21,071 research outputs found
A New Approach to Time-Optimal Path Parameterization based on Reachability Analysis
Time-Optimal Path Parameterization (TOPP) is a well-studied problem in
robotics and has a wide range of applications. There are two main families of
methods to address TOPP: Numerical Integration (NI) and Convex Optimization
(CO). NI-based methods are fast but difficult to implement and suffer from
robustness issues, while CO-based approaches are more robust but at the same
time significantly slower. Here we propose a new approach to TOPP based on
Reachability Analysis (RA). The key insight is to recursively compute reachable
and controllable sets at discretized positions on the path by solving small
Linear Programs (LPs). The resulting algorithm is faster than NI-based methods
and as robust as CO-based ones (100% success rate), as confirmed by extensive
numerical evaluations. Moreover, the proposed approach offers unique additional
benefits: Admissible Velocity Propagation and robustness to parametric
uncertainty can be derived from it in a simple and natural way.Comment: 15 pages, 9 figure
Admissible Velocity Propagation : Beyond Quasi-Static Path Planning for High-Dimensional Robots
Path-velocity decomposition is an intuitive yet powerful approach to address
the complexity of kinodynamic motion planning. The difficult trajectory
planning problem is solved in two separate, simpler, steps: first, find a path
in the configuration space that satisfies the geometric constraints (path
planning), and second, find a time-parameterization of that path satisfying the
kinodynamic constraints. A fundamental requirement is that the path found in
the first step should be time-parameterizable. Most existing works fulfill this
requirement by enforcing quasi-static constraints in the path planning step,
resulting in an important loss in completeness. We propose a method that
enables path-velocity decomposition to discover truly dynamic motions, i.e.
motions that are not quasi-statically executable. At the heart of the proposed
method is a new algorithm -- Admissible Velocity Propagation -- which, given a
path and an interval of reachable velocities at the beginning of that path,
computes exactly and efficiently the interval of all the velocities the system
can reach after traversing the path while respecting the system kinodynamic
constraints. Combining this algorithm with usual sampling-based planners then
gives rise to a family of new trajectory planners that can appropriately handle
kinodynamic constraints while retaining the advantages associated with
path-velocity decomposition. We demonstrate the efficiency of the proposed
method on some difficult kinodynamic planning problems, where, in particular,
quasi-static methods are guaranteed to fail.Comment: 43 pages, 14 figure
Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control
This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York
Perception-aware time optimal path parameterization for quadrotors
The increasing popularity of quadrotors has given rise to a class of
predominantly vision-driven vehicles. This paper addresses the problem of
perception-aware time optimal path parametrization for quadrotors. Although
many different choices of perceptual modalities are available, the low weight
and power budgets of quadrotor systems makes a camera ideal for on-board
navigation and estimation algorithms. However, this does come with a set of
challenges. The limited field of view of the camera can restrict the visibility
of salient regions in the environment, which dictates the necessity to consider
perception and planning jointly. The main contribution of this paper is an
efficient time optimal path parametrization algorithm for quadrotors with
limited field of view constraints. We show in a simulation study that a
state-of-the-art controller can track planned trajectories, and we validate the
proposed algorithm on a quadrotor platform in experiments.Comment: Accepted to appear at ICRA 202
Variable density sampling based on physically plausible gradient waveform. Application to 3D MRI angiography
Performing k-space variable density sampling is a popular way of reducing
scanning time in Magnetic Resonance Imaging (MRI). Unfortunately, given a
sampling trajectory, it is not clear how to traverse it using gradient
waveforms. In this paper, we actually show that existing methods [1, 2] can
yield large traversal time if the trajectory contains high curvature areas.
Therefore, we consider here a new method for gradient waveform design which is
based on the projection of unrealistic initial trajectory onto the set of
hardware constraints. Next, we show on realistic simulations that this
algorithm allows implementing variable density trajectories resulting from the
piecewise linear solution of the Travelling Salesman Problem in a reasonable
time. Finally, we demonstrate the application of this approach to 2D MRI
reconstruction and 3D angiography in the mouse brain.Comment: IEEE International Symposium on Biomedical Imaging (ISBI), Apr 2015,
New-York, United State
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