432 research outputs found
Sampling-based optimal kinodynamic planning with motion primitives
This paper proposes a novel sampling-based motion planner, which integrates
in RRT* (Rapidly exploring Random Tree star) a database of pre-computed motion
primitives to alleviate its computational load and allow for motion planning in
a dynamic or partially known environment. The database is built by considering
a set of initial and final state pairs in some grid space, and determining for
each pair an optimal trajectory that is compatible with the system dynamics and
constraints, while minimizing a cost. Nodes are progressively added to the tree
{of feasible trajectories in the RRT* by extracting at random a sample in the
gridded state space and selecting the best obstacle-free motion primitive in
the database that joins it to an existing node. The tree is rewired if some
nodes can be reached from the new sampled state through an obstacle-free motion
primitive with lower cost. The computationally more intensive part of motion
planning is thus moved to the preliminary offline phase of the database
construction at the price of some performance degradation due to gridding. Grid
resolution can be tuned so as to compromise between (sub)optimality and size of
the database. The planner is shown to be asymptotically optimal as the grid
resolution goes to zero and the number of sampled states grows to infinity
db-A*: Discontinuity-bounded Search for Kinodynamic Mobile Robot Motion Planning
We consider time-optimal motion planning for dynamical systems that are
translation-invariant, a property that holds for many mobile robots, such as
differential-drives, cars, airplanes, and multirotors. Our key insight is that
we can extend graph-search algorithms to the continuous case when used
symbiotically with optimization. For the graph search, we introduce
discontinuity-bounded A* (db-A*), a generalization of the A* algorithm that
uses concepts and data structures from sampling-based planners. Db-A* reuses
short trajectories, so-called motion primitives, as edges and allows a maximum
user-specified discontinuity at the vertices. These trajectories are locally
repaired with trajectory optimization, which also provides new improved motion
primitives. Our novel kinodynamic motion planner, kMP-db-A*, has almost surely
asymptotic optimal behavior and computes near-optimal solutions quickly. For
our empirical validation, we provide the first benchmark that compares search-,
sampling-, and optimization-based time-optimal motion planning on multiple
dynamical systems in different settings. Compared to the baselines, kMP-db-A*
consistently solves more problem instances, finds lower-cost initial solutions,
and converges more quickly.Comment: Accepted at IROS 202
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
Completeness of Randomized Kinodynamic Planners with State-based Steering
Probabilistic completeness is an important property in motion planning.
Although it has been established with clear assumptions for geometric planners,
the panorama of completeness results for kinodynamic planners is still
incomplete, as most existing proofs rely on strong assumptions that are
difficult, if not impossible, to verify on practical systems. In this paper, we
focus on an important class of kinodynamic planners, namely those that
interpolate trajectories in the state space. We provide a proof of
probabilistic completeness for these planners under assumptions that can be
readily verified from the system's equations of motion and the user-defined
interpolation function. Our proof relies crucially on a property of
interpolated trajectories, termed second-order continuity (SOC), which we show
is tightly related to the ability of a planner to benefit from denser sampling.
We analyze the impact of this property in simulations on a low-torque pendulum.
Our results show that a simple RRT using a second-order continuous
interpolation swiftly finds solution, while it is impossible for the same
planner using standard Bezier curves (which are not SOC) to find any solution.Comment: 21 pages, 5 figure
db-CBS: Discontinuity-Bounded Conflict-Based Search for Multi-Robot Kinodynamic Motion Planning
This paper presents a multi-robot kinodynamic motion planner that enables a
team of robots with different dynamics, actuation limits, and shapes to reach
their goals in challenging environments. We solve this problem by combining
Conflict-Based Search (CBS), a multi-agent path finding method, and
discontinuity-bounded A*, a single-robot kinodynamic motion planner. Our
method, db-CBS, operates in three levels. Initially, we compute trajectories
for individual robots using a graph search that allows bounded discontinuities
between precomputed motion primitives. The second level identifies inter-robot
collisions and resolves them by imposing constraints on the first level. The
third and final level uses the resulting solution with discontinuities as an
initial guess for a joint space trajectory optimization. The procedure is
repeated with a reduced discontinuity bound. Our approach is anytime,
probabilistically complete, asymptotically optimal, and finds near-optimal
solutions quickly. Experimental results with robot dynamics such as unicycle,
double integrator, and car with trailer in different settings show that our
method is capable of solving challenging tasks with a higher success rate and
lower cost than the existing state-of-the-art.Comment: submitted to ICRA 202
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