19 research outputs found
Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection
Semidefinite Programming (SDP) and Sums-of-Squares (SOS) relaxations have led
to certifiably optimal non-minimal solvers for several robotics and computer
vision problems. However, most non-minimal solvers rely on least-squares
formulations, and, as a result, are brittle against outliers. While a standard
approach to regain robustness against outliers is to use robust cost functions,
the latter typically introduce other non-convexities, preventing the use of
existing non-minimal solvers. In this paper, we enable the simultaneous use of
non-minimal solvers and robust estimation by providing a general-purpose
approach for robust global estimation, which can be applied to any problem
where a non-minimal solver is available for the outlier-free case. To this end,
we leverage the Black-Rangarajan duality between robust estimation and outlier
processes (which has been traditionally applied to early vision problems), and
show that graduated non-convexity (GNC) can be used in conjunction with
non-minimal solvers to compute robust solutions, without requiring an initial
guess. Although GNC's global optimality cannot be guaranteed, we demonstrate
the empirical robustness of the resulting robust non-minimal solvers in
applications, including point cloud and mesh registration, pose graph
optimization, and image-based object pose estimation (also called shape
alignment). Our solvers are robust to 70-80% of outliers, outperform RANSAC,
are more accurate than specialized local solvers, and faster than specialized
global solvers. We also propose the first certifiably optimal non-minimal
solver for shape alignment using SOS relaxation.Comment: 10 pages, 5 figures, published at IEEE Robotics and Automation
Letters (RA-L), 2020, Best Paper Award in Robot Vision at ICRA 202
Asynchronous and Parallel Distributed Pose Graph Optimization
We present Asynchronous Stochastic Parallel Pose Graph Optimization (ASAPP),
the first asynchronous algorithm for distributed pose graph optimization (PGO)
in multi-robot simultaneous localization and mapping. By enabling robots to
optimize their local trajectory estimates without synchronization, ASAPP offers
resiliency against communication delays and alleviates the need to wait for
stragglers in the network. Furthermore, ASAPP can be applied on the
rank-restricted relaxations of PGO, a crucial class of non-convex Riemannian
optimization problems that underlies recent breakthroughs on globally optimal
PGO. Under bounded delay, we establish the global first-order convergence of
ASAPP using a sufficiently small stepsize. The derived stepsize depends on the
worst-case delay and inherent problem sparsity, and furthermore matches known
result for synchronous algorithms when there is no delay. Numerical evaluations
on simulated and real-world datasets demonstrate favorable performance compared
to state-of-the-art synchronous approach, and show ASAPP's resilience against a
wide range of delays in practice.Comment: full paper with appendice
Synchronization Problems in Computer Vision
The goal of \u201csynchronization\u201d is to infer the unknown states of a network of nodes, where only the ratio (or difference) between pairs of states can be measured. Typically, states are represented by elements of a group, such as the Symmetric Group or the Special Euclidean Group. The former can represent local labels of a set of features, which refer to the multi-view matching application, whereas the latter can represent camera reference frames, in which case we are in the context of structure from motion, or local coordinates where 3D points are represented, in which case we are dealing with multiple point-set registration. A related problem is that of \u201cbearing-based network localization\u201d where each node is located at a fixed (unknown) position in 3-space and pairs of nodes can measure the direction of the line joining their locations. In this thesis we are interested in global techniques where all the measures are considered at once, as opposed to incremental approaches that grow a solution by adding pieces iteratively
Robust and large-scale quasiconvex programming in structure-from-motion
Structure-from-Motion (SfM) is a cornerstone of computer vision. Briefly speaking,
SfM is the task of simultaneously estimating the poses of the cameras behind a set of images of a
scene, and the 3D coordinates of the points in the scene.
Often, the optimisation problems that underpin SfM do not have closed-form solutions, and finding
solutions via numerical schemes is necessary. An objective function, which measures the discrepancy
of a geometric object (e.g., camera poses, rotations, 3D coordi- nates) with a set of image
measurements, is to be minimised. Each image measurement gives rise to an error function. For
example, the reprojection error, which measures the distance between an observed image point and
the projection of a 3D point onto the image, is a commonly used error function.
An influential optimisation paradigm in SfM is the ℓ₀₀ paradigm, where the objective function takes
the form of the maximum of all individual error functions (e.g. individual reprojection errors of
scene points). The benefit of the ℓ₀₀ paradigm is that the objective function of many SfM
optimisation problems become quasiconvex, hence there is a unique minimum in the objective
function. The task of formulating and minimising quasiconvex objective functions is called
quasiconvex programming.
