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Optimal Motion Planning with constraints for mobile robot navigation
Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to [email protected], referencing the URI of the item.Includes bibliographical references (leaves 34-36).Motion planning is the process of planning a sequence of motions to move an object from one configuration to another. Recently, randomized techniques known as PRMs have shown great potential for solving motion planning problems in complicated high-dimensional space. Motion Planning, or path planning for robots, becomes increasing difficult as the dimension of the planning space increases with the robot's degrees of freedom (dof). While the running time of deterministic motion planning algorithms grows exponentially with an increase in dof, PRMs can produce solutions in times that do not depend on the dof but only the difficulty of the problem. PRMs randomly generate collision free configurations in a robot's Configuration-space (Cspace), representing feasible positions and orientations for the robot. Nearby configurations are linked together by so-called local planners, and these connections are edges in a roadmap, a graph containing representative discrete paths the robot may travel. We present methods to extract optimal paths from roadmap-based motion planners. Our system uses Markov-like states and flexible goal states so that general optimization criteria including collision detection, kinematic/dynamic constraints, or minimum clearance can be used in various applications. Our algorithm is an augmented version of Dijkstra's shortest path algorithm. We present simulation results maximizing minimum path clearance, minimizing localization effort, and enforcing kinematic/ dynamic constraints
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
An Extensible Benchmarking Infrastructure for Motion Planning Algorithms
Sampling-based planning algorithms are the most common probabilistically
complete algorithms and are widely used on many robot platforms. Within this
class of algorithms, many variants have been proposed over the last 20 years,
yet there is still no characterization of which algorithms are well-suited for
which classes of problems. This has motivated us to develop a benchmarking
infrastructure for motion planning algorithms. It consists of three main
components. First, we have created an extensive benchmarking software framework
that is included with the Open Motion Planning Library (OMPL), a C++ library
that contains implementations of many sampling-based algorithms. Second, we
have defined extensible formats for storing benchmark results. The formats are
fairly straightforward so that other planning libraries could easily produce
compatible output. Finally, we have created an interactive, versatile
visualization tool for compact presentation of collected benchmark data. The
tool and underlying database facilitate the analysis of performance across
benchmark problems and planners.Comment: Submitted to IEEE Robotics & Automation Magazine (Special Issue on
Replicable and Measurable Robotics Research), 201
RMPD - A Recursive Mid-Point Displacement Algorithm for Path Planning
Motivated by what is required for real-time path planning, the paper starts
out by presenting sRMPD, a new recursive "local" planner founded on the key
notion that, unless made necessary by an obstacle, there must be no deviation
from the shortest path between any two points, which would normally be a
straight line path in the configuration space. Subsequently, we increase the
power of sRMPD by using it as a "connect" subroutine call in a higher-level
sampling-based algorithm mRMPD that is inspired by multi-RRT. As a consequence,
mRMPD spawns a larger number of space exploring trees in regions of the
configuration space that are characterized by a higher density of obstacles.
The overall effect is a hybrid tree growing strategy with a trade-off between
random exploration as made possible by multi-RRT based logic and immediate
exploitation of opportunities to connect two states as made possible by sRMPD.
The mRMPD planner can be biased with regard to this trade-off for solving
different kinds of planning problems efficiently. Based on the test cases we
have run, our experiments show that mRMPD can reduce planning time by up to 80%
compared to basic RRT
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