Fast and accurate clothoid fitting

An effective solution to the problem of Hermite $G^1$ interpolation with a clothoid curve is provided. At the beginning the problem is naturally formulated as a system of nonlinear equations with multiple solutions that is generally difficult to solve numerically. All the solutions of this nonlinear system are reduced to the computation of the zeros of a single nonlinear equation. A simple strategy, together with the use of a good and simple guess function, permits to solve the single nonlinear equation with a few iterations of the Newton--Raphson method. The computation of the clothoid curve requires the computation of Fresnel and Fresnel related integrals. Such integrals need asymptotic expansions near critical values to avoid loss of precision. This is necessary when, for example, the solution of interpolation problem is close to a straight line or an arc of circle. Moreover, some special recurrences are deduced for the efficient computation of asymptotic expansion. The reduction of the problem to a single nonlinear function in one variable and the use of asymptotic expansions make the solution algorithm fast and robust.Comment: 14 pages, 3 figures, 9 Algorithm Table

Path following hybrid control for vehicle stability applied to industrial forklifts

The paper focuses on a closed-loop hybrid controller (kinematic and dynamic) for path following approaches with industrial forklifts carrying heavy loads at high speeds, where aspects such as vehicle stability, safety, slippage and comfort are considered. The paper first describes a method for generating Double Continuous Curvature (DCC) paths for non-holonomic wheeled mobile robots, which is the basis of the proposed kinematic controller. The kinematic controller generates a speed profile, based on slow-in and fast-out policy, and a curvature profile recomputing DCC paths in closed-loop. The dynamic controller determines maximum values for decelerations and curvatures, as well as bounded sharpness so that instantaneous vehicle stability conditions can be guaranteed against lateral and frontal tip-overs. One of the advantages of the proposed method, with respect to full dynamic controllers, is that it does not require dynamic parameters to be estimated for modelling, which in general can be a difficult task. The proposed kinematic dynamic controller is afterwards compared with a classic kinematic controller like Pure-Pursuit. For that purpose, in our hybrid control structure we have just replaced the proposed kinematic controller with Pure-Pursuit. Several metrics, such as settling time, overshoot, safety and comfort have been analysed.This work was supported by VALi+d and PROMETEO Programs (Conselleria d'Educacio, Generalitat Valenciana), DIVISAMOS (DPI-2009-14744-C03-01) and SAFEBUS (IPT-2011-1165-370000): Ministry of Economy and Competitivity.Girbés, V.; Armesto Ángel, L.; Tornero Montserrat, J. (2014). Path following hybrid control for vehicle stability applied to industrial forklifts. Robotics and Autonomous Systems. 62(6):910-922. https://doi.org/10.1016/j.robot.2014.01.004S91092262

Planeamento de trajectórias para robôs tipo carro

Dissertação de mestrado em Automação Robótica, apresentada ao Departamento de Engenharia Electrotécnica e de Computadores da Fac. de Ciências e Tecnologia da Univ. de Coimbr