited configuration of the manipulator they should use for a given task. Also, the different parameters associated with the complexity of the serial and parallel singularities are tabulated, which further enhance the selection of the different configuration of the manipulator by comparing the complexity of the singularity equations.Comment: 4th IFTOMM International Symposium on Robotics and Mechatronics, Jun 2015, Poitiers, France. 201

A Pair of Measures of Rotational Error for Axisymmetric Robot End-Effectors

International audienceThis paper deals with the problem of representing the rotational error of spatial robots with three orientational degrees of freedom (DOF). Typically, the errors on each of three Euler angles defining the orientation of an end-effector are analysed separately. However, this is wrong since an accuracy measure should depend only on the "distance" between the nominal pose and the actual one, and not on the choice of reference frame in which these are represented. Several bi-invariant metrics for rotational error exist but are single-parameter and, by definition, disregard the shape of the robot end-effector. Yet, robot end-effectors are typically axisymmetric. Therefore, we propose a two-parameter measure of rotational errors that is better suited for such robot end-effectors

Piston-driven numerical wave tank based on WENO solver of well-balanced shallow water equations

A numerical wave tank equipped with a piston type wave-maker is presented for long-duration simulations of long waves in shallow water. Both wave maker and tank are modelled using the nonlinear shallow water equations, with motions of the numerical piston paddle accomplished via a linear mapping technique. Three approaches are used to increase computational efficiency and accuracy. First, the model satisfies the exact conservation property (C-property), a stepping stone towards properly balancing each term in the governing equation. Second, a high-order weighted essentially non-oscillatory (WENO) method is used to reduce accumulation of truncation error. Third, a cut-off algorithm is implemented to handle contaminated digits arising from round-off error. If not treated, such errors could prevent a numerical scheme from satisfying the exact C-property in long-duration simulations. Extensive numerical tests are performed to examine the well-balanced property, high order accuracy, and shock-capturing ability of the present scheme. Correct implementation of the wave paddle generator is verified by comparing numerical predictions against analytical solutions of sinusoidal, solitary, and cnoidal waves. In all cases, the model gives satisfactory results for small-amplitude, low frequency waves. Error analysis is used to investigate model limitations and derive a user criterion for long wave generation by the model