A Novel Approach for Ellipsoidal Outer-Approximation of the Intersection Region of Ellipses in the Plane

In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection of the ellipses are found in an efficient manner. To do so, the intersection points of the ellipses that fall on the boundary of the intersection region are determined, and a set of points is generated on the elliptic arcs connecting every two neighbouring intersection points. By finding the tangent lines to the ellipses at the extended set of points, a set of half-planes is obtained, whose intersection forms a polygon. To find the polygon more efficiently, the points are given an order and the intersection of the half-planes corresponding to every two neighbouring points is calculated. If the polygon is convex and bounded, these calculated points together with the initially obtained intersection points will form its vertices. If the polygon is non-convex or unbounded, we can detect this situation and then generate additional discrete points only on the elliptical arc segment causing the issue, and restart the algorithm to obtain a bounded and convex polygon. Finally, the smallest area ellipse that contains the vertices of the polygon is obtained by solving a convex optimization problem. Through numerical experiments, it is illustrated that the proposed technique returns a tighter outer-approximation of the intersection of multiple ellipses, compared to conventional techniques, with only slightly higher computational cost

Computing Forward Reachable Sets for Nonlinear Adaptive Multirotor Controllers

In multirotor systems, guaranteeing safety while considering unknown disturbances is essential for robust trajectory planning. Computing the forward reachable set (FRS), the set of all possible states with bounded disturbances, can be a viable solution to find robust and collision-free trajectories. However, in many cases, the FRS is not calculated in real time and is too conservative to be used in actual applications. In this paper, we mitigate these problems by applying a nonlinear disturbance observer (NDOB) and an adaptive controller to the multirotor system. We formulate the FRS of the closed-loop system combined with the adaptive controller in augmented state space by exploiting the Hamilton-Jacobi reachability analysis and then present the ellipsoidal approximation in a closed-form expression to compute the small FRS in real time. Moreover, tighter disturbance bounds in the prediction horizon are inferred from the NDOB so that a much smaller FRS can be generated. Numerical examples validate the computational efficiency and the smaller scale of the proposed FRS compared to the baseline.Comment: 7 pages, 3 figures, submitted to ACC 202

A wrench-sensitive touch pad based on a parallel structure

Trabajo presentado al ICRA 2008 celebrado en Pasadena (USA) del 19 al 23 de mayo.Many different robotic in-parallel structures have been conceived as six-component force sensors. In general, they perform well for most applications but, when accuracy is a must, two main limitations arise. First, in most designs, the legs are connected to the base and the platform through ball-and-socket joints. Although the dry friction in each of these joints can be individually neglected, the integrated effect of twelve such elements becomes noticeable. Second, dynamical measurements might not be very accurate because the natural resonance frequency of the used structures is quite low even for relatively small dimensions. This dynamical response can be obviously modified with a proper mechanical design, but this increases the complexity of the sensor. This paper discusses the design and implementation of a touch pad based on a 6-axis force sensor and shows how the above limitations degrade its behavior. Moreover, it is shown how using a tensegrity structure both problems could be alleviated because ball-and- socket joints can be substituted by point contacts and the resonance frequency of the structure can be controlled by adjusting the static tensions of the tendons.This work was supported by projects: 'Analysis and motion planning of complex robotic systems' (4802), 'Plataforma torsométrica basada en estructuras de tensigridad' (3707), 'Estació de muntatge universal' (I-00907). This work has been partially supported by the Spanish Ministry of Education and Science through the I+D project DPI2007-60858, by the XARTAP network of the Catalan Government, and by the Spanish I3 project with reference 2006-5-01-077.Peer Reviewe