47 research outputs found
Toric partial density functions and stability of toric varieties
Let denote a polarized toric K\"ahler manifold. Fix a
toric submanifold and denote by the
partial density function corresponding to the partial Bergman kernel projecting
smooth sections of onto holomorphic sections of that vanish to
order at least along , for fixed such that . We
prove the existence of a distributional expansion of as , including the identification of the coefficient of as a
distribution on . This expansion is used to give a direct proof that if
has constant scalar curvature, then must be slope semi-stable
with respect to . Similar results are also obtained for more general partial
density functions. These results have analogous applications to the study of
toric K-stability of toric varieties.Comment: Accepted by Mathematische Annalen on 13 September 201
CloudGripper: An Open Source Cloud Robotics Testbed for Robotic Manipulation Research, Benchmarking and Data Collection at Scale
We present CloudGripper, an open source cloud robotics testbed, consisting of
a scalable, space and cost-efficient design constructed as a rack of 32 small
robot arm work cells. Each robot work cell is fully enclosed and features
individual lighting, a low-cost custom 5 degree of freedom Cartesian robot arm
with an attached parallel jaw gripper and a dual camera setup for
experimentation. The system design is focused on continuous operation and
features a 10 Gbit/s network connectivity allowing for high throughput
remote-controlled experimentation and data collection for robotic manipulation.
CloudGripper furthermore is intended to form a community testbed to study the
challenges of large scale machine learning and cloud and edge-computing in the
context of robotic manipulation. In this work, we describe the mechanical
design of the system, its initial software stack and evaluate the repeatability
of motions executed by the proposed robot arm design. A local network API
throughput and latency analysis is also provided. CloudGripper-Rope-100, a
dataset of more than a hundred hours of randomized rope pushing interactions
and approximately 4 million camera images is collected and serves as a proof of
concept demonstrating data collection capabilities. A project website with more
information is available at https://cloudgripper.org.Comment: Under review at IEEE ICRA 202
Quasi-static Soft Fixture Analysis of Rigid and Deformable Objects
We present a sampling-based approach to reasoning about the caging-based
manipulation of rigid and a simplified class of deformable 3D objects subject
to energy constraints. Towards this end, we propose the notion of soft fixtures
extending earlier work on energy-bounded caging to include a broader set of
energy function constraints and settings, such as gravitational and elastic
potential energy of 3D deformable objects. Previous methods focused on
establishing provably correct algorithms to compute lower bounds or
analytically exact estimates of escape energy for a very restricted class of
known objects with low-dimensional C-spaces, such as planar polygons. We
instead propose a practical sampling-based approach that is applicable in
higher-dimensional C-spaces but only produces a sequence of upper-bound
estimates that, however, appear to converge rapidly to actual escape energy. We
present 8 simulation experiments demonstrating the applicability of our
approach to various complex quasi-static manipulation scenarios. Quantitative
results indicate the effectiveness of our approach in providing upper-bound
estimates for escape energy in quasi-static manipulation scenarios. Two
real-world experiments also show that the computed normalized escape energy
estimates appear to correlate strongly with the probability of escape of an
object under randomized pose perturbation.Comment: Paper submitted to ICRA 202
An Efficient and Continuous Voronoi Density Estimator
We introduce a non-parametric density estimator deemed Radial Voronoi Density
Estimator (RVDE). RVDE is grounded in the geometry of Voronoi tessellations and
as such benefits from local geometric adaptiveness and broad convergence
properties. Due to its radial definition RVDE is moreover continuous and
computable in linear time with respect to the dataset size. This amends for the
main shortcomings of previously studied VDEs, which are highly discontinuous
and computationally expensive. We provide a theoretical study of the modes of
RVDE as well as an empirical investigation of its performance on
high-dimensional data. Results show that RVDE outperforms other non-parametric
density estimators, including recently introduced VDEs.Comment: 12 page
BITKOMO: Combining Sampling and Optimization for Fast Convergence in Optimal Motion Planning
Optimal sampling based motion planning and trajectory optimization are two
competing frameworks to generate optimal motion plans. Both frameworks have
complementary properties: Sampling based planners are typically slow to
converge, but provide optimality guarantees. Trajectory optimizers, however,
are typically fast to converge, but do not provide global optimality guarantees
in nonconvex problems, e.g. scenarios with obstacles. To achieve the best of
both worlds, we introduce a new planner, BITKOMO, which integrates the
asymptotically optimal Batch Informed Trees (BIT*) planner with the K-Order
Markov Optimization (KOMO) trajectory optimization framework. Our planner is
anytime and maintains the same asymptotic optimality guarantees provided by
BIT*, while also exploiting the fast convergence of the KOMO trajectory
optimizer. We experimentally evaluate our planner on manipulation scenarios
that involve high dimensional configuration spaces, with up to two 7-DoF
manipulators, obstacles and narrow passages. BITKOMO performs better than KOMO
by succeeding even when KOMO fails, and it outperforms BIT* in terms of
convergence to the optimal solution.Comment: 6 pages, Accepted at IROS 202