8,836 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
Robust semi-automated path extraction for visualising stenosis of the coronary arteries
Computed tomography angiography (CTA) is useful for diagnosing and planning treatment of heart disease. However, contrast agent in surrounding structures (such as the aorta and left ventricle) makes 3-D visualisation of the coronary arteries difficult. This paper presents a composite method employing segmentation and volume rendering to overcome this issue. A key contribution is a novel Fast Marching minimal path cost function for vessel centreline extraction. The resultant centreline is used to compute a measure of vessel lumen, which indicates the degree of stenosis (narrowing of a vessel). Two volume visualisation techniques are presented which utilise the segmented arteries and lumen measure. The system is evaluated and demonstrated using synthetic and clinically obtained datasets
FaSTrack: a Modular Framework for Real-Time Motion Planning and Guaranteed Safe Tracking
Real-time, guaranteed safe trajectory planning is vital for navigation in
unknown environments. However, real-time navigation algorithms typically
sacrifice robustness for computation speed. Alternatively, provably safe
trajectory planning tends to be too computationally intensive for real-time
replanning. We propose FaSTrack, Fast and Safe Tracking, a framework that
achieves both real-time replanning and guaranteed safety. In this framework,
real-time computation is achieved by allowing any trajectory planner to use a
simplified \textit{planning model} of the system. The plan is tracked by the
system, represented by a more realistic, higher-dimensional \textit{tracking
model}. We precompute the tracking error bound (TEB) due to mismatch between
the two models and due to external disturbances. We also obtain the
corresponding tracking controller used to stay within the TEB. The
precomputation does not require prior knowledge of the environment. We
demonstrate FaSTrack using Hamilton-Jacobi reachability for precomputation and
three different real-time trajectory planners with three different
tracking-planning model pairs.Comment: Published in the IEEE Transactions on Automatic Contro
Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems
Development of robust dynamical systems and networks such as autonomous
aircraft systems capable of accomplishing complex missions faces challenges due
to the dynamically evolving uncertainties coming from model uncertainties,
necessity to operate in a hostile cluttered urban environment, and the
distributed and dynamic nature of the communication and computation resources.
Model-based robust design is difficult because of the complexity of the hybrid
dynamic models including continuous vehicle dynamics, the discrete models of
computations and communications, and the size of the problem. We will overview
recent advances in methodology and tools to model, analyze, and design robust
autonomous aerospace systems operating in uncertain environment, with stress on
efficient uncertainty quantification and robust design using the case studies
of the mission including model-based target tracking and search, and trajectory
planning in uncertain urban environment. To show that the methodology is
generally applicable to uncertain dynamical systems, we will also show examples
of application of the new methods to efficient uncertainty quantification of
energy usage in buildings, and stability assessment of interconnected power
networks
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