13 research outputs found
Fast Nonlinear Least Squares Optimization of Large-Scale Semi-Sparse Problems
Many problems in computer graphics and vision can be formulated as a nonlinear least squares optimization problem, for which numerous off-the-shelf solvers are readily available. Depending on the structure of the problem, however, existing solvers may be more or less suitable, and in some cases the solution comes at the cost of lengthy convergence times. One such case is semi-sparse optimization problems, emerging for example in localized facial performance reconstruction, where the nonlinear least squares problem can be composed of hundreds of thousands of cost functions, each one involving many of the optimization parameters. While such problems can be solved with existing solvers, the computation time can severely hinder the applicability of these methods. We introduce a novel iterative solver for nonlinear least squares optimization of large-scale semi-sparse problems. We use the nonlinear Levenberg-Marquardt method to locally linearize the problem in parallel, based on its firstorder approximation. Then, we decompose the linear problem in small blocks, using the local Schur complement, leading to a more compact linear system without loss of information. The resulting system is dense but its size is small enough to be solved using a parallel direct method in a short amount of time. The main benefit we get by using such an approach is that the overall optimization process is entirely parallel and scalable, making it suitable to be mapped onto graphics hardware (GPU). By using our minimizer, results are obtained up to one order of magnitude faster than other existing solvers, without sacrificing the generality and the accuracy of the model. We provide a detailed analysis of our approach and validate our results with the application of performance-based facial capture using a recently-proposed anatomical local face deformation model
DeformerNet: Learning Bimanual Manipulation of 3D Deformable Objects
Applications in fields ranging from home care to warehouse fulfillment to
surgical assistance require robots to reliably manipulate the shape of 3D
deformable objects. Analytic models of elastic, 3D deformable objects require
numerous parameters to describe the potentially infinite degrees of freedom
present in determining the object's shape. Previous attempts at performing 3D
shape control rely on hand-crafted features to represent the object shape and
require training of object-specific control models. We overcome these issues
through the use of our novel DeformerNet neural network architecture, which
operates on a partial-view point cloud of the manipulated object and a point
cloud of the goal shape to learn a low-dimensional representation of the object
shape. This shape embedding enables the robot to learn a visual servo
controller that computes the desired robot end-effector action to iteratively
deform the object toward the target shape. We demonstrate both in simulation
and on a physical robot that DeformerNet reliably generalizes to object shapes
and material stiffness not seen during training. Crucially, using DeformerNet,
the robot successfully accomplishes three surgical sub-tasks: retraction
(moving tissue aside to access a site underneath it), tissue wrapping (a
sub-task in procedures like aortic stent placements), and connecting two
tubular pieces of tissue (a sub-task in anastomosis).Comment: Submitted to IEEE Transactions on Robotics (T-RO). 18 pages, 25
figures. arXiv admin note: substantial text overlap with arXiv:2110.0468
ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact
We present a differentiable dynamics solver that is able to handle frictional
contact for rigid and deformable objects within a unified framework. Through a
principled mollification of normal and tangential contact forces, our method
circumvents the main difficulties inherent to the non-smooth nature of
frictional contact. We combine this new contact model with fully-implicit time
integration to obtain a robust and efficient dynamics solver that is
analytically differentiable. In conjunction with adjoint sensitivity analysis,
our formulation enables gradient-based optimization with adaptive trade-offs
between simulation accuracy and smoothness of objective function landscapes. We
thoroughly analyse our approach on a set of simulation examples involving rigid
bodies, visco-elastic materials, and coupled multi-body systems. We furthermore
showcase applications of our differentiable simulator to parameter estimation
for deformable objects, motion planning for robotic manipulation, trajectory
optimization for compliant walking robots, as well as efficient self-supervised
learning of control policies.Comment: Moritz Geilinger and David Hahn contributed equally to this wor