Although tremendous progress in SfM techniques under the ℓ₀₀ paradigm has been made, there are still
unsatisfactorily solved problems, specifically, problems associated with large-scale input data and
outliers in the data. This thesis describes novel techniques to
tackle these problems.
A major weakness of the ℓ₀₀ paradigm is its susceptibility to outliers. This thesis improves the
robustness of ℓ₀₀ solutions against outliers by employing the least median of squares (LMS)
criterion, which amounts to minimising the median error. In the context of triangulation, this
thesis proposes a locally convergent robust algorithm underpinned by a novel quasiconvex plane
sweep technique. Imposing the LMS criterion achieves significant outlier tolerance, and, at the
same time, some properties of quasiconvexity greatly simplify the process of solving the LMS
problem.
Approximation is a commonly used technique to tackle large-scale input data. This thesis introduces
the coreset technique to quasiconvex programming problems. The coreset technique aims find a
representative subset of the input data, such that solving the same problem on the subset yields a
solution that is within known bound of the optimal solution on the complete input set. In
particular, this thesis develops a coreset approximate algorithm to handle large-scale
triangulation tasks.
Another technique to handle large-scale input data is to break the optimisation into multiple
smaller sub-problems. Such a decomposition usually speeds up the overall optimisation process,
and alleviates the limitation on memory. This thesis develops a large-scale optimisation algorithm
for the known rotation problem (KRot). The proposed method decomposes the original quasiconvex
programming problem with potentially hundreds of thousands of parameters into multiple sub-problems
with only three parameters each. An efficient solver based on a novel minimum enclosing ball
technique is proposed to solve the sub-problems.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Computer Science, 201
Towards Safe Autonomy in Assistive Robots
Robots have the potential to support older adults and persons with disabilities on a direct and personal level. For example, a wearable robot may help a person stand up from a chair, or a robotic manipulator may aid a person with meal preparation and housework. Assistive robots can autonomously make decisions about how best to support a person. However, this autonomy is potentially dangerous; robots can cause collisions or falls which may lead to serious injury. Therefore, guaranteeing that assistive robots operate safely is imperative.
This dissertation advances safe autonomy in assistive robots by developing a suite of tools for the tasks of perception, monitoring, manipulation and all prevention. Each tool provides a theoretical guarantee of its correct performance, adding a necessary layer of trust and protection when deploying assistive robots. The topic of interaction, or how a human responds to the decisions made by assistive robots, is left for future work.
Perception: Assistive robots must accurately perceive the 3D position of a person's body to avoid collisions and build predictive models of how a person moves. This dissertation formulates the problem of 3D pose estimation from multi-view 2D pose estimates as a sum-of-squares optimization problem. Sparsity is leveraged to efficiently solve the problem, which includes explicit constraints on the link lengths connecting any two joints. The method certifies the global optimality of its solutions over 99 percent of the time, and matches or exceeds state-of-the-art accuracy while requiring less computation time and no 3D training data.
Monitoring: Assistive robots may mitigate fall risk by monitoring changes to a person’s stability over time and predicting instabilities in real time. This dissertation presents Stability Basins which characterize stability during human motion, with a focus on sit-to-stand. An 11-person experiment was conducted in which subjects were pulled by motor-driven cables as they stood from a chair. Stability Basins correctly predicted instability (stepping or sitting) versus task success with over 90 percent accuracy across three distinct sit-to-stand strategies.
Manipulation: Robotic manipulators can support many common activities like feeding, dressing, and cleaning. This dissertation details ARMTD (Autonomous Reachability-based Manipulator Trajectory Design) for receding-horizon planning of collision-free manipulator trajectories. ARMTD composes reachable sets of the manipulator through workspace from low dimensional trajectories of each joint. ARMTD creates strict collision-avoidance constraints from these sets, which are enforced within an online trajectory optimization. The method is demonstrated for real-time planning in simulation and on hardware on a Fetch Mobile Manipulator robot, where it never causes a collision.
Fall Prevention: Wearable robots may prevent falls by quickly reacting when a user trips or slips. This dissertation presents TRIP-RTD (Trip Recovery in Prostheses via Reachability-based Trajectory Design), which extends the ARMTD framework to robotic prosthetic legs. TRIP-RTD uses predictions of a person’s response to a trip to plan recovery trajectories of a prosthetic leg. TRIP-RTD creates constraints for an online trajectory optimization which ensure the prosthetic foot is placed correctly across a range of plausible human responses. The approach is demonstrated in simulation using data of non-amputee subjects being tripped.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169822/1/pdholmes_1.pd