1,819 research outputs found
ZMP support areas for multi-contact mobility under frictional constraints
We propose a method for checking and enforcing multi-contact stability based
on the Zero-tilting Moment Point (ZMP). The key to our development is the
generalization of ZMP support areas to take into account (a) frictional
constraints and (b) multiple non-coplanar contacts. We introduce and
investigate two kinds of ZMP support areas. First, we characterize and provide
a fast geometric construction for the support area generated by valid contact
forces, with no other constraint on the robot motion. We call this set the full
support area. Next, we consider the control of humanoid robots using the Linear
Pendulum Mode (LPM). We observe that the constraints stemming from the LPM
induce a shrinking of the support area, even for walking on horizontal floors.
We propose an algorithm to compute the new area, which we call pendular support
area. We show that, in the LPM, having the ZMP in the pendular support area is
a necessary and sufficient condition for contact stability. Based on these
developments, we implement a whole-body controller and generate feasible
multi-contact motions where an HRP-4 humanoid locomotes in challenging
multi-contact scenarios.Comment: 14 pages, 10 figure
Implicitization of curves and (hyper)surfaces using predicted support
We reduce implicitization of rational planar parametric curves and (hyper)surfaces to linear algebra, by interpolating the coefficients of the implicit equation.
For predicting the implicit support, we focus on methods that exploit input and output structure in the sense of sparse (or toric) elimination theory, namely by computing the Newton polytope of the implicit polynomial, via sparse resultant theory.
Our algorithm works even in the presence of base points but, in this case, the implicit equation shall be obtained as a factor of the produced polynomial.
We implement our methods on Maple, and some on Matlab as well, and study their numerical stability and efficiency on several classes of curves and surfaces.
We apply our approach to approximate implicitization,
and quantify the accuracy of the approximate output,
which turns out to be satisfactory on all tested examples; we also relate our measures to Hausdorff distance.
In building a square or rectangular matrix, an important issue is (over)sampling the given curve or surface: we conclude that unitary complexes offer the best tradeoff between speed and accuracy when numerical methods are employed, namely SVD, whereas for exact kernel computation random integers is the method of choice.
We compare our prototype to existing software and find that it is rather competitive
p-Adic Stability In Linear Algebra
Using the differential precision methods developed previously by the same
authors, we study the p-adic stability of standard operations on matrices and
vector spaces. We demonstrate that lattice-based methods surpass naive methods
in many applications, such as matrix multiplication and sums and intersections
of subspaces. We also analyze determinants , characteristic polynomials and LU
factorization using these differential methods. We supplement our observations
with numerical experiments.Comment: ISSAC 2015, Jul 2015, Bath, United Kingdom. 201
Adaptive Path Planning for Depth Constrained Bathymetric Mapping with an Autonomous Surface Vessel
This paper describes the design, implementation and testing of a suite of
algorithms to enable depth constrained autonomous bathymetric (underwater
topography) mapping by an Autonomous Surface Vessel (ASV). Given a target depth
and a bounding polygon, the ASV will find and follow the intersection of the
bounding polygon and the depth contour as modeled online with a Gaussian
Process (GP). This intersection, once mapped, will then be used as a boundary
within which a path will be planned for coverage to build a map of the
Bathymetry. Methods for sequential updates to GP's are described allowing
online fitting, prediction and hyper-parameter optimisation on a small embedded
PC. New algorithms are introduced for the partitioning of convex polygons to
allow efficient path planning for coverage. These algorithms are tested both in
simulation and in the field with a small twin hull differential thrust vessel
built for the task.Comment: 21 pages, 9 Figures, 1 Table. Submitted to The Journal of Field
Robotic
Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT
In this paper, we develop a shape optimization-based algorithm for the
electrical impedance tomography (EIT) problem of determining a piecewise
constant conductivity on a polygonal partition from boundary measurements. The
key tool is to use a distributed shape derivative of a suitable cost functional
with respect to movements of the partition. Numerical simulations showing the
robustness and accuracy of the method are presented for simulated test cases in
two dimensions
- …