9 research outputs found
The Critical Radius in Sampling-based Motion Planning
We develop a new analysis of sampling-based motion planning in Euclidean
space with uniform random sampling, which significantly improves upon the
celebrated result of Karaman and Frazzoli (2011) and subsequent work.
Particularly, we prove the existence of a critical connection radius
proportional to for samples and dimensions:
Below this value the planner is guaranteed to fail (similarly shown by the
aforementioned work, ibid.). More importantly, for larger radius values the
planner is asymptotically (near-)optimal. Furthermore, our analysis yields an
explicit lower bound of on the probability of success. A
practical implication of our work is that asymptotic (near-)optimality is
achieved when each sample is connected to only neighbors. This is
in stark contrast to previous work which requires
connections, that are induced by a radius of order . Our analysis is not restricted to PRM and applies to a
variety of PRM-based planners, including RRG, FMT* and BTT. Continuum
percolation plays an important role in our proofs. Lastly, we develop similar
theory for all the aforementioned planners when constructed with deterministic
samples, which are then sparsified in a randomized fashion. We believe that
this new model, and its analysis, is interesting in its own right
Probabilistic completeness of RRT for geometric and kinodynamic planning with forward propagation
The Rapidly-exploring Random Tree (RRT) algorithm has been one of the most
prevalent and popular motion-planning techniques for two decades now.
Surprisingly, in spite of its centrality, there has been an active debate under
which conditions RRT is probabilistically complete. We provide two new proofs
of probabilistic completeness (PC) of RRT with a reduced set of assumptions.
The first one for the purely geometric setting, where we only require that the
solution path has a certain clearance from the obstacles. For the kinodynamic
case with forward propagation of random controls and duration, we only consider
in addition mild Lipschitz-continuity conditions. These proofs fill a gap in
the study of RRT itself. They also lay sound foundations for a variety of more
recent and alternative sampling-based methods, whose PC property relies on that
of RRT
Near-Optimal Multi-Robot Motion Planning with Finite Sampling
An underlying structure in several sampling-based methods for continuous
multi-robot motion planning (MRMP) is the tensor roadmap (TR), which emerges
from combining multiple PRM graphs constructed for the individual robots via a
tensor product. We study the conditions under which the TR encodes a
near-optimal solution for MRMP---satisfying these conditions implies near
optimality for a variety of popular planners, including dRRT*, and the discrete
methods M* and CBS when applied to the continuous domain. We develop the first
finite-sample analysis of this kind, which specifies the number of samples,
their deterministic distribution, and magnitude of the connection radii that
should be used by each individual PRM graph, to guarantee near-optimality using
the TR. This significantly improves upon a previous asymptotic analysis,
wherein the number of samples tends to infinity, and supports guaranteed
high-quality solutions in practice, within bounded running time. To achieve our
new result, we first develop a sampling scheme, which we call the staggered
grid, for finite-sample motion planning for individual robots, which requires
significantly less samples than previous work. We then extend it to the much
more involved MRMP setting which requires to account for interactions among
multiple robots. Finally, we report on a few experiments that serve as a
verification of our theoretical findings and raise interesting questions for
further investigation.Comment: Submitted to the International Conference on Robotics and Automation
(ICRA), 202
Optimistic Motion Planning Using Recursive Sub- Sampling: A New Approach to Sampling-Based Motion Planning
Sampling-based motion planning in the field of robot motion planning has provided an effective approach to finding path for even high dimensional configuration space and with the motivation from the concepts of sampling based-motion planners, this paper presents a new sampling-based planning strategy called Optimistic Motion Planning using Recursive Sub-Sampling (OMPRSS), for finding a path from a source to a destination sanguinely without having to construct a roadmap or a tree. The random sample points are generated recursively and connected by straight lines. Generating sample points is limited to a range and edge connectivity is prioritized based on their distances from the line connecting through the parent samples with the intention to shorten the path. The planner is analysed and compared with some sampling strategies of probabilistic roadmap method (PRM) and the experimental results show agile planning with early convergence
Sampling-Based Motion Planning: A Comparative Review
Sampling-based motion planning is one of the fundamental paradigms to
generate robot motions, and a cornerstone of robotics research. This
comparative review provides an up-to-date guideline and reference manual for
the use of sampling-based motion planning algorithms. This includes a history
of motion planning, an overview about the most successful planners, and a
discussion on their properties. It is also shown how planners can handle
special cases and how extensions of motion planning can be accommodated. To put
sampling-based motion planning into a larger context, a discussion of
alternative motion generation frameworks is presented which highlights their
respective differences to sampling-based motion planning. Finally, a set of
sampling-based motion planners are compared on 24 challenging planning
problems. This evaluation gives insights into which planners perform well in
which situations and where future research would be required. This comparative
review thereby provides not only a useful reference manual for researchers in
the field, but also a guideline for practitioners to make informed algorithmic
decisions.Comment: 25 pages, 7 figures, Accepted for Volume 7 (2024) of the Annual
Review of Control, Robotics, and Autonomous System
Asymptotically Optimal Sampling-Based Motion Planning Methods
Motion planning is a fundamental problem in autonomous robotics that requires
finding a path to a specified goal that avoids obstacles and takes into account
a robot's limitations and constraints. It is often desirable for this path to
also optimize a cost function, such as path length.
Formal path-quality guarantees for continuously valued search spaces are an
active area of research interest. Recent results have proven that some
sampling-based planning methods probabilistically converge toward the optimal
solution as computational effort approaches infinity. This survey summarizes
the assumptions behind these popular asymptotically optimal techniques and
provides an introduction to the significant ongoing research on this topic.Comment: Posted with permission from the Annual Review of Control, Robotics,
and Autonomous Systems, Volume 4. Copyright 2021 by Annual Reviews,
https://www.annualreviews.org/. 25 pages. 2 figure
Multilevel Motion Planning: A Fiber Bundle Formulation
Motion planning problems involving high-dimensional state spaces can often be
solved significantly faster by using multilevel abstractions. While there are
various ways to formally capture multilevel abstractions, we formulate them in
terms of fiber bundles, which allows us to concisely describe and derive novel
algorithms in terms of bundle restrictions and bundle sections. Fiber bundles
essentially describe lower-dimensional projections of the state space using
local product spaces. Given such a structure and a corresponding admissible
constraint function, we can develop highly efficient and optimal search-based
motion planning methods for high-dimensional state spaces. Our contributions
are the following: We first introduce the terminology of fiber bundles, in
particular the notion of restrictions and sections. Second, we use the notion
of restrictions and sections to develop novel multilevel motion planning
algorithms, which we call QRRT* and QMP*. We show these algorithms to be
probabilistically complete and almost-surely asymptotically optimal. Third, we
develop a novel recursive path section method based on an L1 interpolation over
path restrictions, which we use to quickly find feasible path sections. And
fourth, we evaluate all novel algorithms against all available OMPL algorithms
on benchmarks of eight challenging environments ranging from 21 to 100 degrees
of freedom, including multiple robots and nonholonomic constraints. Our
findings support the efficiency of our novel algorithms and the benefit of
exploiting multilevel abstractions using the terminology of fiber bundles.Comment: Submitted to IJR