933 research outputs found
Combining Homotopy Methods and Numerical Optimal Control to Solve Motion Planning Problems
This paper presents a systematic approach for computing local solutions to
motion planning problems in non-convex environments using numerical optimal
control techniques. It extends the range of use of state-of-the-art numerical
optimal control tools to problem classes where these tools have previously not
been applicable. Today these problems are typically solved using motion
planners based on randomized or graph search. The general principle is to
define a homotopy that perturbs, or preferably relaxes, the original problem to
an easily solved problem. By combining a Sequential Quadratic Programming (SQP)
method with a homotopy approach that gradually transforms the problem from a
relaxed one to the original one, practically relevant locally optimal solutions
to the motion planning problem can be computed. The approach is demonstrated in
motion planning problems in challenging 2D and 3D environments, where the
presented method significantly outperforms a state-of-the-art open-source
optimizing sampled-based planner commonly used as benchmark
Path Planning for Concentric Tube Robots: a Toolchain with Application to Stereotactic Neurosurgery
We present a toolchain for solving path planning problems for concentric tube
robots through obstacle fields. First, ellipsoidal sets representing the target
area and obstacles are constructed from labelled point clouds. Then, the
nonlinear and highly nonconvex optimal control problem is solved by introducing
a homotopy on the obstacle positions where at one extreme of the parameter the
obstacles are removed from the operating space, and at the other extreme they
are located at their intended positions. We present a detailed example (with
more than a thousand obstacles) from stereotactic neurosurgery with real-world
data obtained from labelled MPRI scans.Comment: 8 pages, 7 figures. Paper under revie
Batch Informed Trees (BIT*): Informed Asymptotically Optimal Anytime Search
Path planning in robotics often requires finding high-quality solutions to
continuously valued and/or high-dimensional problems. These problems are
challenging and most planning algorithms instead solve simplified
approximations. Popular approximations include graphs and random samples, as
respectively used by informed graph-based searches and anytime sampling-based
planners. Informed graph-based searches, such as A*, traditionally use
heuristics to search a priori graphs in order of potential solution quality.
This makes their search efficient but leaves their performance dependent on the
chosen approximation. If its resolution is too low then they may not find a
(suitable) solution but if it is too high then they may take a prohibitively
long time to do so. Anytime sampling-based planners, such as RRT*,
traditionally use random sampling to approximate the problem domain
incrementally. This allows them to increase resolution until a suitable
solution is found but makes their search dependent on the order of
approximation. Arbitrary sequences of random samples approximate the problem
domain in every direction simultaneously and but may be prohibitively
inefficient at containing a solution. This paper unifies and extends these two
approaches to develop Batch Informed Trees (BIT*), an informed, anytime
sampling-based planner. BIT* solves continuous path planning problems
efficiently by using sampling and heuristics to alternately approximate and
search the problem domain. Its search is ordered by potential solution quality,
as in A*, and its approximation improves indefinitely with additional
computational time, as in RRT*. It is shown analytically to be almost-surely
asymptotically optimal and experimentally to outperform existing sampling-based
planners, especially on high-dimensional planning problems.Comment: International Journal of Robotics Research (IJRR). 32 Pages. 16
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A New Mixed Iterative Algorithm to Solve the Fuel-Optimal Linear Impulsive Rendezvous Problem
International audienceThe optimal fuel impulsive time-fixed rendezvous problem is reviewed. In a linear setting, it may be reformulated as a non convex polynomial optimization problem for a pre-specified fixed number of velocity increments. Relying on variational results previously published in the literature, an improved mixed iterative algorithm is defined to address the issue of optimization over the number of impulses. Revisiting the primer vector theory, it combines variational tests with sophisticated numerical tools from algebraic geometry to solve polynomial necessary and sufficient conditions of optimality. Numerical examples under circular and elliptic assumptions show that this algorithm is efficient and can be integrated into a rendezvous planning tool
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